Heat transfer engineering an international journal, tập 32, số 5, 2011

Heat Transfer Engineering, 32(5):359–368, 2011 Copyright C Taylor and Francis Group, LLC ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457632.2010.483851 Boiling of R404A Refrigeration Medium Under the Conditions of Periodically Generated Disturbances ´ TADEUSZ BOHDAL and WALDEMAR KUCZYNSKI Thermal Engineering and Refrigerating Engineering, Koszalin University of Technology, Koszalin, Poland An attempt was made to evaluate the impact of external, periodically generated disturbances on the boiling process of the refrigeration medium in a flow The experimental investigations were conducted under the conditions of periodic changes (increase and fading) of the mass flux density of the refrigeration medium for constant refrigeration chamber heat loads This led to a change of the pressure and temperature along the path of the flow of the medium in a coil tube of the evaporator It was confirmed that the boiling process of the refrigeration medium in a flow exhibits wave properties, which are characterized by finite values of the displacements of the disturbances By way of dimensional analysis, nondimensional dependences were determined that specify the velocity of the displacement of the pressure change signal and the temperature change signal The investigations were conducted with the use of an environmentally friendly R404A refrigeration medium INTRODUCTION The principle of operation of some power engineering machines and devices is based on the use of the phase changes of an energy medium in a thermodynamic cycle An energy medium is understood to be both an energy carrier and a thermodynamic medium that is subject to changes and that participates in energy conversion in a direct or indirect manner Energy media include, among others, water, refrigeration media, and water saline solutions It has been established that phase changes of energy media that occur in evaporators and condensers in machines and devices are very “sensitive” to any disturbances that occur during operation, including both external and internal disturbances [1] External disturbances are usually the result of an interaction between various components of the system For example, they are the result of the work of automatic elements, disturbances of the work of machines (e.g., pumps, turbines, compressors), and power stoppages The causes of the occurrence of internal disturbances can generally be divided into two groups They can be directly embedded in the mechanism of phase changes or in the structure and properties of the working medium Both external and internal disturbances can be of an individual [2] or Address correspondence to Professor Tadeusz Bohdal, Thermal Engineering and Refrigerating Engineering, Koszalin University of Technology, Koszalin, Poland E-mail: tadeusz.bohdal@tu.koszalin.pl periodic [3–5] nature; i.e., they can be periodically generated with a specific amplitude and frequency Impulse and periodically generated disturbances cause specific phenomena, which trigger the following changes: (a) an abrupt drop or increase of the pressure of the medium, (b) a decay or an increase of the mass flux density, (c) an increase or a drop of the resistances of the medium flow, and (d) periodic problems connected with the starting of the device A two-phase system of liquid (either a gas, or a single or multicomponent fluid) is a set of particles of a substance with two states of aggregation, which are separated by an interface The interaction between particular phases and the displacement velocity of a disturbance triggered by an external or internal cause depend on the internal structure of the system This can be clearly seen via the example of the propagation of a sound wave in an adiabatic two-phase system The velocity of a sound wave depends, above all, on the value of the filling degree φ and the pressure of the two-phase mixture The sound velocity in a two-phase mixture increases together with an increase of the pressure However, this tendency only occurs up to a specific value of the pressure (whose value depends from the filling degree) and then, with adequately high pressures, it is almost constant and is equal to 1300 m/s [6] During the propagation of the wave of disturbances in a two-phase one-component mixture with thermal parameters determined for the states on the saturation line, the propagation of the wave of disturbances causes a periodic change of the local 359 360 ´ T BOHDAL AND W KUCZYNSKIRH pressure values In turn, this results in a continuous process of phase changes On the boundary of the phases, a condensation process occurs locally when the pressure increases; when the pressure decreases, an evaporation process occurs The local values of the parameters of the two-phase system change, including the saturation pressure pS , saturation temperature TS , density ρ, dryness degree x, and filling degree ϕ These phenomena cause the “damping effect” associated with the dissipation of energy and the change of the propagation velocity of the disturbances [7–9] In a two-phase system, in nonequilibrium conditions, an evolution of the disturbance signals occurs A two-phase flow also possesses dispersion wave properties, which are evident in the fact that the propagation velocity of small disturbances depends on their frequency [6, 10] It should be emphasized that a close examination of the mechanism of the displacement of disturbances in a two-phase medium is very important in order to guarantee the stable operation of machines and devices The determination of the velocity of these disturbances plays a vital part in the description of the operation of thermal and refrigeration systems under conditions of an automatic control, by preventing breakdowns and minimizing of their results [11–13] BOILING PROCESS OF THE MEDIUM IN A COIL TUBE An evaporator constitutes the basic element of a refrigeration system; it is important in determining the effectiveness of its operation The use of the disposable surface of the heat exchange of the evaporator usually constitutes the basic criterion of the optimization of the whole system [10] A considerable number of evaporators in fan air coolers with small and medium outputs are usually fed with a refrigeration medium with the aid of thermostatic expansion valves However, these days, a new generation of automatic cooling devices is being used increasingly frequently in the form of electronic expansion valves or whole systems of automatic control for filling evaporators with the medium The “saturation” of a refrigerating system with any type of electronic element and computer assistance, or with a monitoring system, makes it more susceptible to any disturbance that occurs during operation A disturbance of the operation of a system that feeds the evaporator has an impact on the boiling process of the refrigeration medium used The boiling of a refrigeration medium in a flow is usually considered to be a phenomenon that occurs in coil tubes composed of horizontal or vertical straight pipes connected with elbows for vapor dryness values between x = to However, it happens that the boiling process is incomplete and it takes place between x > to x < (e.g., x = 0.3 to 0.9), which is practically in the area of saturated damp vapor [14] If the cooler is fed with the medium with the aid of a thermostatic or electronic expansion valve, then the refrigeration medium flows to the expansion valve in the form of a liquid that has not been heated up to the saturation temperature During the heat transfer engineering T TS TF ∆ΤS TS two - phase zone one-phase zone L Figure Division of coil tube length L into the zones of two-phase and singlephase flow in the case where the coil tube is fed through the expansion valve flow through the expansion valve, a damping conversion occurs (the medium expands while it does not perform any external work) During this time, a part of the liquid passes to the vapor state, while the temperature of the medium is lowered to the evaporation temperature level The remaining liquid evaporates during the flow through the coil tube If the quantity of the refrigeration medium that evaporates in the evaporator is too small for the boiling process to occur on the whole length of the coil tube, then after the completion of the phase change of boiling (sometimes referred to as proper boiling), the dry saturated vapor is overheated In fan air coolers, the active length L of the coil tube can be divided into two sections: a two-phase length (zone) (in which heat exchange during boiling in a flow occurs) and a single-phase length (zone) (in which a convective exchange of the heat of a single-phase medium, i.e., overheated vapor, occurs)—see Figure The size of the overheating zone can be adjusted by changing the setting of a thermostatic expansion valve or the time characteristics of an electronic valve The occurrence of disturbances in the feeding “mechanism” of the evaporator, for example, in the form of an instantaneous decrease or fading of the mass rate of flow of the medium, is crucial for its correct operation In the present paper, the results of experimental investigations of the boiling process of the R404A refrigeration medium in a coil tube are presented for the case where periodically generated disturbances are present The determination of the impact of these disturbances on the operation of the entire refrigerating system has a substantial cognitive and application-focused significance on the construction, operation, and economic analysis of the system EXPERIMENTAL FACILITY The experimental investigations of the boiling process were conducted on a measuring facility, which is schematically presented in Figure Its main elements include an isolated refrigeration chamber and the air cooler tested placed in it, which vol 32 no 2011 ´ T BOHDAL AND W KUCZYNSKIRH 361 Figure Schematic diagram of the experimental facility: 1, isolated refrigeration chamber; 2, lamelled air cooler; 3, flow channel of the lamelled block of the air cooler; 4, compressor and condensation installation (components of the installation: COM, piston compressor; CON, water-chilled condenser; LPS, low-pressure control system; HPS, high-pressure control system; TL, tank with the liquid R404A medium; 5, cutoff valve; 6, a classical flow rate measuring system; 7, Massflow type electronic flowmeter; 8, computer measuring and recording system; 9, pressure measuring and recording system; 10, temperature measuring and recording system; 11, inspection opening; 12, feeding block; 13, filter/dewaterer; 14, evaporator of auxiliary refrigeration system; 15, electric air heater; 16, measurement of the environment parameters constituted an element of a single-stage compressor refrigeration system Air cooler was fed with R404A refrigerant from refrigeration and condensation installation 4, which is equipped with the following subassemblies: a piston compressor COM (a compressor of K373H/4P-102Y type), a condenser CON chilled with water, a liquid tank TL, and control instrumentation From the liquid tank TL, the R404A refrigeration medium flowed through the filter–dewaterer 13 and inspection hole 11 for the flow-rate measuring systems The liquid refrigeration medium flowed to the feeding system 12 and the air cooler placed in a flow channel Additional control elements were placed in the test chamber 1; i.e., an electric air heater 15 and evaporators 14 were placed on the sidewalls inside chamber and were fed from an auxiliary refrigeration system A forced air movement through the cooler tested was realized with the aid of an axial fan, with the possibility of an adjustment of the volumetric rate of airflow (Figure 3) The experimental facility allowed us to investigate the scope of a constant adjustable level of the heat load in the test chamber [15] The main element of the fan cooler was a heat exchanger: an evaporator made in the form of a single coil tube lamelled block, whose dimensional diagram is given in Figure Over the length of the coil tube of the lamelled block L = 13.86 m, 12 sensors for pressure measurements and 12 sensors for temperature measurements were placed at regular intervals In each of the 12 cross sections of the coil tube, there was one heat transfer engineering piezoelectric sensor for pressure measurements and one thermoelectric sensor for the measurements of the temperature of the medium (Table 1) A dimensional diagram of the arrangement of the sensors along the length of the coil tube is given in Figure The computer system used for the measurement, control, and registration of the basic parameters of the refrigeration medium, air, and environment constituted an integral component of the experimental facility This system included the following: (a) NiCr–Ni type thermoelectric sensors with 0.35 mm diameter Ventilator Exchanger Channel Figure Schematic diagram of cooler housing in channel vol 32 no 2011 ´ T BOHDAL AND W KUCZYNSKIRH 362 480 [mm] TEV 360 [mm] L1 Figure Measurement diagram of lamelled block viewed from the side of air inflow thermocouple wires (for which individual calibration characteristics were previously made) were included in the system of voltage amplifiers along with a computer converter card for the voltage measurement, PCL 818HG type; (b) piezoelectric pressure sensors (the ICP type with a M102A07 symbol), which cooperate with the tare system and a computer voltage measuring card; and (c) a MASS2100-type electronic Massflow flowmeter, manufactured by the Danfoss company, with software, which was included in the measuring and data processing system All of the impulses obtained from the temperature, pressure, and flow rate measuring sensors were converted into voltage signals and were supplied to the computer system It is evident from the conducted analysis that the temperature values were determined with an accuracy of ±0.1◦ C and the densities of heat flux q and mass flux (wρ) were measured with an accuracy of ±6% The velocities of the displacements of the pressure and temperature changes were determined with an accuracy of ±10% The scope of the experimental investigations conducted was limited by the capabilities of the measuring facility They allowed us to make measurements related to the following: (a) Table Arrangement of the cross sections where sensors for pressure and temperature measurements were placed L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 Figure Schematic diagram of the distribution of sensors for measuring the temperature and pressure of the refrigeration medium during flow in the coil tube (where TEV is the thermostatic expansion valve) the density of the mass flux of the refrigeration medium (wρ) = to 300 kg/(m2-s), (b) the boiling temperature of the medium Ts = to –40◦ C, and (c) the density of the heat flux q = to 6000 W/m2 RESULTS OF EXPERIMENTAL INVESTIGATIONS 440 [mm] Number L2 Distance from feeding block Number Distance from feeding block L1 = 855 mm L2 = 1965 mm L3 = 3073 mm L4 = 4183 mm L5 = 5250 mm L6 = 6377 mm 10 11 12 L7 = 7484 mm L8 = 8582 mm L9 = 9772 mm L10 = 10,887 mm L11 = 11,977 mm L12 = 13,081 mm heat transfer engineering In the present paper, the notion of a “periodically generated disturbance” is to be understood as a disturbance produced by feeding the evaporator with a refrigeration medium, in conditions of a change of the time to open and close the valve that supplies the medium to the coil tube Such an action results in an increase or a decay of the mass flux density of the R404A medium This, in turn, results in periodic changes of the pressure and temperature along the flow path in the coil tube In the experimental investigations, a single coil tube lamelled block was used, while an additional cutoff was installed on the coil tube inlet (thus allowing the disturbances to be turned off) In the experiments, it was assumed that a constant opening and closing time of the cutoff valve was realized in the measuring session While the opening time of the valve was always constant for all of the measuring series (5 s), the closing time of the valve in the individual measuring series varied and was τc = 5, 10, 15, 20, 25, and 30 s The sum of the opening and closing times constituted the duration of the period that formed the basis for the determination of the frequencies of the disturbances generated f [mHz] (f = 100, 67, 50, 40, 33, 29 mHz) Figures to present example characteristics of the course of the mass rate flow of the R404A refrigeration medium (Figure 6), changes of the evaporation pressure (Figure 7), and the temperature profile (Figure 8) For the purpose of the construction of the pressure and temperature characteristics presented, the registration of the pressure and temperature by sensors denoted with subsequent numbers (given according to Figure 5) was taken into account The introduction of periodic disturbances resulted in the occurrence of the pulsation of the medium flow rate During the period of the closing of the cutoff valve, the medium was “sucked off” by the compressor from the coil tube Because of this, there was a pressure drop and an increased overheating of the vapor This caused gradual increase in the temperature of refrigerant in the monophase area of the tubular channel At the same time, in the two-phase boiling area, the boiling temperature of refrigerant decreased, which depends on vol 32 no 2011 ´ T BOHDAL AND W KUCZYNSKIRH Figure Changes of mass rate flow m˙ of the R404A refrigeration medium during periodic disturbances; initial value m˙ = 50 [kg/h] the absolute pressure Opening of the valve resulted in the reversal of the process An inflow of a new portion of refrigerant caused a pressure increase in the channel, which in turn resulted in an increase of the vaporization temperature and a decrease of the overheating of vapors on the outlet from the pipe coil The changes of the pressure and temperature of the refrigeration medium that occur during its flow in a coil tube with periodic disturbances are characterized by a “time shift.” This proves the finite velocity with which the signals of these values relocate after the opening or closing of the cutoff valve Therefore, it can be recognized that there is a reaction with a wave nature, which is characterized by two velocities: vp (the velocity of the relocation of the pressure change signal), and vT (the velocity of the temperature change relocation) The commencement of the boiling process results in an intensification of the heat exchange, which is manifested by a decrease of the channel wall temperature For this reason, the relocation of the signal produced by a decreased temperature can be identified with the relocation of the front of the boiling medium, i.e., the so-called boiling front, which displaces with velocity vT [10, 16, 17] Figure Course of changes of pressure p0 in time τ of the medium flow in the coil tube heat transfer engineering 363 Figure Temperature profile T of the medium in time τ during its flow in the coil tube During experimental investigations, boiling of the medium was realized under the conditions of periodical external disturbances Opening or closing of the cutoff valve resulted in a periodical change of refrigerant parameters under nonstationary conditions The consequence of the disturbances occurring was the formation of a pressure wave, which relocated along the channel It is the opinion of the authors that the relocation of the pressure wave was the reason for the formation of a temperature wave as a secondary effect However, no large temperature changes of the medium or of the tubular channel wall were observed It means this does not involve such temperatures, which should be the result of the value of the saturation pressure change in the channel This is the result of the impact of the thermal inertia of the system as well as a significant frequency of disturbances generated The investigations demonstrated that velocities vp and vT depend, among other things, on the size of the disturbance triggered, which is characterized by the pressure drop p Figure presents as an example an experimental dependence vp = f ( p) The size of the pressure drop p that occurs during periodically generated disturbances depends on the mass flux density in the coil tube This phenomenon is the result of the work of the compressor, which sucks in the refrigeration medium vapor from the evaporator When the cutoff valve from the inlet of the medium to the coil tube is closed, there is a pressure drop The longer the valve is closed, the greater the pressure drop is Once the cutoff valve is opened again (with a greater reduction of the pressure in the evaporator), an increase of the medium flow rate occurs Figure 10 presents the dependence of the mass flux density (wρ) of the R404A refrigeration medium on the pressure drop p The mass flux density (wρ) exerts a substantial influence on the values of velocities vp and vT , as shown in Figure 11 It is evident from the conducted investigations that velocities vp and vT differ from one another with regard to their values, as the velocity of the pressure signal relocation changed between 45 and 330 m/s, while the velocity of the boiling front relocation was substantially smaller, and ranged from close to vol 32 no 2011 364 ´ T BOHDAL AND W KUCZYNSKIRH Figure Dependence of the pressure change displacement velocity vp on the pressure drop p generated by closing the cut-off valve; vp = f ( p) Figure 10 Dependence of the mass flux density (wρ) of the refrigeration medium on the pressure drop p Figure 12 Dependence of the temperature change displacement velocity vT in the coil tube on the velocity vp of the pressure signal displacement zero to 4.5 m/s Low values of vT serve to confirm the results obtained by the authors of reference [8], where a model was given to enable the determination of the boiling front forming velocity on the surface heated It was assumed in the analysis that the boiling front velocity on the surface heated depends on local liquid overheating TS and the thermophysical properties of the refrigerant in saturated conditions The obtained results of theoretical computations were compared with the results of experimental investigations The experiments were conducted for the range of low-pressure values and a high-value liquid overheating (up to 155 K) was obtained This corresponded to a boiling front velocity vT of up to 35 m/s The authors of reference [18] confirm that with higher absolute pressures, such large velocities vT are not achieved In practice, it is not possible to overheat a liquid by dozens of degrees Kelvin because the boiling process commences spontaneously at a substantially lower liquid overheating value This results in a substantial reduction of velocity vT even to values approaching zero Experimental investigations also demonstrated that the velocities of the relocation of the pressure signal vp and temperature signal vT are interdependent, which is shown in Figure 12 ANALYSIS OF EXPERIMENTAL RESULTS Figure 11 Dependence of the pressure change displacement velocity vp on the mass flux density (wρ) of the refrigeration medium; vp = f (wρ) heat transfer engineering The experimental investigations of the influence of periodic disturbances on the boiling process of a refrigeration medium demonstrated that there is a direct interdependence between the propagation velocity of the pressure disturbances vp and the relocation velocity of the temperature change signal vT and the frequency of the disturbances applied An increase of the disturbances generation frequency resulted in a velocity drop distribution change of pressure signal vp and temperature signal vT This frequency was described with the aid of nondimensional number Ta, which takes into account the ratio of the time τo required to open the valve on the inlet of the medium to the coil vol 32 no 2011 ´ T BOHDAL AND W KUCZYNSKIRH 365 took into consideration Buckingham’s theorem, according to which the number of non-dimensional modules is equal to the number of independent physical parameters reduced by the number of basic measurements in the SI system (such as meter, second, and kilogram) [19, 20] The relocation velocity of the pressure change vp signal triggered by periodic disturbances was made functionally dependent on the following parameters: v p = f ( p, ps , ν, d, w, τo , τc ) Figure 13 Dependence of the pressure change displacement velocity vp in the coil tube on the nondimensional Ta number tube to the total time of its being closed τc and opened τo : Ta = τo τc + τo where: vp is the relocation velocity of the pressure change signal [m/s], p is the oscillation amplitude of the boiling pressure during disturbances [N/m2], ps is the average evaporation pressure of the refrigeration medium [N/m2], d is the internal diameter of the coil tube [m], w is the average velocity of the two-phase mixture of the refrigeration medium [m/s], τo is the time of opening of the valve on the medium inlet to the coil tube [s], τc is the time of closing of the valve on the medium inlet to the coil tube [s], and ν is the kinematic coefficient of the viscosity of the two-phase mixture [m2/s], which is defined as: (1) The time of the opening of the valve was constant and was τo = s, while an increase of the value of the closing time of the valve τc corresponded to a drop of the frequency of disturbances f and caused a reduction of the value of the nondimensional number Ta Ta represents, in an indirect manner, the force of the disturbances acting on the system [9, 10] This determines the dependence of the speed of the pressure change vp and the velocity of the relocation of the temperature change signal vT from the Ta number (Figures 13 and 14) An attempt was made to generalize, in the form of a regression function, the experimental results obtained The problem concerned the description of the relocation velocity of the pressure change vp signal and the temperature change vT signal For this purpose, dimensional analysis procedures were used that (2) ν= µTPF ρTPF (3) with µTPF = 1−x 1 1−x + and = + µg µ1 ρTPF ρg ρl (4) It is evident from the assumptions accepted that the relocation velocity of a triggered disturbance was made dependent on its amplitude, frequency, and the physical properties of the refrigeration medium The frequency of the disturbances is indirectly covered by the time of the opening and closing of the valve at the medium inlet to the evaporator The size of the pressure oscillation amplitude p depends on the change of the dryness level x and the filling degree ϕ of the boiling refrigeration medium A drop of the medium boiling pressure results in an increase of the values of x and ϕ while a rise of the pressure makes these values lower By way of a dimensional analysis [19], Eq (2) was converted to the following form: B v+ p = A × ReT P F × p+ C × T aD (5) where: v Figure 14 Dependence of the temperature change displacement velocity vT in the coil tube on the nondimensional Ta number heat transfer engineering p v+ p = w is the nondimensional velocity (determined via the ratio of the relocation velocity of the pressure change signal to the two-phase mixture velocity) ReT P F = (wρ)×d is the nondimensional Reynolds number for a µT P F two-phase flow p + = p0p is the nondimensional pressure drop (as a ratio of the pressure oscillation amplitude and the boiling pressure of the refrigeration medium) Ta is a nondimensional number that takes into account the relationship between the time τo of the opening of the valve on vol 32 no 2011 366 ´ T BOHDAL AND W KUCZYNSKIRH Figure 15 Dependence of the nondimensional velocity vp +cal calculated from Eq (3) on the value obtained from experimental measurements of vp +exp the inlet of the medium to the coil tube and the total time of its being closed τc and opened τo , as described by Eq (1) The calculation of the leading constant A and exponents B, C, and D in Eq (5) was carried out with the use of the nonlinear regression model In this model, the maximum likelihood method was used, which constitutes an alternative to the method of the sum of the least squares The standard deviation of the value observed from the one expected was determined with the use of the applied model, which is the so-called loss function A maximization of the likelihood function (selection of the proper parameters that fulfill this condition) was conducted with the quasi-Newton and Symplex method, which was carried out using standard computational modules in the Statistica software package [20] The following values of the unknowns occurring in Eq (5) were obtained: A = 489 × 104 , B = −1.05, C = 0.07, D = −0.76 with a variance of 92% and a correlation coefficient of 0.91 The values of the nondimensional experimental velocity v + p were compared with the results of calculations according to dependence (5) A satisfactory compatibility was obtained in the range of ±25%, which is presented in Figure 15 In an analogous manner, the value of nondimensional velocity vT + was determined, which takes into account the displacement of the temperature change vT Its value was made functionally dependent from the following parameters: vT = f ( T, Ts , ν, d, w, τo , τc ) (6) where additional denotations were introduced: vT is the displacement velocity of the temperature change signal [m/s], T is the amplitude of the temperature oscillations caused by disturbances [K], and Ts is the average boiling temperature of the refrigeration medium [K] heat transfer engineering Figure 16 Dependence of the nondimensional velocity vT +cal calculated from Eq (5) on the value obtained from experimental measurements of vT +exp After the application of the dimensional analysis, a dependence was obtained in the following form: vT+ = A × ReTB P F × T+ C × T aD, (7) where: vT+ = vwT is the nondimensional velocity determined via the ratio of the displacement velocity of the temperature change signal vT to the velocity of the two-phase mixture T + TTs is the nondimensional temperature drop determined via the ratio of the temperature amplitude to the boiling temperature of the refrigeration medium T0 [K] The following values of constants were obtained for Eq (7): A = 107 × 105 , B = −1.05, C = 1.43, D = −0.76 with a variation of 92% and a correlation coefficient of 0.94 The value of the experimental nondimensional velocity vT+ was compared with the results of calculations according to dependence of Eq (7) A satisfactory compatibility was obtained in the range of ±25%, which is presented in Figure 16 Empirical dependences of Eqs (5) and (7) were checked with regard to the following range of parameters: saturation temperature Ts = (0 to –40◦ C); saturation pressure ps = (0.1 to 0.24 MPa); mass flux density (wρ) = (50 to 300 kg/m2-s); displacement velocity of the pressure change signal vp = (40 to 330 m/s); displacement velocity of the temperature change signal vT = (1 to 4.50 m/s); nondimensional number Ta = (0.14 to 0.50); and criterion number ReTPF = (2280 to 12800) In a two-phase medium with a boiling refrigeration medium, the pressure is strictly related to the saturation temperature value In view of this fact, dependence of Eq (7) (which allows the value of the nondimensional displacement velocity of the temperature change signal vT+ to be determined) can be transformed to a form where the nondimensional temperature drop T + is replaced with the nondimensional pressure drop p+: vT+ = 107 × 105 × Re−1.05 T PF × vol 32 no 2011 p+ 0.11 × T a −0.76 , (8) ´ T BOHDAL AND W KUCZYNSKIRH Dependences of Eqs (7) and (8) are identical and can be used alternatively, depending on the assumptions accepted and the current requirements CONCLUSIONS An attempt was made to assess the impact of periodically generated external disturbances on the boiling process of a refrigeration medium in a flow The experimental investigations were conducted under conditions whereby periodic changes (an increase and a decay) of the mass flux density of the refrigeration medium were made for constant heat load levels of the refrigeration chamber This led to periodic changes of the pressure and temperature along the path of the flow of the medium in the coil tube of the evaporator The investigations were carried out with the use of an environmentally friendly R404A refrigeration medium Based on an analysis of the boiling of the refrigeration medium under the conditions of periodically generated disturbances, the following were established: The boiling process of the refrigeration medium in a flow exhibits wave properties, which are characterized by two velocities: vp , the displacement velocity of the pressure change signal; and vT , the displacement velocity of the temperature change signal; Velocities vp and vT depend on the parameters of the twophase medium and the magnitude of the disturbance generated, which are described by the value of the pressure drop p or temperature drop T There is an analogy in the displacement of the pressure change signal and the temperature change signal, which is manifested by an interdependence between the values of the velocities vp and vT ; a higher value of velocity vp corresponds to a higher value of velocity vT , and vice versa This is also confirmed by the notation given by empirical equations (3)–(6) The displacement velocity of the disturbances in a boiling refrigeration medium depends on the frequency of their generation This is taken into account in the nondimensional Ta number, which constitutes the ratio of time τo of the opening of the valve at the inlet of the refrigeration medium (from the coil tube) to the total time of its closing τc and opening τo The dependences worked out on the basis of the experimental investigations allow one to determine the displacement velocity of the pressure change signal vp and the temperature change signal velocity vT generated with periodic disturbances NOMENCLATURE d f L internal diameter of coil tube [m] frequency [s−1] length of coil tube [m] heat transfer engineering m˙ p p q Re T T Ta v w (wρ) x 367 mass rate of flow [kg/h] pressure [MPa] pressure drop (pressure amplitude during disturbances) [MPa] heat flux density [W/m2] Reynolds number temperature [◦ C] temperature drop (temperature amplitude during disturbances) [K] dimensionless number that covers the frequency of the disturbances generated velocity of displacement of disturbances [m/s] velocity [m/s], mass flux density [kg/m2-s] dryness level Greek Symbols ϕ µ ν ρ τ filling level, relative air humidity dynamic viscosity coefficient [kg/m-s] kinematic viscosity coefficient [m2/s] density [kg/m3] time [s] Subscripts c cal exp F g l o p s T TPF shutting of cutoff valve calculation value experimental value medium gas liquid opening of cutoff valve pressure saturation, overheating temperature two-phase flow Superscript + dimensionless quantity REFERENCES [1] Bergles, A E., Review of Instabilities in Two-Phase System, Hemisphere Publishing Corporation, Bristol, UK, 1977 [2] Bohdal, T., Investigation of Boiling of Refrigerating Medium Under Conditions of Impulse Disturbances, International Journal of Experiental Heat Transfer, vol 17, no 2, pp 103–117, 2004 [3] Wedekind, G L., An Experimental Investigation Into the Oscillatory Motion of the Mixture–Vapor Transition Point vol 32 no 2011 G YAKAR AND R KARABACAK 401 Air In Tin 30º 30º D S d Tf1 Tw D Tf Tw S ØD Ød Tf Tw d 30º (a) θ = 30 To3 To To1 Air Out Tout L=0cm L=15cm L=45cm L=75cm L=90cm 60º 60º Figure Temperature measurement points on the air side of heat exchanger 60º S was installed on a table (number 15) The heating water was carried to the heat exchanger by a tube (number 16) The heating water, on the other hand, was heated by electrical heaters (number 22) that are placed inside the 250-L water tank (number 21) The water used to heat the air was carried from the water tank (number 21) to heat exchanger by a pump (number 20) The body into which the finned tube was placed was insulated with an insulating material (number 24) of 10 mm thickness Moreover, the route of the air around the heating tube was lengthened by means of deflectors (number 25) placed in the inner surface of the external body In this study, the external diameter of the body into which the finned tube was placed was 154 mm, the heating tube external diameter was kept fixed at 29 mm, the fin diameter was 87 mm, and the fin thickness was 0.5 mm The distance between the fins, on the other hand, varied to be one of five different values; these were 4, 8, 10, 12, and 15 mm The heating tube length was kept fixed at 900 mm In accordance with the goal of the experimental study, convective heat transfer was intended to be increased by reducing the thickness of the boundary layer on the fins by using 6-mm-diameter holes that were opened at different angles on the circular fin that was placed on the heating tube These same-diameter holes on each fin could follow each other at the same selected angle Experimental studies were carried out at two different angular locations; 30◦ and 60◦ Figure shows the circular finned heating tubes that had 6-mm-diameter holes at angles of 30◦ and 60◦ To determine the effects of the flow directions of the heating and heated fluid to each other, experiments were carried out in parallel-flow and counterflow arrangements and with air mass flow rates of 0.04 and 0.08 kg/s All measurements were recorded by a computer and analyzed by a program Uncertainty Each of the measurement devices used in experiments has a measurement uncertainty Uncertainty analysis has been carried out according to the standard procedures in the literature If R depends on n independent variables (x1 , x2 , xn ), then heat transfer engineering S (b) θ = 60 Figure Finned heating tubes with 6-mm-diameter holes at the angular locations 30◦ and 60◦ the error in R, wR , depends on these variables according to: ∂R w1 ∂x1 wR = + ∂R wn ∂xn + ∂R w2 ∂x2 + ∂R w3 ∂x3 + 1/2 (1) The results of the error analysis can be seen in Tables and MATHEMATICAL FORMULATION AND DATA REDUCTION Total heat transfer rate (Qt ) from the hot water to air consists of radiation (QR ) and convective (Qc ) components When the temperature distribution along the fin is known, it is theoretically possible to calculate the amounts of both convective and radiative heat transfer from the cell realized by the two neighboring fins If the energy balance is written for the elementary area dA, as shown in Figure 4, then the following Table Uncertainties of the values measured in experiments Measured value Pressure difference on the air side Temperature on the air side Velocity on the air side Tube diameter on the air inlet side Distance between two fins Fin diameter Flow on the water side Pressure on the water side Temperature on the water side vol 32 no 2011 Uncertainty in measurements ±0.16 mbar ±0.5◦ C ±0.2 m/s ±2 mm ±1 mm ±0.5 mm ±0.4 L/h ±0.2 mbar ±0.1◦ C 402 G YAKAR AND R KARABACAK Table Uncertainty in the values calculated with the units measured in the experiment Calculated value Percent error ˙ air (kg/s) m um (m/s) Qt (W) Qc (W) To (◦ C) Tw (◦ C) Tf (◦ C) Red Nud 0.34 0.35 0.16 0.34 0.58 0.58 0.58 0.84 0.85 D d S equation is obtained: d2 T dT 2hf (T − To ) = + dr2 r dr λf t Figure Closed cell component formed between two fins Since the sum of currents in each node of the electrical circuit is zero, one can write for any point ri , i = 1, and j = 1, 2, 3, 4, ⎡ 2σεi ⎣ + Fdr−w T4 − T4w + Fdr−o T4 − T4o λf t ebi − ri ⎤ ro 1−εi εi dFdr−dr T4 − T ⎦ + (2) ri The expression given in Eq (2) is usually a nonlinear integrodifferential equation In addition, shape factors contain complex integral expressions depending on fin geometry, thus making the equation hard to solve So in the current study by using the arithmetic averages of the experimentally determined fin base and tip temperatures as fin temperature, radiative and convective heat transfer rates are calculated as described next j Fij =0 (3) where ebi = σT4i is the black body radiation power (W/m2), ri is the surface radiation (W/m2), and εi is the emissivity coefficient for the surface Radiation from (1) and (2) surfaces are the same according to Figure 6, and (r1 = r3 ) and (r4 = eb4 ) Besides the equality condition of q14 = q34 , radiative heat transfer from the cell formed by two fins to outer air medium can be stated as q4 = 2q14 + q24 (4) where q is the radiation heat flux (W/m2), and q14 = F14 (r1 − r4 ) Heat Transferred by Radiation When calculating the amount of radiative heat transfer from the circular fin surfaces placed on the heating tube, it is necessary to first determine the shape factors of the surfaces The shape factors depend on the fin parameters of the surface in the closed cell made by two neighboring fins, as shown in Figure and also given in reference [15] To calculate the radiative heat transfer from the fin surfaces to the surrounding air, an analogous electrical circuit, as shown in Figure 6, was used for the thermal interaction between the surfaces dA qo dqc r3 A F 23 e b2 A F13 1− ε2 ε2A r2 A F 24 A F 34 r4 = e b A F14 A F12 r1 − ε1 ε1A ro ri D r d − ε1 A 3ε1 dq r qi ri (5) e b3 dqc dq r r rj − ri + ro dr e b1 S Figure Circular and horizontal finned tube heater heat transfer engineering Figure Electrical analogy circuit pertaining to the closed cell formed between the two fins vol 32 no 2011 G YAKAR AND R KARABACAK q24 = F24 (r2 − r4 ) (6) In the horizontal heater formed by n circular fins, radiative heat transfer from all of the heater cells is: QR1 = (n − 1) A4 q4 (7) As a result of these equations, QR1 = K Tw 100 +M Tf 100 −N To 100 (8) where Tf is the average fin temperature; Tw is the heating tube surface temperature; and To is the temperature of the heated air from the upper part of the fin in the already-mentioned equation The values of the K, M, and N coefficients given in Eq (8) were taken from reference [14] For the galvanized steel fin and the galvanized steel heating tube material, emissivity coefficients measured to be εgal = 0.06 and εd = 0.15, respectively, were used for the solution of Eq (8) Radiative heat transfer from fin tips is as follows: QR2 = (AF )tip σεi Tftip 100 − To 100 (9) The total radiative heat transfer from all of the heating surfaces, on the other hand, is: QR = QR1 + QR2 (10) Heat Transferred by Convection The convective heat transfer rate is Qc = ho (ηo Ao ) (Tw − To ) (11) where Ao = Aw + Af is the total heat transfer area and ηo represents the efficiency of the finned surface The value of efficiency can be calculated by using the following equation [16]: Af (1 − ηf ) ηo = − Ao (12) Fin efficiency ηf was given in reference [14] according to the fin parameters Moreover, Aw is the area of the outer surface of heating tube while Af represents the total surface area of the fin The visible heat convective coefficient ho is determined by the following equation when total power input Qt is known: ho = Qt − QR ηo Ao (Tw − To ) (13) Equations (12) and (13) were solved simultaneously Iteration is continued until the ηo , ηf , and ho values converge to within 1% Depending on the value of ho obtained from the iteration, the Nusselt number is determined as follows (depending on the outer diameter of the heating tube): Nud = ho d λ (14) heat transfer engineering 403 Modified Reynolds Number The heated air flows through the spaces between the fins and the body inside the finned heat exchanger Depending on the free flow area the air decelerates and accelerates First it flows parallel, then vertical, and then parallel again Because of the deflectors used in the system, flow direction of the air on the heating tube changes continuously Nonetheless, mass flow rate remains the same throughout the flow in the test section Considering this, the Reynolds number that characterizes the air flow should be defined in terms of the mass velocity: ˙ air ˙ =m G As (15) ˙ air is the mass flow rate of the air passing through the where m heater and As represents the area of reference section perpendicular to the flow direction between two fins (As = D.s) in the already-mentioned equation On the other hand, not all of the air mass passes through the section between two fins under experimental conditions Some of it passes through the intersection between the fin end and the outer body, while some passes through the holes that are at certain angular locations Therefore, the Reynolds number cannot be exactly defined as in the case of perpendicular flow to the tube The Reynolds number should contain the effects of the other flows This case is rather complicated So instead of the Reynolds number, a new modified Reynolds number should be defined The Reynolds number, which characterizes the flow, should take into account the convective heat transfer calculated for a unit surface (qc = AQoc ) since convective heat transfer is dependent on movement of the air Consequently, the modified Reynolds number should be described according to (qc = AQoc ) After the required adjustments are made, the modified Reynolds number, which is obtained in such a way as to take the measured values into account, can be stated as follows: Red = Red Nud = ˙ qc Gd µλ (Tw − To ) (16) Physical properties of the air in the equation were obtained by using the film temperature as follows: Tfilm = Tw + To (17) RESULTS AND DISCUSSION To show the effect of the s/d geometric ratio on the Reynolds and Nusselt numbers, experimental studies were carried out for five different s/d ratios (0.138, 0.276, 0.345, 0.414, and 0.517, respectively) Red and Nud values were determined for the counterflow and parallel-flow arrangements and for air flows at 0.04 and 0.08 kg/s according to the 30◦ and 60◦ angular locations of the holes opened on the fins of finned heating tubes vol 32 no 2011 404 G YAKAR AND R KARABACAK Experimental System Validation To the knowledge of the authors, there is no experimental study to exactly compare the results of the current study with perforated fins So by using imperforate fin results [14] at the same working conditions for the same geometrical parameters with the perforated fins at 30◦ and 60◦ angular locations, comparisons have been made in terms of effectiveness values Imperforate fin results were in very good agreement with the values given in reference [16] For counterflow arrangement with imperforate fins NTU, capacity rate ratios and effectiveness values in [16] are as follows: NTU = 0.295, Cmin Cair Cmin = 0.0087, = Cmax Cmax Cwater Nud s/d = 0.138 s/d = 0.276 60 55 50 45 40 35 30 25 20 1.1x10 1100000 s/d = 0.345 s/d = 0.414 s/d = 0.517 6 3.1x10 3100000 5.1x10 5100000 Re d (a) m air = 0.04 kg/s , and s/d = 0.138 ε = 0.260 s/d = 0.276 and the results from the current study give: From these values, it is clearly seen that imperforate fin results are in very good agreement with the literature For the same geometrical parameters (D/d = 3, s/d = 0.345) at an angular location of 60◦ for a counterflow arrangement, the perforated fin effectiveness of ε = 0.313 is 18.1% higher than the value of ε = 0.265 obtained from imperforate fin geometry s/d = 0.414 100 Nud Cmin NTU = 0.295, = 0.0087, and ε = 0.265 Cmax s/d = 0.345 120 s/d = 0.517 80 60 40 20 3.5x10 3500000 8.5x10 8500000 13 5x10 13500000 Re d (b) m air = 0.08 kg/s Effect of s/d Ratios on Heat Transfer Figure Effect of modified Reynolds number on Nusselt number for θ = 300 (parallel flow) Figures to 10 show the effect of modified Reynolds number and s/d ratios on Nusselt number for the mass flow rates of 0.04 and 0.08 kg/s Considering Figures to 10, it can be seen that the Red values at 0.138 are higher than the Red values at the other s/d values in both counterflow and parallel flow, and that the Nud values at 0.414 and 0.517 are higher than the ones at the other values of s/d As the s/d ratio becomes lower, the distance between two fins is also reduced, and therefore the flow area decreases Nonetheless, the speed of the fluid increases because of the decreased flow area, and the Reynolds number increases for this situation For both mass flow rates, similar Nusselt number characteristics have been observed In addition, an increase in Nusselt number was observed with increasing modified Reynolds number Moreover, from the heat transfer point of view, a parallel-flow arrangement is found to give better results than a counterflow arrangement for both 30◦ and 60◦ In Figures 7a and b, corresponding Red values for mass flow rates of 0.04 and 0.08 kg/s are in the range of 14 × 105–40 × 105 and 43 × 105–12 × 106, respectively; similarly, in Figures 8a and b they are in the range of 15 × 105–40 × 105 and 35 × 105–10 × 106, respectively When different fin spacing to heating tube external diameter ratios were examined for angular locations of 30◦ and 60◦ for parallel flow only, it was shown that from the heat transfer point of view the obtained results for 30◦ are better than the results for 60◦ for s/d ratios of 0.138 and 0.276 On the other hand, the obtained results for 60◦ are better than the results for 30◦ for s/d ratios of 0.345, 0.414, and 0.517 For a parallel-flow arrangement, no significant difference has been observed in pressure drop values Figures and 10 show the results for counter flow arrangement Figures 9a and 9b comprise the results for a modified Reynolds number range between 90 × 104 and 30 × 105 and for 20 × 105–8 × 106, respectively Figures 10a and 10b comprises the results for a modified Reynolds number range between 90 × 104 and 37×105 and for 30 × 105–10 × 106, respectively Results of parallel-flow and counterflow arrangements for the 30◦ angular location, presented in Figures and 9, show that better results are obtained with both the parallel-flow arrangement and counterflow arrangement for s/d values of 0.276, 0.414, and 0.517 For 60◦ angular location, higher heat transfer rates were obtained for parallel flow at s/d values of 0.414 and 0.517, and for counterflow at s/d ratios of 0.276, 0.414, and 0.517, as shown in Figures and 10 The best overall performance for both angular locations was obtained for s/d ratio of 0.414 in the parallel-flow arrangement At s/d = 0.414, 11% and 8.6% heat transfer engineering vol 32 no 2011 G YAKAR AND R KARABACAK s/d = 0.138 s/d = 0.276 s/d = 0.276 s/d = 0.345 60 s/d = 0.414 35 s/d = 0.517 30 s/d = 0.345 Nud Nud s/d = 0.138 70 50 405 40 s/d = 0.414 s/d = 0.517 25 20 30 15 20 1.1E+06 1x106 22E+06 1x106 33E+06 1x106 1x106 4E+06 5x106 3E+06 0500000 5x106 12E+06 2.5x1064E+06 3.5x106 Re d Re d (a) m air = 0.04 kg/s (a) m air = 0.04 kg/s s/d = 0.138 s/d = 0.138 s/d = 0.276 120 s/d = 0.345 60 s/d = 0.345 100 s/d = 0.414 50 s/d = 0.414 80 s/d = 0.517 40 s/d = 0.517 Nud Nud s/d = 0.276 60 30 40 20 20 3x106 3000000 8x10 8000000 10 6 6 6 x10 2x10 4000000 4x10 6000000 6x10 8000000 8x10 10 2000000 1E+07 13x10 13000000 Re d (b) m air = 0.08 kg/s Re d (b) m air = 0.08 kg/s Figure Effect of modified Reynolds number on Nusselt number for θ = 60◦ (parallel flow) Figure Effect of modified Reynolds number on Nusselt number for θ = 30◦ (counterflow) increase in heat transfer was obtained for parallel flow compared to counterflow for angular locations of 30◦ and 60◦ , respectively In addition, 3.5% and 3.8% lower pressure drops were attained for 30◦ and 60◦ locations, respectively The correlation for heat transfer can be expressed as follows: CONCLUSIONS Nud = c1 Red c2 (18) The corresponding correlations for five different fin spacing to heating tube external diameter ratios in parallel-flow position in the present study are shown in Table Table Experimental study on finned tube heat exchangers with five different ratios of fin spacing to heating tube external diameter has been carried out The main conclusions can be summarized as follows: It was observed that from the heat transfer point of view the parallel-flow arrangement is found to give better results than the counterflow arrangement for both 30◦ and 60◦ Correlations of Nusselt number in parallel-flow arrangement s/d Ratio Range of Red Nud = f(Red ) Maximum relative error 0.9797 0.138 = 30◦ = 60◦ 34 × 105–40 × 105 34 × 105–40 × 105 Nud = 10−5 Red 0.276 = 30◦ = 60◦ = 30◦ = 60◦ = 30◦ = 60◦ = 30◦ = 60◦ 24 × 105–29 × 105 21 × 105–27 × 105 15 × 105–17 × 105 16 × 105–19 × 105 18 × 105–22 × 105 19 × 105–22 × 105 14 × 105–15 × 105 15 × 105–19 × 105 Nud = × 10−7 Red 1.2275 Nud = × 10−5 Red 0.9664 0.345 0.414 0.517 heat transfer engineering Nud = 8x10−6 Red 1.0793 Nud = 2x10−6 Red 1.1912 vol 32 no 2011 8.10% 4.47% 2.46% 1.64% 1.73% 406 G YAKAR AND R KARABACAK s/d = 0.138 Nud s/d = 0.276 40 s/d = 0.345 35 s/d = 0.414 s/d = 0.517 30 25 20 0.5 x10 150000 x10 250000 2.5 x10 350000 3.5 x10 450000 4.5 x10 500000 Re0 d 0 (a) m air = 0.04 kg/s s/d = 0.138 Nud s/d = 0.276 60 s/d = 0.345 55 s/d = 0.414 50 s/d = 0.517 45 40 35 30 25 x10 2000000 7000000 x10 Cair Cwater D d ebi Fij ˙ G hf hw ho K, M, N L ˙ m ˙ water m ˙ air m Nud NTU p qc Qt Qc QR Qw 12000000 12 x10 Re d (b) m air = 0.08 kg/s Figure 10 Effect of modified Reynolds number on Nusselt number for θ = 60◦ (counterflow) The best overall heat transfer performance for both angular locations of 30◦ and 60◦ was obtained for an s/d ratio of 0.414 in the parallel-flow arrangement At s/d = 0.414, 11% and 8.6% increase in heat transfer was obtained for parallel flow compared to counterflow for angular locations of 30◦ and 60◦ , respectively For the parallel-flow arrangement at s/d = 0.414, 3.5% and 3.8% lower pressure drops were attained for 30◦ and 60◦ locations, respectively, compared to the counterflow arrangement Qf q Red ri Red s t Tfilm Tw To Tf Tftip Twateri Twatero Twater Tair NOMENCLATURE Ao Aw As Af c cwater cair c1 , c2 C total heat transfer area (m2) heating tube surface area except total fin surface area (m2) area of reference section perpendicular to the flow direction between two fins (m2) total area of the fins on the tube (m2) specific heat capacity (kJ/kg-◦ C) specific heat capacity of water (kJ/kg-◦ C) specific heat capacity of air (kJ/kg-◦ C) coefficient of formulation ˙ capacity rate (W/◦ C) ( C = mc) heat transfer engineering Tairi Tairo um U ˙ V wR capacity rate of air (W/◦ C) capacity rate of water (W/◦ C) fin diameter (m) outer diameter of heating tube (m) black-body radiation power (W/m2) view factor between i surface and j surface mass flow velocity (kg/m2s) heat convective coefficient around fin (W/m2-◦ C) heat convective coefficient around body (W/m2-◦ C) visible heat convective coefficient (W/m2-◦ C) coefficient of formulation length of heating tube (m) mass flow rate (kg/s) mass flow rate of water (kg/s) mass flow rate of air (kg/s) Nusselt number number of transfer units (NTU = Ao U/Cmin ) pressure drop (mbar) convective heat flux (W/m2) heat power supplied from hot fluid (W) convective heat flow rate (W) total radiative heat flow rate (W) amount of the heat transferred by air over heating tube (W) amount of the heat transferred by air over fins (W) radiation heat flux (W/m2) Reynolds number surface radiation (W/m2) modified Reynolds number distance between fins (m) fin thickness (m) film temperature (◦ C) temperature of heating tube surface (◦ C) temperature of the heated air (◦ C) average fin temperature (◦ C) fin tip temperature (◦ C) input temperature of water to tube (◦ C) output temperature of water from tube (◦ C) difference between the input and output temperature of water in heating tube (◦ C) difference between the input and output temperature of air from heat exchanger (◦ C) input temperature of air into heat exchanger (◦ C) output temperature of air from heat exchanger (◦ C) average velocity of air (m/s) overall heat transfer coefficient (W/m2◦ C) volumetric flow rate of air (m3/h) uncertainty Greek Symbols εi ε λ emissivity coefficient for surface effectiveness thermal conductivity (W/m-◦ C) vol 32 no 2011 G YAKAR AND R KARABACAK λf σ ηo ηf ν µ θ thermal conductivity of fin material (W/m-◦ C) Stefan–Boltzmann constant (W/m2-K4) finned-surface efficiency fin efficiency kinematic viscosity (m2/s) dynamic viscosity (kg/ms) angular location (degrees) [9] [10] Subscripts air c f i o R tip t water w [11] air side convection fin input output radiation fin tip total water side tube wall [12] [13] REFERENCES [1] Xiao, Q., and Tao, W Q., Effect of Fin Spacing on Heat Transfer and Pressure Drop of Two-Row Corrugated-Fin and Tube Heat Exchangers, Int Communications in Heat and Mass Transfer, vol 17, pp 577–586, 1990 [2] Karabacak, R., The Effects of Fin Parameters on the Radiation and Free Convection Heat Transfer From a Finned Horizontal Cylindrical Heater, Energy Conversion Management, vol 33, pp 997–1005, 1992 [3] Kayansayan, N., Thermal Characteristics of Fin-and-Tube Heat Exchanger Cooled By Natural Convection, Experimental Thermal and Fluid Science, vol 7, pp 177–188, 1993 [4] Karabacak, R., Experimental Relationships For Heat Flux, Nusselt Number and Temperature Difference in a Finned Heater, Energy Conversion and Management, vol 37, pp 591–597, 1996 [5] Yan, W M., and Sheen, P J., Heat Transfer and Friction Characteristics of Fin-and-Tube Heat Exchangers, Heat and Mass Transfer, vol 43, pp 1651–1659, 2000 [6] Wang, C C., Hwang, Y M., and Lin, Y T., Empirical Correlations for Heat Transfer and Flow Friction Characteristic of Herringbone Wavy Fin and Tube Heat Exchangers, International Journal of Refrigeration, vol 25, pp 673–680, 2001 [7] Souidi, N., and Bontemps, A., Countercurrent Gas— Liquid Flow in Plate-Fin Heat Exchangers with Plain and Perforated Fins, International Journal of Heat and Fluid Flow, vol 22, pp 450–459, 2001 [8] Leu, J S M., Liu, S., Liaw, J S., and Wang, C C., A Numerical Investigation of Louvered Fin and Tube Heat Exchangers Having Circular and Oval Tube Configuraheat transfer engineering [14] [15] [16] 407 tions, International Journal of Heat and Mass Transfer, vol 44, pp 4235–4243, 2001 Wierzbowski, M., and Stasiek, J., Liquid Crystal Technique Application for Heat Transfer Investigation in a FinTube Heat Exchanger Element, Experimental Thermal and Fluid Science, vol 26, pp 319–323, 2002 Yakut, K., and Sahin, B., Flow-Induced Vibration Analysis of Conical Rings Used for Heat Transfer Enhancement in Heat Exchangers, Applied Energy, vol 78, pp 273–288, 2004 Zhang, Z., Ma, D., Fang, X., and Gao, X., Experimental and Numerical Heat Transfer in a Helically Baffled Heat Exchanger Combined with One Three-Dimensional Finned Tube, Chemical Engineering and Processing, vol 47, pp 1738–1743, 2008 Chen, H T., and Hsu, W T., Estimation of Heat Transfer Characteristics on a Vertical Annular Circular Fin of Finned Tube Heat Exchangers in Forced Convection, International Journal of Heat and Mass Transfer, vol 51, pp 1920–1932, 2008 Tang, L H., Min, Z., Xie, G N., and Wang, Q W., Fin Pattern Effects on Air-Side Heat Transfer and Friction Characteristics of Fin-and-Tube Heat Exchangers With Large Number of Large-Diameter Tube Rows, Heat Transfer Engineering, vol 30, pp 171–180, 2009 Yakar, G., The Effect of Turbulence Created in Fin-Tube Type Heat Exchangers With Perforated Fin on Heat Transfer and Pressure Drop, Ph.D thesis, Pamukkale University, Denizli, Turkey, 2007 Karabacak, R., The Effect of Fin Geometric Parameters on Natural Convection from a Horizontal Cylinder, Ph.D thesis, Dokuz Eylul University, Izmir, Turkey, 1989 Holman, J P., Heat Transfer, McGraw-Hill, Kogakusha, Tokyo, 1976 ¨ Gulay YAKAR received her Ph.D from Pamukkale University, Denizli, Turkey, in 2007 Her research interests include heat exchangers, absorption refrigeration, and second-law analysis of thermal systems She currently continues her experimental studies on enhancing heat transfer in shell and tube type heat exchangers Rasim KARABACAK is the dean of the Technical Education Faculty in Pamukkale University He received his Ph.D from Dokuz Eyl¨ul University, Izmir, Turkey, in 1989 His research interests include heat exchangers, heat pumps, cooling systems, dehydration, heat economy, and second-law analysis of thermal systems He currently continues his studies on heat pumps and dehydration Moreover, he offers heat transfer, thermodynamics, steam boilers, and refrigeration machines courses at the Mechanical Engineering Department of Pamukkale University vol 32 no 2011 Heat Transfer Engineering, 32(5):408–417, 2011 Copyright C Taylor and Francis Group, LLC ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457632.2010.483880 Corrosion Fouling of Carbon Steel for Convective Heat Transfer in an Annulus QASIM J M SLAIMAN and EMAD Y M ARABO Chemical Engineering Department, Nahrain University, Baghdad, Iraq Heat transport through a corroded carbon steel pipe in a double-pipe heat exchanger, with an aerated 0.1 N NaCl solution flowing in the annular space, has been investigated Experiments under heat transfer turbulent flow conditions were carried out in a Reynolds number range of 5000–15,000, at three bulk temperatures (30, 40, and 50◦ C), and a heat flux of 15 kW/m2 Rates of heat transfer were determined by measuring surface temperature, while mass transfer rates (corrosion rates), due to the diffusion-controlled oxygen reduction reaction, were estimated by measuring the limiting current density Fouling due to corrosion deposits that form on heat transfer surfaces has an asymptotic form The value of the asymptotic fouling resistance ranged from 2.17 × 10−4 to 2.54 × 10−4 m2 ◦ C/W with 200 h of exposure time INTRODUCTION Corrosion fouling is a type of fouling occurring on a heat transfer surface as a result of corrosion of that surface (chemical reaction between the material of the surface and the fluid stream) producing corrosion deposits that form a thermal resistance Corrosion fouling is influenced by many factors, including temperature, dissolved gases, dissolved solids, pH, solution velocity, and the composition and nature of the metallic surface being attacked [1] Corrosion fouling has not attracted as much attention as have other categories of fouling, probably because it was not widely recognized until about 1960 that the products of corrosion processes can affect heat transfer at a corroding system [2, 3] McAllister et al [4] reported quantitative data on the rates of fouling and corrosion in condenser tubes (concentric tube heat exchanger type) using river water, contaminated with seawater, as the cooling medium Alloys tested were 90–10 copper–nickel, aluminum–brass, admiralty-brass, 304 stainless steel, and others The values of the fouling thermal resistance ranged from 3.6 × 10−4 to 6.2 × 10−5 m2 ◦ C/W with a test duration of 130 days Somerscales and Kassemi [5] carried out tests of corrosion fouling on specimens of 1010 carbon steel in the form of an electrically heated wire suspended in a bath of distilled water, and reported that the average value of the final constant deposit thermal resistance was 2.8 × 10−4 m2 ◦ C/W for six specimens with test durations of 166–483 h Somerscales [6] put the equation of corrosion fouling in dimensionless form A comprehensive review of corrosion fouling was reported by Somerscales [2, 3] In this work, fouling due to corrosion products that form on the heat transfer surface of carbon steel in an annulus under turbulent flow of 0.1 N NaCl solution and produce a thermal resistance was studied through its effect on surface temperature Also the growth of these corrosion products influences the transfer of a participating reactant (dissolved oxygen) to the surface and was studied electrochemically using the limiting current density technique (LCDT) This study aims to obtain a mathematical expression of fouling thermal resistance as a function of time of exposure of a heat transfer surface to fouling conditions, and also to predict the parameters of this expression from corrosion rates data This means that the effect of corrosion fouling on the heat transfer process can be predicted from corrosion rates (mass transfer rates) EXPERIMENTAL WORK The Apparatus Address correspondence to Dr Emad Y M Arabo, PO Box 1436, Lane Cove, NSW 1595, Australia E-mail: emadarabo@yahoo.com The apparatus as shown in Figure consists mainly of five parts: the flow system, the electrochemical corrosion cell, the 408 Q J M SLAIMAN AND E Y M ARABO Wires 409 Wires ~ Voltmeter ~ Four Thermocouples Selector Channel Capillary tube Temperature Reader Rheostat SCE Venting Valve - Power Supply + Hoses Ammeter Dissolved Oxygen meter pH meter Rubber Hose Flask Heater & Thermostat Test Section Ammeter By-Pass Line Variac 0.1N NaCl Solution Flowmeter Outlet Tap Water (Cooling Water) Voltmeter Electrolyte Reservoir Cooling Bath Inlet Tap Water (Cooling Water) Valve Pump Figure Experimental rig electrical circuit, the heat flux supply unit, and the surface temperature measurement unit The flow system is composed of a glass container of 30 L in volume to contain the electrolytic solution, a stainlesssteel heater with thermostat to control the temperature of the electrolytic solution within an accuracy of ± 0.1◦ C, a centrifuge polyvinyl chloride (PVC) pump, a PVC liquid flowmeter (range 300–3000 L/h), and the test section The test section is composed of an outer PVC tube connected at both ends to PVC fittings that allowed the entry and exit of the solution, and in addition these fittings hold the inner PVC tube concentrically within the outer tube The carbon steel cathode section, on which the mass transfer and heat transfer took place, formed part of the inner tube and was situated at a distance from the test section entrance to ensure fully developed flow conditions Seventy equivalent diameters were allowed as an entrance length [7, 8] Twenty equivalent diameters were allowed as an exit length to avoid disturbance at the outlet Part of the outer tube was graphite and acted as anode in the electrolysis cell, and was situated concentrically opposite to cathode section The test section was mounted vertically and the electrolyte was pumped upward through the test section in order to ensure that the test section was full of flowing working solution Details of duct section are shown in Figure heat transfer engineering The electrochemical cell consists of working, counter, and reference electrodes The working electrode was cylindrical bar of 20 mm in diameter and 10 cm in length The diameter of the working electrode was the same as the outer diameter of the inner PVC tube At both ends of the working electrode, there were increments of smaller diameter that served to support the working electrode within the inner PVC tube so that the working electrode formed part of the inner tube Details of this electrode are shown in Figure The material of the working electrode was carbon steel (1019 AISI type according to American Iron and Steel Institute classification) The analysis of specimen was performed by the Engineering Inspection Department at the Al-Daura Oil Refinery in Baghdad Two holes of 1.5 mm in diameter were drilled in each specimen through a length of 15 mm from the upper edge of the 10-cm working electrode Two metallic rods of 1.5 mm in diameter and of sufficient length were inserted in these two holes and secured in place using an epoxy resin An electrical wire was attached to these rods to serve as a connection to the electrical circuit A high conductivity graphite (carbon) electrode was used as a counter electrode The graphite electrode was a cylindrical tube of 35 mm inner diameter and 20 cm long, as shown in Figure The inner diameter of the counter electrode was the same as the inner diameter of the outer PVC tube At both ends vol 32 no 2011 410 Q J M SLAIMAN AND E Y M ARABO 15 10 15 Holes dia 1.5 mm A 15 20 A PVC Tubes Holes dia 1.0 mm for thermocouples Holes dia 1.0 mm 100 Holes dia 1.5 mm for electrical connection 25 300 250 396 10 mm dia Hole for cartridge heater 10 20 100 Carbon Steel 200 15 Graphite 20 Section A-A Note: All dimensions are in mm 16 20 1146 1000 1050 1642 Figure Working electrode (carbon steel) 100 65 25 PVC Tubes As shown in Figure 4, there is a hole of mm diameter to allow the capillary tube passing through it to reach the cathode surface Also there is a hole of 2.5 mm diameter in the centre of the graphite electrode length in a radial direction from outside of the graphite to a distance of mm in its wall A metallic rod of 2.5 mm diameter was inserted in this hole and connected to PVC Divider 200 Note: All dimensions are in mm 250 PVC Reducer mm dia Hole for capillary entrance 20 Figure Schematic diagram of test section of the counter electrode, there were increments of larger inner diameter so that the graphite electrode could be inserted within the outer PVC tube; thereby the graphite electrode formed part of the outer tube The counter electrode (anode) surface area was larger than the working electrode (cathode) area to ensure that the current density at the anode was smaller than that at the cathode, and the process at the anode has no noticeable effect on the shape of the applied potential–current curve [9, 10] The ratio of surface area of anode to cathode was 3.5, which is sufficient to achieve the required condition heat transfer engineering 2.5 mm dia Hole for electrical connection Note: All dimensions are in mm 25 35 35 40 45 Figure Counter electrode (graphite) vol 32 no 2011 Q J M SLAIMAN AND E Y M ARABO an electrical wire The electrical wire was wound entirely and attached firmly around the graphite length to ensure uniform current distribution around the anode, and was insulated using electrical insulating tape The presence of inner and outer PVC pipes in the test section provides electrical insulation of the counter electrode from the working electrode The reference electrode was the saturated calomel electrode (SCE) All potentials were measured with reference to this electrode through a capillary tube The tip of the capillary tube was placed about mm away from the cathode surface, close to its upper edge [7, 11–13] The concentration boundary layer thickness ranges from 10 to 100 µm [12], so the capillary tube tip was well outside the mass transfer boundary layer The tip of the capillary tube was placed 15 mm from the upper edge of the working electrode The opening at the tip of the capillary tube was about 0.7 to mm in diameter The capillary tube was passed in a straight line through a hole of mm diameter in the graphite in order to reach cathode surface A rubber hose or tube of mm inside diameter was used to make a connection between the end of the capillary tube and a 250-ml conical flask, which was used as a reservoir to put the SCE in it The electrical cell as shown in Figure consists of the following devices: a DC power supply, a rheostat (variable resistance box), and two digital multimeters The DC power supply was used to obtain a constant applied voltage between the electrodes The potential of the working electrode was monitored using a voltmeter, while the current was observed with the aid of an ammeter The value of the potential was changed using the rheostat, and the corresponding steady state current was noted A series of values of potential and current was recorded This method of obtaining the potential and current is known as the “potentiostatic method” [14, 15] The heat flux supply unit is composed of a steel cartridge heater of 10 mm in diameter, 10 cm in length, 220 V, and 300 W The 10-cm working electrode (as shown in Figure 3) was drilled at its center line through its entire length with a hole of 10 mm in diameter, in which the cartridge heater was inserted and secured using epoxy resin A Variac was used to control and adjust the electrical voltage, which also means to control the electrical power, supplied to the steel heater The electrical voltage from the Variac was monitored by a voltmeter, while the current passing through this unit was measured by an ammeter The power was estimated from Ohm’s law, P = I V = I R = V /R, where I is the flowing current in amperes (A), V is the applied voltage in volts (V), and R is the electrical resistance of steel heater in ohms ( ) This power is equal to the heat flow rate to the system (i.e., Q = P) To prevent heat leakages from specimen ends, the two incremental ends of the 10-cm working electrode were insulated by fiberglass The surface temperature measurement unit consists of four copper–constantan (type K) thermocouples (1 mm wire diameter, point-welded joint about mm diameter), a selector channel (type K) to change the reading at various locations in the carbon steel specimen, and a digital temperature reader (type K) Four holes of mm diameter were drilled mm below the workheat transfer engineering 411 ing electrode specimen surface to a distance of 20 mm from its upper edge [16–19], as shown in Figure These four holes were arranged at 90◦ intervals The four thermocouples were mounted in these holes and held in place by epoxy resin Experimental Procedure Prior to each experiment, the carbon steel surface was treated with increasingly fine grades of emery paper (180, 320, 400, and 600) Then it was washed with tap water followed by distilled water, dried with clean tissue paper, degreased with ethanol to remove any dirt, oil, or grease, and finally dried with acetone and then with clean tissue to avoid water-deposited films [15] Sodium chloride at 0.1 N was used as an electrolyte This electrolyte was prepared from Analar sodium chloride (purity of NaCl > 99.8 wt%) The presence of NaCl increases the electroconductivity of the solution, so that the cathode potential was not appreciably influenced by the resistance drop in the bulk of the solution as this drop was small, and additionally the potential was measured close to the cathode surface by using a capillary tube [11] Increasing the conductivity of the solution is one of the reasons for using NaCl solution The pH of the solution was measured before each test using a digital pH meter The value of pH of the solution was 7.0 with negligible variation during a test run The solubility of O2 (dissolved oxygen concentration) in 0.1 N NaCl solution was measured using a dissolved oxygen meter The dissolved oxygen content was close to saturated conditions throughout a test Thirty liters of 0.1 N NaCl solution were prepared in the reservoir The combined unit of heater and thermostat was adjusted to the desired temperature and switched on The electrolyte was circulated through the bypass line until the desired temperature was reached The electrical circuit was switched on and as the electrolyte solution entered the test section, the heat flux supply unit was turned on and adjusted to the desired heat flux by Variac Also the surface temperature-measuring unit was activated, and the four readings from the thermocouples were recorded The average value of these readings was taken as the surface temperature The specimen (working electrode) was cathodically polarized from a potential of about –1.4 V (vs SCE) to the corrosion potential Ecorr where iapp = The potential and current were recorded during the run in steps of 30–40 mV [8], and was allowed for steady-state conditions to be reached after each potential increment [20] At the beginning of a fouling experiment (t = 0), the values for cathodic polarization and surface temperature were recorded These values represent a clean surface where no corrosion products had formed During the polarization no free corrosion occurs, except at low currents near the corrosion potential, because the specimen will be cathodically protected At the end of the first readings, the electrical circuit was switched off and the specimen was allowed to corrode freely under the influence of the 0.1 N NaCl corrosive solution This meant that corrosion products had begun to form The cathodic polarization and surface vol 32 no 2011 Q J M SLAIMAN AND E Y M ARABO 2 ° temperature results were taken every 4–8 h for the first 48 h, and every 14–20 h for the remaining experimental time The reason is at the beginning of a test there is a rapid increase of fouling effects with time The corrosion fouling experiment continued for 200 h The electrical circuit was switched on whenever cathodic polarization results were recorded, and then switched off after accomplishing the results, and so on Corrosion fouling experiments were carried out at three different temperatures 30, 40, and 50◦ C, at Reynolds numbers of 5000, 10,000, and 15,000, and for 15 kW/m2 heat flux Surface temperature measuring experiments can be performed simultaneously with cathodic polarization experiments or can be separately carried out No appreciable variation in results was observed R f X 10 ,m C/ W 412 0.1 N NaCl L = 10 cm q = 15 kW/m Tb = 30 o C Re=5000 Re=10000 Re=15000 RESULTS AND DISCUSSION The fouling thermal resistance Rf is calculated using [5, 21, 22]: 1 Rf = − h hc 0 (1) 40 80 120 Time, hr 160 200 240 Figure Effect of Reynolds number on fouling thermal resistance or Ts − Ts,0 q (2) where h, and hc are the heat transfer coefficients with fouling and without fouling (clean surface at t = 0), respectively, and Ts , and Ts,0 are the surface temperatures with fouling and without fouling (clean surface at t = 0), respectively; q is the heat flux and is given by q= Q = h(Ts − Tb ) A and higher corrosion rate; (2) the dissolved oxygen required for corrosion is reduced at higher temperatures due to the decreasing solubility of oxygen in the solution [27]; and (3) increasing bulk temperature at constant Reynolds number decreases the quantity (flow rate or velocity) of the solution passing over the heat transfer surface The influence of these factors leads to a slight decrease in Rf with increasing bulk temperature at constant Re, as shown in Figure (3) Plotting the fouling thermal resistance Rf against time, as shown in Figure 5, shows that there is a rapid increase in fouling effects at the beginning of the test and then Rf tends to approach a constant value This type of fouling curve is of asymptotic form The fouling rate depends on two processes: deposition and removal [23] The rapid increase in Rf at the beginning of the test is because the deposition rate is predominant over the removal rate, and then the deposition rate and removal rate ultimately become equal, resulting in an asymptotic form of the fouling time curve [21, 24] An increase in Reynolds number at constant bulk temperature leads to a reduction of the rate of increase in surface temperature and a decrease in the fouling thermal resistance Rf as shown in Figure With increasing Reynolds number or velocity, the removal rate increases, which tends to decrease the corrosion fouling effects This decrease in Rf with increase in velocity has been reported in the literature [4, 25] The increase in bulk temperature leads to the following: (1) a decrease and a deterioration in the stability of the corrosion layer [26], and this means higher removal rate but at the same time more oxygen to pass to the corroded heat transfer surface heat transfer engineering Rf X 104 ,m2 C/ W Rf = ° 0.1 N NaCl L = 10 cm q = 15 kW/m2 Re = 15000 Tb = 30o C Tb = 40 o C Tb = 50o C 0 40 80 120 160 200 Time, hr Figure Effect of bulk temperature on fouling thermal resistance vol 32 no 2011 240 Q J M SLAIMAN AND E Y M ARABO 413 -400 D Electrode Potential vs SCE, mV -600 Electrode potential vs SCE E corr 0.1 N NaCl L = 10 cm q = 15 kW/m Tb = 30 oC Re = 5000 C B time=0 hr time=4 hr -800 time=11 hr time=17 hr time=48 hr time=67 hr -1000 time=100 hr time=200 hr -1200 -1400 A -1600 i1 i 10 Log i Figure Typical cathodic region of the polarization curve of carbon steel in air saturated 0.1 N NaCl solution A typical cathodic potential–current curve for the behavior of carbon steel in air-saturated 0.1 N NaCl solution is shown in Figure The curve ABCD is called the cathodic region of the polarization curve, where AB is the secondary reaction (hydrogen evolution) region, BCD is the interest reaction (oxygen reduction reaction) region, and D is the corrosion potential Ecorr ; i1 is the final limiting value of oxygen reduction reaction, while i2 refers to final stage of hydrogen evolution reaction [28] The limiting current density of oxygen reduction iL is determined from the plateau BC This plateau is not absolutely flat, as shown in Figure 7; thus, the limiting current density value iL was obtained by the method previously suggested [29]: i1 + i2 iL z FCb 10000 In order to understand the effect of fouling on the limiting current density iL and the mass transfer coefficient km with time, the following expressions are defined: %i L r ed = i L ,0 − i L × 100 i L ,0 (6) where iL is the limiting current density at any time t, iL, is the limiting current density at t = 0, and % i L red is the percentage 450 (4) Figure shows the variation of the cathodic polarization curve and the decrease in limiting current density with time At the beginning, there is a rapid decrease in iL and then it tends to reach a constant value with increase in time as shown in Figure In other words, there is also an asymptotic form of the limiting current density The forming of corrosion products on the heat transfer surface leads to a decrease in the amount of oxygen reaching the surface, and this leads to decrease the corrosion rate (limiting current density) From the limiting current density data of oxygen reduction, the mass transfer coefficient km can be obtained [8, 9]: km = 1000 Figure Variation of the cathodic polarization curve with time 400 Limiting Current Density ( i L ), µ A/cm iL = 100 Current Density, µ A/cm 0.1 N NaCl L = 10 cm q = 15 kW/m Tb = 30 o C 350 Re=5000 Re=10000 300 Re=15000 250 200 150 100 (5) 50 where F is the Faraday constant (96,487 coulombs/equivalent), z is the number of electrons transferred (z = for oxygen reduction), and Cb is the bulk concentration of oxygen in the solution heat transfer engineering 40 80 120 160 200 Time, hr Figure Limiting current density versus time for various Reynolds number vol 32 no 2011 Q J M SLAIMAN AND E Y M ARABO 70 70 60 60 50 50 % k m red (% i L red.) % k m red (% i L red.) 414 40 30 0.1 N NaCl L = 10 cm q = 15 kW/m T b = 30 o C 20 40 30 0.1 N NaCl L = 10 cm q = 15 kW/m2 Re = 15000 20 Re=5000 Tb = 30o C Re=10000 10 Tb = 40 oC Re=15000 Tb = 50o C 10 0 40 80 120 160 200 240 Time, hr 40 80 120 160 200 240 Time, hr Figure 10 Effect of Reynolds number on %km red ( %i L red.) Figure 11 Effect of bulk temperature on %km red ( %i L red.) of reduction in limiting current density with time, and km,0 − km %km red = × 100 km,0 (7) where km is the mass transfer coefficient at any time t, km, is the mass transfer coefficient at t = 0, and %km red is the percentage of reduction in mass transfer coefficient with time Since km is directly proportional to iL according to Eq (5), %km red = %i L red The %km red (or %i L red.) ranges from a zero value at t = to a final constant asymptotic value similar in form to the fouling thermal resistance Rf An increase in Reynolds number at constant bulk temperature leads to a decrease in %i L red (or %km red.), as shown in Figure 10 Also the increase in bulk temperature at constant Re leads to a decrease in %i L red (or %km red.), as shown in Figure 11 %km red = (%km red.)∗ − exp(−bm t) (9) where (%km red.)∗ is the asymptotic value (constant final value) of percentage reduction in mass transfer coefficient, and 1/bm is the time constant The values of these two constants can be obtained using a regression technique (Table 2) CORRELATING THE CORROSION FOULING DATA As stated previously, the corrosion fouling data obtained in the present work have the asymptotic form, as demonstrated by Kern and Seaton [23]: R f = R ∗f − exp(−bt) creases with increasing bulk temperature at constant Reynolds number The value of the asymptotic fouling resistance R ∗f (final constant value) ranged from 2.17 × 10−4 to 2.54 × 10−4 m2 ◦ C/W with 200 h of exposure time These values are close to those obtained in the literature McAllister et al [4] reported values of the fouling thermal resistance ranges from 6.2 × 10−5 to 3.6 × 10−4 m2 ◦ C/W for different materials with test duration of 130 days Somerscales and Kassemi [5] reported that the average value of the final constant deposit thermal resistance was 2.8 × 10−4 m2 ◦ C/W for six specimens of 1010 carbon steel with test durations of 166–483 h In a similar manner, an asymptotic form for %km red with time can be obtained using the following equation: Table Values of R ∗f and b obtained using a regression technique Tb (◦ C) R ∗f × 104 (m2 ◦ C/W) b (1/h) Coefficient of correlation 30 30 30 40 50 2.54 2.43 2.29 2.24 2.17 0.0297 0.0246 0.0232 0.0213 0.0182 0.989 0.994 0.997 0.996 0.993 (8) R ∗f where is the asymptotic fouling resistance for t = ∞, and the quantity 1/b is defined as the time constant Table shows the values of asymptotic fouling resistance R ∗f and the values of b obtained using a regression technique The asymptotic fouling resistance R ∗f decreases with increasing Reynolds number at constant bulk temperature, and also deheat transfer engineering Re 5000 10,000 15,000 15,000 15,000 vol 32 no 2011 Q J M SLAIMAN AND E Y M ARABO Table Values of (%km red.)∗ and bm obtained using a regression technique Tb (◦ C) (%km red.)∗ bm (1/h) Coefficient of correlation 30 30 30 40 50 59.79 55.24 50.20 47.83 46.50 0.1458 0.1217 0.0990 0.0949 0.0768 0.975 0.983 0.977 0.975 0.986 2 o 5000 10,000 15,000 15,000 15,000 R f X 10 ,m2 C/ W Re 415 0.1 N NaCl L = 10 cm q = 15 kW/m Tb = 40 o C Re = 15000 Experimental Data Prediction From Mass Data R* X 10 ,m C/ W 0 ° 40 80 120 160 200 240 Time, hr Figure 14 Comparison of predicted fouling thermal resistance from mass data with experimental results for Re = 15,000 and Tb = 40◦ C f The terms R ∗f and b are related to (%km red.)∗ and bm , respectively, by the following equations and as shown in Figures 12 and 13: R ∗f = 2.14 × 10−5 (%km red.)∗ 0.605 (10) 1.0 100 (% k m red.)* Figure 12 The power relation between asymptotic fouling thermal resistance and (%km red.)∗ 0.030 b = 0.0065 + 0.157bm (11) The coefficients of correlation for these two equations are 0.993 and 0.982, respectively Hence, the values of fouling thermal resistance can be predicted from percentage reduction of mass transfer coefficient values and vice versa, as shown in Figure 14 CONCLUSIONS 0.025 b, 1/hr Two methods were used to observe the effect of corrosion fouling: a surface temperature method, and a polarization or limiting current density method From these two methods, it can be observed: 0.020 0.015 0.050 0.075 0.100 0.125 0.150 0.175 b m , 1/hr Figure 13 The linear relation between b and bm heat transfer engineering Surface temperature provides information about fouling thermal resistance and its effect on heat transport and the heat transfer coefficient, while limiting current density provides information about the amount of corrosion involved and the mass transfer coefficient More accurate measurement of surface temperature, especially for small changes, can be obtained than for the limiting current density vol 32 no 2011 [...]... respectively, and the outlet temperatures of the hot and cold fluids are T2 and t2 , respectively In the analysis, it is assumed that this heat source 384 M EL HAJ ASSAD AND V W KOTIAHO is uniform and constant over the length of the heat exchanger Other assumptions for the analysis are that fluid specific heats are constant, overall heat transfer coefficient is constant, and there is no heat transfer between... counterflow heat exchanger with a heat source in the hot fluid stream heat transfer engineering dimensionless REFERENCES [1] Kays, W M., and London, A L., Compact Heat Exchangers, McGraw-Hill, New York, 1984 [2] Incropera, F P., and DeWitt, D P., Fundamentals of Heat and Mass Transfer, 2nd ed., Wiley, New York, 1990 [3] Holman, J P., Heat Transfer, McGraw-Hill, New York, 2001 [4] Kakac, S., and Liu, Q H., Heat. .. heat exchanger effectiveness with heat source rate for different number of transfer units As it can be seen from Figure 2, the heat exchanger effectiveness heat transfer engineering is monotonically increasing with heat source rate Figure 2 also shows that for a given heat source rate, increasing the number of transfer units results in an increase in heat exchanger effectiveness As N T U → ∞, the heat. .. International Communications in Heat and Mass Transfer, vol 34 pp 248–258, 2007 Gao, S., and Voke, P R., Large-Eddy Simulation of Turbulent Heat Transport in Enclosed Impinging Jets, International Journal of Heat and Fluid Flow, vol 16, pp 349–356, 1995 Voke, P R., and Gao, S., Numerical Study of Heat Transfer From an Impinging Jet, International Journal of Heat and Mass Transfer, vol 41, pp 671–680, 1998... shows that increasing the heat source rate and number of transfer units, increases the heat exchanger effectiveness The figure shows that the heat exchanger effectiveness can be higher than 1 as the heat source rate and number of transfer units increase The variation of heat exchanger effectiveness with heat source rate is illustrated in Figure 4 for different values of number of transfer units Figure 4... No 1 55, Espoo, Finland, 2008 [8] Jenks, J., and Narayanan, V., An Experimental Study of Ammonia–Water Bubble Absorption in a Large Aspect Ratio Microchannel, ASME Paper No IMECE2006-14026, pp 243–249, 2006 [9] Narayanan, V., Kanury, M., and Jenks, J., Heat Exchanger Analysis Modified to Account for a Heat Source, ASME Journal of Heat Transfer, vol 130, no 12, p 124502, 2008 [10] El Haj Assad, M., and... absorber heat exchanger Expressions of effectiveness and number of transfer units of a counterflow heat exchanger with a heat source in the hot fluid stream are also given from minimum and maximum heat capacities points of view INTRODUCTION Heat exchangers are widely used in many thermal systems Condensers, boilers, intercoolers, and preheaters are some examples of heat exchanger devices used in power plants... condensation and boiling of refrigerants in conventional channels and in mini-channels vol 32 no 5 2011 Heat Transfer Engineering, 32(5):369–383, 2011 Copyright C Taylor and Francis Group, LLC ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457632.2010.483857 Investigation of Thermal Striping in Prototype Fast Breeder Reactor Using Ten-Jet Water Model R KRISHNA CHANDRAN,1 INDRANIL BANERJEE,2 G... counterflow heat exchanger with a heat source The analysis presented in this work is very useful in many applications such as ammonia–water absorber heat exchanger Moreover, it demonstrates an analytical procedure in order to analyze and explain data obtained from parallel-flow heat exchangers with a heat source in the hot fluid stream Analytical expressions are also given to analyze the performance of... Thermal Engineering and Refrigerating Engineering of the Koszalin University of Technology, Poland He is also a member of the Commission B1 of the International Institute of Refrigeration in Paris His general scientific interests are heat transfer during flow boiling and condensation, intensification of heat transfer in refrigeration and air-conditioning heat exchangers, and application of thermomechanics