Heat transfer engineering an international journal, tập 31, số 6, 2010

Heat Transfer Engineering, 31(6):431–432, 2010 Copyright C Taylor and Francis Group, LLC ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457630903408268 editorial Selected Papers From the 19th National & 8th ISHMT-ASME Heat and Mass Transfer Conference SHRIPAD T REVANKAR1 and SRINATH V EKKAD2 School of Nuclear Engineering, Purdue University, West Lafayette, Indiana, USA Department of Mechanical Engineering, Virginia Tech, Blacksburg, Virginia, USA We are glad to present this special issue of Heat Transfer Engineering with a selection of papers presented at the 19th National & 8th ISHMT-ASME Heat and Mass Transfer Conference, held January 3–5, 2008 The conference was jointly sponsored by the Indian Society of Heat and Mass Transfer (ISHMT) and the American Society of Mechanical Engineers (ASME) and was held at the Jawaharlal Nehru Technological University (JNTU), College of Engineering Kukatpally in Hyderabad, India The National Heat and Mass Transfer Conferences (HMTC) have been held biennially at various places in India since the inception of ISHMT in 1971 The American Society of Mechanical Engineers (ASME) formally joined the ISHMT in organizing and sponsoring these conferences in 1994 This has generated greater interaction between researchers from India and other participating countries Many well-known experts from abroad have participated, exchanged technical information, and shared their expertise with Indian researchers through these conferences and various follow-up workshops and short courses on topics in heat and mass transfer At the 19th National & 8th ISHMT-ASME Heat and Mass Transfer Conference, in total 330 papers including plenary and 14 keynote papers were presented The conference was co-chaired by S Srinivasa Murthy of Indian Institute of Technology (IIT) Madras and Srinath V Ekkad of Virginia Tech, with K V Sharma of JNTU Hyderabad and T Sundararajan of IIT Madras as conference secretaries About 500 participants including about 80 from 19 different countries participated in this heat transfer conference Address correspondence to Prof Shripad T Revankar, School of Nuclear Engineering, Purdue University, West Lafayette, IN 47907, USA E-mail: shripad@ecn.purdue.edu Here in this special issue eight selected papers covering heat transfer in turbines, electronic cooling, heat exchangers, refrigeration systems, and materials and efficiencies in power plants are included The first paper, “Methods for Conceptual Thermal Design,” presents three models and application methods that can be used to analyze temperature development in an electronic product during conceptual design The first model applies to electronic products used under normal conditions The second model calculates hotspot temperature that can be used to evaluate structural concepts during early design stages The third model can be used to estimate temperatures in steady-state situations with known boundary conditions obtained from a thermal mock-up for a functional model These models are developed in a resistor–capacitor (RC) network model and can be easily used as tools for conceptual thermal design The second paper, “Correlation for Heat Transfer Under Nucleate Boiling on Horizontal Cylindrical Surface,” presents experimental data on nucleate boiling heat transfer on horizontal cylindrical heating elements made out of copper in the medium of Forane around atmospheric conditions A heat of boiling/heat transfer correlation is developed based on three nondimensional π groups The π groups incorporate the dynamics of bubble growth, dynamics of flow of the surrounding fluid during the bubble dilatation, and the influence of the thermal aspects associated with liquid 431 432 S T REVANKAR AND S V EKKAD vaporization responsible for the growth of the bubble The third paper, “A Parametric Study of an Irreversible Closed Intercooled Regenerative Brayton Cycle,” presents a thermodynamic analysis of an irreversible regenerated closed Brayton cycle with variable-temperature heat reservoirs The optimization is carried out using an entropy generation minimization principle, and numerical results are presented on the effects of the heat transfer irreversibility in the hot- and cold-side heat exchangers and the regenerator, the irreversible compression and expansion losses in the compressor and turbine, the pressure drop loss at the heater, cooler, and regenerator as well as in the piping, and the effect of the finite thermal capacity rate of the heat reservoirs on the power and efficiency The fourth paper, “Conjugate Heat Transfer Analysis in the Trailing Region of a Gas Turbine Vane,” presents simulation results on the local values of pressure, wall, and fluid temperature, and area-averaged values of friction factor and Nusselt number between the smooth and pinned channels and cambered converged channels with and without pin fins, simulating the trailing region internal cooling passages of a gas turbine vane The paper highlights interaction between the complex flow pattern and conjugate heat transfer The fifth paper, “Experimental Investigation of Cooling Performance of Metal-Based Microchannels,” presents Al- and Cu-based high-aspect-ratio microchannel heat exchanger fabrication, and demonstrates through experiment that the metal-based micro heat exchangers provide improvement in cooling efficiency for microelectronic systems Given the energy needs of the world and given coal as the primary fossil fuel of today, integvrated gasification combined cycle (IGCC) technology has been identified as an efficient and economic method for generating power from coal with substantially reduced emissions The sixth paper, “Numerical Simulation of Pressure Effects on the Gasification of Australian and Indian Coals in a Tubular Gasifier,” shows that that the gasification performance increases for both types of coal when the pressure is increased The seventh paper, “Shell-and-Tube Minichannel Condenser for Low Refrigerant Charge,” presents a design of a shell-andtube heat pump condenser using 2-mm-ID minichannels with the expected refrigerant charge less than half the quantity required by a brazed plate condenser giving the same capacity Experimental data for heat transfer and pressure drop in this novel condenser are reported The last paper, “Experimental Investigation of the Effect of Tube-to-Tube Porous Medium Interconnectors on the Thermohydraulics of Confined Tube Banks,” presents experiments on the effect of tube-to-tube copper porous interconnectors on the thermohydraulic performance of an inline and staggered confined tube bank The data show that a reduction in the pressure drop by 18% is observed in the inline heat transfer engineering configuration, while the heat transfer is enhanced by 100% in the staggered configuration, when compared to their respective configurations without the porous medium We thank all the authors of these papers for their efforts in reporting their results, and all the reviewers who have helped provide timely and informative reviews We also thank Dr Afshin Ghajar, editor-in-chief of Heat Transfer Engineering, for his interest in and support of this special issue Shripad T Revankar is a professor of nuclear engineering and director of the Multiphase and Fuel Cell Research Laboratory in the School of Nuclear Engineering at Purdue University He received his B.S., M.S., and Ph.D in physics from Karnatak University, India, M.Eng in Nuclear Engineering from McMaster University, Canada, and postdoctoral training at Lawrence Berkeley Laboratory and at the Nuclear Engineering Department of the University of California, Berkeley, from 1984 to 1987 His research interests are in the areas of nuclear reactor thermalhydraulics and safety, multiphase heat transfer, multiphase flow in porous media, instrumentation and measurement, fuel cell design, simulation and power systems, and nuclear hydrogen generation He has published more than 200 technical papers in archival journals and conference proceedings He is currently chair of the ASME K-13 Committee, executive member of the Transport and Energy Processes Division of the American Institute of Chemical Engineers, and chair of the Nuclear and Radiological Division of the American Society for Engineering Education He has served as chair of the Thermal Hydraulics Division of the American Nuclear Society He is on the editorial board of the following four journals: Heat Transfer Engineering, International Journal of Heat Exchangers, Journal of Thermodynamics, and ASME Journal of Fuel Cell Science and Technology He is a fellow of the ASME Srinath V Ekkad received his B.Tech degree from JNTU in Hyderabad, India, and then his M.S from Arizona State University and Ph.D from Texas A&M University, all in mechanical engineering He was a research associate at Texas A&M University and a senior project engineer at Rolls-Royce, Indianapolis, before he joined Louisiana State University as an assistant professor in 1998 He moved to Virginia Tech as an associate professor of mechanical engineering in Fall 2007 His research is primarily in the area of heat transfer and fluid mechanics with applications to heat exchangers, gas turbines, and electronic cooling He has written more than 100 articles in various journal and proceedings and one book on gas turbine cooling His research focuses on enhanced heat transfer designs, with a variety of applications He has served as coordinator for the 8th ISHMT/ASME Joint Heat and Mass Transfer Conference held in Hyderabad, India, in January 2008 He was also the chief organizer for the heat transfer track at the 2004 ASME Turbo Expo He is also an associate editor for Journal of Enhanced Heat Transfer and International Journal of Thermal Sciences He was the inaugural recipient of the ASME Bergles–Rohsenow Young Investigator in Heat Transfer Award in 2004 and the ASME Journal of Heat Transfer Outstanding Reviewer vol 31 no 2010 Heat Transfer Engineering, 31(6):433–448, 2010 Copyright C Taylor and Francis Group, LLC ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457630903408318 Methods for Conceptual Thermal Design RUBEN STRIJK, HAN BREZET, and JORIS VERGEEST Faculty of Industrial Design Engineering, Delft University of Technology, Delft, The Netherlands This article describes three generic models and application methods that can be used to analyze temperature development in an electronic product during conceptual design The models are based on generally known heat transfer and resistor– capacitor network theory and are theoretically and numerically approximated The result is three easy-to-use tools for conceptual thermal design Application of the models in design practice has been assessed using a usability experiment and several in-depth interviews with industrial design engineers from the field INTRODUCTION The latest changes in industry require companies to focus on fast innovations The result is that time to market is shortened and development speed is increased [1] Therefore, we have less time to develop products that are reliable and have good quality In addition, the amount of electronics around us is increasing, ubiquitous electronics [2], and the power density is increasing by continuous miniaturization The result is that reliability becomes an increasing important issue in development of electronic products [3] and thermal design becomes a bottleneck in the development process It is therefore necessary to provide electronic and mechanical engineers with tools and methods to take temperature into account in preliminary phases in design Some research has been done to improve thermal analysis in the conceptual phases Ishizuka and Hayama [4], for instance, describe models to simplify analysis of natural convective cooling in preliminary analysis Yazawa and Bar-Cohen’s studies on flow models [5] also contribute to this issue However, in our best knowledge there are no generic models available that can be used in conceptual design of electronic systems Our goal is to extend the present knowledge on resistor–capacitor networks (RC networks) and flow modeling to develop generic models for application in conceptual thermal design During our preliminary studies several designers from practice have been interviewed with the aim of verifying the application of thermal management techniques in practice Different Address correspondence to Professor Ruben Strijk, Faculty of Industrial Design Engineering, Delft University of Technology, Landbergstraat 15, 2628 CE Delft, The Netherlands E-mail: r.strijk@tudelft.nl views indicate how practicing designers work in the field of thermal design Three key issues derived from interviews and literature are: Designers are unfamiliar with heat transfer and thermal design theories Such designers lack the knowledge that would enable them to make basic design choices and evaluate how important temperature is to the design The choice between passive and active cooling is currently based on experience and trial and error An evaluation of structural concepts on temperature development is not supported by a standard approach Temperature measurements for mock-ups and functional models are crucial in thermal design practice for finding reliable boundary conditions, but are time-consuming The process of measuring could possibly be optimized by properly integrating easy-to-use formulas that could be calibrated using measurements determined from a thermal mock-up or functional model The effects of design changes could be predicted by predefined rules of experience and estimations Furthermore, as has been concluded from studying the literature and has been clearly expressed by participants during interviews, any tool used for conceptual design should be easy to use To resolve the three issues just listed, three models have been developed that contain the following three characteristics: Model supports risk assessments put forth by the designer, even if he or she has no knowledge of heat transfer or thermal design [6–8] Model supports finding and analyzing the main heat path in structural concepts and is useful for estimating rough temperatures in an electronic product [8–10] Model 433 434 R STRIJK ET AL supports the determination of the total transient behavior in a device [8, 11] The contribution of this article is the proposal and evaluation of these three models and application methods APPROACH This article is constructed of several sections to propose and evaluate the three models In the approach for model 1, basic heat transfer calculations are combined with measurements for existing products Heat transfer calculations show maximum boundary conditions of heat transfer for a surface area This is done using several surface temperature differences within the environment Measurements combined with these values show a transition area that can be used as a guideline for a particular design For model 2, an RC network is developed and programmed into a small software program The industrial designer can use this program to fill in variables and calculate temperatures Finally, model describes a mathematical model for temperature prediction in an electronic product As a basis for the model, an electronic product will be viewed as if it were one single hotspot within an encasing In reality, the hotspot could be a power-dissipating component, such as a coil, integrated circuit (IC), or the average temperature of a printed circuit board The model can be used to describe the effect of design changes on hotspot temperature Several design variables will be taken into account, including an open or closed encasing, passive cooling or active cooling, and materials used for the encasing In this article, four steps that define the models will be listed: model description, results and discussion, practical application, and conclusion Step 1: Model description Describing the three proposed models based on general heat transfer theory and thermal RC networks Step 2: Results and discussion The application of the three models will be described for example situations and real products The heat transfer variables that are needed in the equations are derived from standard conduction, convection, and radiation equations The section follows with a description of the results of the measurements The differences between the measured and calculated values are discussed and directions for improving the accuracy of the model are given Step 3: Practical application The practical use of the models in a design situation is described Step 4: Conclusion Drawing conclusions from the research in described in this article limits for an electronic product is explained The theoretical cooling limit is derived by combining convective and radiative heat transfer coefficients from an isothermal surface to an ambient environment As a basis for model 2, an electronic product is examined as one single hotspot within an encasing In reality, the hotspot can include a power dissipating component, such as a coil, an integrated circuit (IC), or the components of a printed circuit board (PCB) Model is a framework for evaluating various cooling concepts and is based on an RC network The objective of the model is to give insight into transient behaviors of the hotspot and encasing temperatures for different cooling configurations Model Passive cooling limits have been calculated for the temperature differences between a hot surface with an ambient environment By comparing these values with measurements for existing products, boundary areas for the passive and active cooling of an electronic product and a maximum power-to-area ratio for electronic products can be defined These calculations are for heat transfers between an isothermal surface temperature Te and the ambient temperature Ta = 296 K (= 23◦ C) A specific dimension for a vertical plate Lc of 0.1m and thermal conductivity of air kair is used to calculate the heat transfer coefficient for convection hc and the heat transfer coefficient for radiation hr at temperature differences T (= Te − Ta ) of K, 15 K and 25 K, shown in Table The heat transfer coefficients hc and hr have been approximated based on general heat transfer theory for a vertical plate with an isothermal temperature distribution across the surface To determine hc , the Hilpert correlation, shown in Eq (1), has been used to approximate the Nusselt number Nu [12] kair NuL [W/m2 K]; Nusselt, NuL = 0.54RaL0.25 (1) L The heat transfer coefficient of radiation hr is determined by using the average temperature Tav , and is shown in Eq (2) Here, qr is the radiation heat transfer [W], ε is the emissivity of the radiating surface [1.0], σ is the Stefan–Boltzmann constant [5.67 × 10−8 ], F1,2 is the radiation shape factor, A is the radiation surface area, T1 is the surface temperature of object 1, T2 is the surface temperature of object 2, and Tav is the average surface temperature between object and object hc = hr = εσF1,2 4Tav [W/m2 K] Table Natural convection and radiation heat transfer coefficients for three temperature differences, calculated using Eq (1) and Eq (2) for an ambient temperature Ta = 296 K h [W/(m2 K)] MODEL DESCRIPTION In this section a description of the proposed models is given For model the theoretical approximation of passive cooling heat transfer engineering (2) T=5K 6.0 3.7 9.7 hr hc htot vol 31 no 2010 T = 15 K 6.3 4.9 11.2 T = 25 K 6.7 5.5 12.2 R STRIJK ET AL The resulting total heat transfer coefficient htot , given in Eq (3), is then calculated by summing hc and hr The temperature difference of 15 K is comparable with previous studies found in literature [5] The temperature differences of K and 25 K define a transition area between passive and active cooling htot = hr + hc (3) Table gives results for the three temperature differences just described The results show that, for the given Ta , hc is significantly dependent on temperature differences between the surface and the environment, while hr is not In addition, it can be concluded that in passive cooling, radiation heat transfer can play a significant role because it is in the same order of magnitude as convection heat transfer However, this only accounts for black- and gray-body radiation, where ε ≈ 1.0 Model As a basis for model and model 3, this article examines an electronic product as one single hotspot within an encasing In reality, the hotspot can include a power dissipating component, such as a coil, an integrated circuit (IC), or the components of a printed circuit board (PCB) Based on this abstraction, various models can be derived, ranging from a very simple RC network, which is discussed in this section, to a complex RC network In this section, mathematical relations of the one-dimensional heat transfer will be derived This is done by proposing a onedimensional RC network, given in Figure 1, that can be applied to a variety of electronic products that are passively cooled and have a closed encasing Based on insights gained through this analysis, the mathematical model may be expanded into something more complex This will be explored in future research if required When designing electronic products, it can be important to predict the behavior of a product within a certain period of time For this particular model, it is necessary to take into account transient temperature development By using transient temperature prediction in the form of state space equations, the model allows for the option of evaluating a usage scenario This usage scenario can then be evaluated and compared with defined criteria Based on such results, the product can be properly designed without overdimensioning, which would bring about higher costs Figure Thermal RC network model heat transfer engineering 435 The system consists of five types of variables: thermal resistors R, temperature T , thermal capacitors C, heat flow q, and energy E Four thermal resistors include the following: • The core of the hotspot to the surface of the hotspot, or R1 The hotspot surface to the interior surface of the encasing, or R2 • The interior surface of the encasing to the exterior surface of the encasing, or R3 • The exterior surface of the encasing to the ambient environment, or R4 • The temperatures in the product result from the hotspot heat flow q and the thermal resistors, q = R T In this model, five temperatures are defined: • • • The temperature inside the hotspot, or Tc The temperature of the hotspot surface, or Th The temperature of the interior surface of the encasing, or Ti • The temperature of the exterior surface of the encasing, or Te • The ambient temperature, or Ta In order to calculate transient temperature development, thermal capacity must be taken into account Generally, electronic products consist of an encasing on the outside and electronics on the inside Between the electronics and the encasing, there is generally air Usually, this means that when a product is heated, there are three thermal capacitors (Figure 1) that cause temperatures to rise at a steady rate: • • • The thermal capacitance of the hotspot, or C1 The thermal capacitance of the inside air, or C2 The thermal capacitance of the encasing, or C3 The main heat flow in the system q causes temperatures to rise Three heat flow paths into thermal capacitances result from this general heat flow The heat flow paths into these three thermal capacitances are defined as follows: • • • Heat flow into C1 , or q1 Heat flow into C2 , or q2 Heat flow into C3 , or q3 The heat flow in the model will result in four basic temperature differences: • From the core of the hotspot to the surface of the hotspot, or Tc − Th • From hotspot surface to the interior of the encasing, or Th −Ti • From the interior of the encasing to the exterior of the encasing, or Ti − Te • From the exterior of the encasing to the ambient environment, or Te − Ta By combining these temperature differences, other temperature differences can be derived, for example, the temperature difference between a hotspot surface and exterior encasing, Th − Te , equals (Th − Ti ) + (Ti − Te ) For practical reasons, vol 31 no 2010 436 R STRIJK ET AL only the temperatures Th , Te and Ta will be measured and compared, with resulting temperature differences of Th −Te , Te −Ta , and Th − Ta Finally, the total energy stored in the capacitances in the system can be defined by the product of thermal capacitance and temperature, or E = CT However, in the present case, of greatest interest are temperature differences with regard to a reference temperature Ta Therefore, the energy stored in the system is defined as reference energies Eref = C1 Ta , Eref = C2 Ta and Eref = C3 Ta for the following thermal capacitances: Energy stored in C1 , or E1 = C1 Tc − Eref → E1 = C1 (Tc − Ta ) • Energy stored in C2 , or E2 = C2 Th − Eref → E2 = C2 (Th − Ta ) • Energy stored in C3 , or E3 = C3 Ti − Eref → E3 = C3 (Ti − Ta ) • State space equations allow for the possibility of dynamically analyzing temperatures A designer may use the equations to calculate temperature from any realistic starting condition For instance, the model can be integrated and computed into a software program in which the designer fulfills required parameters and usage scenarios The program then calculates temperature development in the device This section describes these state space equations and their parameters State space equations basically consist of two equations The first equation defines ˙ air flow into thermal capacitances, X(t) = AX(t) + BU (t) The second equation is used to examine temperature differences Y (t) = CX(t) + DU (t) The matrices are defined as follows [13]: • • • • • • • • ˙ X(t) are the heat flows into thermal capacitances A is the system matrix and contains the values of thermal resistances and capacitances X(t) is the vector describing the state of the system, which is the energy stored in thermal capacitances with regards to the reference temperature Ta U (t) is the input vector and describes the quantity of heat that flows from the hotspot into the system B is the control matrix Y (t) is the output of the system C is the output matrix of the system D is the feed-forward matrix State space equations based on this system can be defined as follows: ⎛ ⎞ ⎛ ⎞ C1 Tc − Eref q1 ˙ X(t) = ⎝ C2 Th − Eref ⎠ ; X(t) = ⎝ q2 ⎠ ; C3 Ti − Eref q3 ⎞ T c − Th ⎜ T h − Ti ⎟ ⎟ U (t) = q; Y (t) = ⎜ ⎝ T i − Te ⎠ Ta − Te ⎧ ⎛ 1 ⎪ ⎪ − ⎪ ⎪ ⎜ C R C R1 ⎪ 1 ⎪ ⎜ ⎪ ⎪ ⎜ ⎪ 1 ⎪ ˙ ⎪ − − X(t) =⎜ ⎪ ⎜ C1 R1 ⎪ C2 R C2 R2 ⎪ ⎜ ⎪ ⎪ ⎝ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ C R2 ⎪ ⎪ ⎪ ⎛ ⎞ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎜ ⎟ ⎪ ⎨ + ⎝ ⎠ U (t) ⎪ ⎪ ⎪ ⎪ ⎛ ⎪ ⎪ 1 ⎪ ⎪ − ⎪ ⎪ ⎜ C1 C2 ⎪ ⎪ ⎜ ⎪ ⎪ ⎜ ⎪ ⎪ ⎜0 ⎪ ⎪ ⎜ ⎪ C2 ⎪ ⎜ Y (t) = ⎜ ⎪ ⎪ ⎪ ⎪ ⎜0 ⎪ ⎪ ⎜ ⎪ ⎪ ⎜ ⎪ ⎪ ⎝ ⎪ ⎪ ⎩ 0 ⎞ C3 R2 − 1 − C3 R2 C3 (R3 + R4 ) (4) ⎞ ⎟ ⎛ ⎞ ⎟ ⎟ ⎟ ⎜ ⎟ − ⎟ ⎜0⎟ C3 ⎟ X(t) + ⎜ ⎟ U (t) ⎟ ⎜0⎟ R3 ⎟ ⎝ ⎠ C3 (R3 + R4 ) ⎟ ⎟ ⎠ R4 C3 (R3 + R4 ) Model In this section, a framework for evaluating various cooling concepts is described The framework is based on an RC network, shown in Figure The objective of the model is to give insight into transient behaviors of the hotspot and encasing temperatures In the thermal RC network, there are several heat flows that must be taken into account The source for the heat flow is q As a result of q, the product begins to heat This property is represented by heat q1 into thermal capacitance C As a result of the heat flow in C, the temperature of the product rises and heat flows to an ambient environment The heat flow to the ambient environment can be divided in two flows First, a possible forced or passively induced flow of air through the device via openings in the encasing may exist This is represented by q2 Second, a flow of heat in the form of natural convection and radiation through the encasing q3 may also be present There are several thermal resistances that determine power flows and temperature distribution within a system First, a thermal resistance models heat transfer through a flow of air through the product R1 This can occur through either natural or forced convection For fully closed encasings, the value of this thermal resistance will be set to infinite ∞ Second, the model contains two thermal resistances that describe the heat flow q3 through the encasing This includes heat flow from the hotspot to the exterior of the encasing R2 and heat flow from the exterior of ⎛ heat transfer engineering ⎟ ⎟ ⎟ ⎟ X(t) ⎟ ⎟ ⎠ Figure Thermal RC-network model vol 31 no 2010 R STRIJK ET AL 437 the encasing to an ambient environment R3 The result of these described thermal resistances and heat flows of a product within a specific ambient temperature Ta is a hotspot temperature of Th and an average encasing exterior temperature of Te Integration of the previous equation results in the following equation: −t T (t) = Tm − e( RC ) (Tm − Ta ) (5) From Eq (5) two equations can be derived given by Eq (6): ⎡ R (R + R ) R (R + R ) ⎤ Th (t) Te (t) = Ta Ta 3 ⎢ R1 + R2 + R3 R1 + R2 + R3 ⎥ ⎥ +⎢ ⎣ ⎦ R1 R3 R1 R R1 + R2 + R3 R1 + R2 + R3 × q −t −qe( RC ) (6) For a closed encasing, the value of R1 can be defined as infinite, resulting in Eq (7): Th (t) Te (t) = Ta Ta + R2 + R3 R2 + R3 R3 R3 q −t −qe( RC ) (7) RESULTS AND DISCUSSION In this section the results and discussion of the three models are presented and described A more extensive elaboration of the results has been described in previous publications [7, 8, 10, 11] Model The surface area A and power dissipation q have been measured for a 66-product total Figure shows both the calculated heat transfer lines (Table 1) and the positioning of the experimental results The values of A varied between 8.0 × 10−3 m2 (portable radio) and 3.0 m2 (washing machine), while q varied between 2.0 × 10−2 W (portable radio) and 2.0 × 103 W (water cooker) Figure shows that most products that dissipate less than W of power are positioned below the K temperature line Product examples in this range include a Discman, radio, MP3 player, and minidisk It is probable that thermal design was not a major issue in the development of these products Examples of products that are positioned around the K line up to the 15 K line include stereos, cathode ray tube TVs, LCD (liquid crystal display) TVs, network switches, and routers It would be likely that thermal design played a significant role in the design process of these products For instance, an LCD TV uses holes in the encasing, combined with a significant amount of cooling fins on the inside of the product, to dissipate heat from the printed circuit board to an ambient environment heat transfer engineering Figure Existing products and theoretical cooling limits, based on own measurements In the “actively cooled” range, between the 15 K and 25 K lines, products such as a laptop computer are positioned These types of products are generally regarded as in critical need of proper thermal design In the area above 25 K, products such as power tools, kitchen appliances, and slide projectors can be found Power tools that use an electromotor usually have a relatively short duty cycle and therefore generally not reach their steady-state temperature Products that are convectively cooled are cooled by airflow induced by a rotating component, sometimes a fan directly connected to the electromotor Other products in this range, such as kitchen appliances and slide projectors, generally give off a great deal of heat Thermal design is very critical in these types of products Temperatures of hotspots in these types of products are usually much higher than in products within the range of 15 K to 25 K Model In order to investigate the accuracy of state space equations and the assumptions made in the previous section, computations will be based on the properties of an actual product, in this case, a standard AC–DC adaptor shown in Figure Comparisons of the measurements with the model will give conclusions about the accuracy and applicability of the model for design engineering purposes The measurements have been executed using thermocouples and an infrared sensor Data has been collected by means of a data logger, which measures and stores the temperatures of the hotspot Th , the encasing Te , and the ambient temperature Ta For the purposes of this comparison, both measurements and computations have been subjected to two different degrees of power dissipation, including W and W The aim is to gain insight into the extent to which the model can predict variations in temperatures, depending on the different amounts of vol 31 no 2010 438 R STRIJK ET AL Figure Overview of an AC-DC adaptor dissipated power The heat transfer coefficients for convection and radiation are influenced by factors such as temperature differences and geometry In this model, a combined heat transfer coefficient for convection and radiation is used Equation (1) has been used to approximate the Nusselt number, Nu The heat transfer coefficient of radiation is approximated by using Eq (2) State space equations have been programmed using a C++ script in order to determine their solutions The script is an algorithm based on the explicit Euler method for calculating differential equations The script can be used to develop a software program from which a practical application can be tested The results of the computed model and measured product are shown in Figures to Two initial tests on the adaptor have been carried out and include 1-W and 2-W heat dissipation Table shows the results of the model and measurements The first approximation results in steady-state temperatures that significantly deviate from the measurements Th − Te has been computed using a factor of 2.46 (12.78/5.20), which is too high Te − Ta has been computed using a factor of 0.48 (5.80/12.20), which is too low In addition, infrared measurements have been carried out on the adaptor for steady-state temperatures shown in Figure Figure Measured and computed temperatures for 1W dissipation heat transfer engineering Figure Measured and computed temperatures for 2W dissipation The approximate location of the hotspot is also shown in this figure The results illustrate that temperatures across the encasing surface are not constant, but vary from 38.0◦ C (= 311 K) to 24.5◦ C (= 297.5 K) The average of these two values is 31.3◦ C (= 304.3 K) From the figure, it can be determined that high temperature concentrations are found at the approximate location of the hotspot From the data in Table 2, several conclusions can be drawn We can see that t98% can be estimated within an accuracy of 17% t98% , computed with the model, appears to be a relatively good approximation with regard to the measured t98% In addition, the model predicts the effects of temperature changes by observing changes in the concept, in this case, a change in power dissipation The present results show that although measured and computed temperatures not correspond, the temperatures of the computations proportionally change with measured temperatures when dissipated power is changed from W to W This is a positive effect, which shows that the model accurately Figure Measured and computed temperatures for improved model results for 1W dissipation vol 31 no 2010 R STRIJK ET AL Table Measurement and computation results Variable R1 [K/W] R2 [K/W] R3 [K/W] R4 [K/W] C1 [J/K] C2 [J/K] C3 [J/K] t98% [s] Ti − Th [K] Th − Te [K] Te − Ta [K] Th − Ta [K] 1-W 2-W 1-W 2-W 1-W measurement measurement model model improved model — 5.20 — 12.20 — — — 3840 — 5.20 12.20 17.40 — 5.20 — 12.20 — — — 5280 — 10.50 22.60 33.1 0.20 12.00 0.79 5.81 47.91 0.08 64.00 4500 0.20 12.78 5.80 18.58 0.20 12.00 0.79 5.81 47.91 0.08 64.00 4500 0.40 25.56 11.61 37.17 0.20 7.19 0.79 5.81 47.91 0.08 64.00 3800 0.20 7.98 5.81 13.63 439 It is unlikely that the dissipated power q, the measured temperature Th , or the surface area Ah encompasses this problem because these values were controlled during the test setup A different explanation is that the thermal resistance R2 has been incorrectly approximated Because the air layer between the hotspot and inside encasing is relatively thin, on average, measuring 2.5 mm, the conductive heat transfer through the inside air should be taken into account If done, the following improvement will result: L= = 2.5 mm hk = predicts the effect of power changes on temperatures for a particular concept However, the results also show that temperature differences from a hotspot to the encasing and from the encasing to an ambient environment are incorrectly computed (Figures and 6) First, the measured Th − Te and Te − Ta values (in Figures 5, 6, and these are squares and dots, respectively) deviate a great deal from computed values However, the sum of the two computed and measured values of Th − Te and Te − Ta , namely, Th − Ta , does not deviate a great deal We can see that the model predicts the hotspot temperature with an accuracy of 8% to 21% The problem with the model is that the wrong computations for Ti − Th and Te − Ta are given The cause of this miscalculation is an incorrect estimation of thermal resistances R2 and R4 R2 has been computed too high, with a factor of 2.46 (12.78/5.20), resulting in a high estimation of Th − Te R4 has been computed too low, with a factor of 0.48 (5.80/12.20), resulting in a low estimation of Te − Ta (Table 2) The remainder of this section discusses the probable causes of both problems Figure Steady-state temperatures of the adaptor heat transfer engineering 44 − 35 − We − Wh − × thickness = 2 kair 24.0 × 10−3 ⇒ hk = = 9.6 W/m2 K L 2.5 × 10−3 Th − Ti = qR2 = = q (hc + hr + hk )Ah = 7.2 K (6.9 + 6.7 + 9.6)0.6 × 10−2 These calculations include the heat transfer coefficient of conduction, hk , with the inside air results in T of 7.98 K This comes far closer to the measured temperature difference of (5.20 K), compared to 12.78 K, derived from previous calculations Therefore, for this product, air conduction inside the product plays a significant role in determining the temperature difference between the encasing and the hotspot when air layers are 2.5 mm Further exploration is advised and should take into account more details of the hotspot and the encasing when calculating heat transfer coefficients and thermal resistance As can be seen in Figure 8, the temperature is not evenly distributed across the surface of the encasing A temperature difference T of 13.5 K between the lowest and highest temperatures is measured If the T between the maximum temperature and the average temperature is calculated, the following results are reached: 38.0◦ C – 31.25◦ C = 6.75◦ C = 6.75 K It is likely that because only one thermocouple was used, a higher than average temperature was measured on one hand, while the average temperature was calculated on the other The differences between measured and calculated temperatures are 12.20◦ C – 5.80◦ C = 6.40◦ C = 6.40 K, which comes close to T between the maximum and average temperatures In the previous section it was concluded that R4 is computed with a too low factor of 0.48 resulting in a low estimation of the temperature difference Te − Ta One option for correcting this factor includes increasing the total heat transfer coefficient This, however, would be a very unrealistic assumption It is unlikely that the convection and radiation heat transfer coefficients, hc in Eq (1) and hr in Eq (2), have been estimated low The heat transfer coefficient for convection has been estimated using a correlation for the Nusselt number of a vertical plate [12] This correlation already vol 31 no 2010 D DEL COL ET AL Figure Experimental and computed refrigerant pressure drop versus mass flow rate, 40–45◦ C water temperature Predictions by Cavallini et al [10, 11], Friedel [12, 13], and Ni˜no et al [14] Saturation temperature drop and heat flow rate are also depicted Bell–Delaware method is not valid for the tube bundle geometrical characteristics of the present prototype However, the disagreement between computational and experimental values in Figure can be explained by considering that the software is based on a simplified schematization of the heat transfer and pressure drop processes, using average values of heat transfer coefficient and frictional pressure gradient over the tube lengths If a step-by-step procedure is applied for the modeling of the heat exchanger, subdividing it into several segments, this may provide a better agreement between predictions and measurements, although it requires a higher computational effort The graphs in Figures and show the comparison between the experimental refrigerant pressure drop and the values obtained from the computational procedure using the three different correlations considered at the two inlet water temperature conditions The saturation temperature drop and the heat flow rate are also reported in the same graphs Predictions have been computed by the Cavallini et al correlation [10, 11], the classical Friedel correlation [12, 13], and the Ni˜no et al correlation [14] The Friedel equation has been developed for conventional tubes, while the others are given for minichannels The pressure drop model by Ni˜no is valid only for annular flows The Cavallini et al correlation [10, 11] is shown to predict very well the experimental data, while the other two equations considered overpredict the measured data It is very interesting to point out that the curve obtained by the Ni˜no correlation is parallel to the one obtained by the Friedel equation, and both display a slope higher than the experimental heat transfer engineering 513 Figure Experimental and computed refrigerant pressure drop versus mass flow rate, 30–35◦ C water temperature Predictions by Cavallini et al [10, 11], Friedel [12, 13], and Ni˜no et al [14] Saturation temperature drop and heat flow rate are also depicted data, while the curve obtained by the Cavallini et al [10, 11] model displays the correct slope In Figure the ratio of the refrigerant pressure drop predicted by the Cavallini et al [10, 11] model to the experimental data is reported: a good agreement is observed since the maximum absolute error is about 10% Figure Comparison between experimental and calculated refrigerant pressure drop Predictions by Cavallini et al [10, 11] vol 31 no 2010 514 D DEL COL ET AL Figure 10 Experimental and computed water pressure drop versus mass flow rate at 19◦ C Predictions obtained from the Bell–Delaware method [18, 19] With regard to the shell-side pressure drop, the graph in Figure 10 reports the comparison between the experimental water pressure drop obtained at 19◦ C and the values predicted by the Bell–Delaware method [18, 19] Shell-side pressure drop is overpredicted by the computational procedure by about 20% It should be remembered here that, because of the nonconventional bundle geometry and small tube diameter, the application of the Bell–Delaware method in the present case may be inappropriate CHARGE ESTIMATION An estimation of the charge required by the present heat exchanger is needed to estimate the possible advantages of operating HVAC equipment with this prototype The current industrial benchmark in charge minimization is given by plate heat exchangers; therefore, the prototype has been compared to a brazed plate heat exchanger (BPHE) available in the market providing about the same thermal performance when using propane In Table the comparison between the expected perforTable Comparison between prototype and BPHE expected performances when using propane, at 110 kW heat flow rate, 40–45◦ C water temperature, K subcooling Propane-side volume is also reported Parameter Prototype Inlet condensing temperature Outlet condensing temperature Propane pressure drop Water pressure drop Propane-side volume 50.3◦ C 49.7◦ C 21.3 kPa 11.5 kPa 2.9 L BPHE 49.7◦ C 49.7◦ C 1.5 kPa 40.3 kPa 8.4 L heat transfer engineering mance when using propane of the prototype and the benchmark BPHE condenser is reported; calculations have been made using the computational procedure described in the present paper in the case of the prototype and using a rating software provided by the BPHE manufacturer The propane side internal volume is 2.9 L in the case of the prototype and 8.4 L in the case of the brazed plate heat exchanger; hence, 65% reduction in terms of internal volume has been obtained However, the actual amount of refrigerant trapped in a device is a function of the void fraction, which depends on the flow conditions, which are very different in the minichannels and in the brazed plate condenser For this reason, a number of void fraction models have been used in order to relate two-phase density to quality; such values have been computed all along the prototype by means of the software simulating the heat transfer process In the case of the BPHE, instead, quality has been assumed to be linear between inlet and outlet Predictions of the total propane charge have been obtained from the following models: Rouhani [17] as published in the HEDH [18], Ni˜no et al (for annular flow) [20], Lockhart and Martinelli [21], CISE by Premoli et al [22], Zivi [23], and Baroczy [24, 25] Among the correlations considered, the Ni˜no et al model for annular flow [20] is the only one specifically developed for minichannels Furthermore, the homogeneous model, which considers that the vapor and liquid phases flow at the same velocity, has also been used; since, in general, vapor phase has higher velocity, the total charge given by this model can be considered as the bottom limit In the paper by Harms et al [1], the measured total charge in three unitary air conditioners has been compared against a computational procedure using a number of void fraction correlations According to their results, obtained at condenser subcooling values varying from K to 20 K, the Baroczy void fraction correlation [24, 25] gave the best overall agreement with measured data; however, good agreement is reported also when using the Zivi [23] and CISE [22] models, particularly at low subcooling Figure 11 reports the comparison between the condenser propane charge predicted in the case of the present prototype and in the case of the BPHE according to the different void fraction correlations considered Simulations have been performed considering 110 kW heat flow rate, 40–45◦ C water temperature, and K subcooling In the case of the minichannel shell-and-tube condenser, the expected charge varies from about 0.25 kg (Ni˜no et al and homogeneous model) to about 0.4 kg (Baroczy and Zivi) In the case of the plate condenser much higher values have been obtained, varying from about 0.8 kg (Ni˜no et al and homogeneous model) to 1.6 kg (Rouhani) Roughly speaking, the propane charge required by the prototype is expected to be less than half the quantity required by a traditional brazed plate condenser Interesting to say, both in the minichannel condenser and in the BPHE, similar charge predictions are provided by the three correlations that display the best agreement with experimental data in Harms et al [1], i.e., the Baroczy [24, 25], Zivi [23], vol 31 no 2010 D DEL COL ET AL 515 CONCLUSIONS Figure 11 Estimated total charge in the minichannel prototype and the BPHE condenser when using propane (110 kW, 40–45◦ C water temperature, K subcooling) and CISE [22] correlations According to these correlations, the propane charge is expected to be around 0.4 kg for the minichannel condenser and around 1.2 kg for the BPHE The value computed in the case of the prototype by the Ni˜no correlation for annular flow [20], which is the only one specifically developed for minichannels, is the lowest Hrnjak and Hoehne [4] compared the void fraction to quality curve given by the Ni˜no model to those given by traditional models, showing that a much higher void fraction is expected to be found in a minichannel as compared to a traditional round tube at the same quality This aspect could represent another advantage of using minichannels in heat exchangers to minimize the charge Regarding the charge predictions in the case of the BPHE, it should be noticed that the void fraction correlations considered here have been empirically developed for round tubes, while the flow conditions and the cross sections in a plate heat exchanger (PHE) are very different from those of a pipe Therefore, the predictions reported here for the BPHE are only intended to asses the big advantage of the minichannels with regard to the charge, since the application of those void fraction correlations to PHEs may be inappropriate The mass flux in the BPHE when using propane is very low (i.e., G = 20 kg/(m2 s)) Besides, the void fraction correlations may require the definition of a channel diameter, which affects the value of the void fraction itself Here, the hydraulic diameter of the channel between two plates has been used in the correlations The high scattering among the charge values computed in the case of the BPHE is essentially related to the facts just described Furthermore, the void fraction models are based on a particular flow regime, while in the condenser both intermittent and annular flow regimes are expected to occur For instance, the Ni˜no correlation, which has been developed for annular flow, has been applied for the entire condensation process, and this is why the charge computed with this correlation in the case of the BPHE is lower than the one predicted by the homogeneous model and thus not realistic heat transfer engineering In this paper, the design of an innovative 100kW capacity shell-and-tube condenser to be used with propane and employing mm ID copper minichannels is presented In order to reduce the refrigerant side internal volume, the propane flows inside the tubes and the water flows on the shell side Experimental data of heat transfer and pressure drop performance are reported The measurements have been obtained using R22, which displays a temperature versus pressure saturation curve and volumetric capacity values pretty close to the ones of propane The data have also been compared against a computational procedure based on a simplified model of the heat transfer and pressure drop processes in shell-and-tube heat exchangers The computed thermal performance of the condenser is higher than the experimental one when using R22, and this may be due to the simplified schematization of the heat exchanger; for the refrigerant pressure drop a good agreement is observed since the maximum absolute error is about 10% Shell-side pressure drop is overpredicted by the computational procedure by about 20% The refrigerant charge has been computed by means of the described software and by adopting different void fraction correlations, finding that the expected inventory is between 0.25 kg and 0.4 kg when using propane This amount is expected to be less than half the quantity required by a conventional brazed plate condenser providing the same heat flow rate NOMENCLATURE D G p TCALC TEXP p TEXP internal tube diameter, m specific mass flow rate, kg/(m−2 s) pressure, kPa calculated saturation temperature, ◦ C experimental saturation temperature, ◦ C pressure drop, kPa average experimental temperature difference, K Greek Symbols saturated liquid density, kg/m3 saturated vapor density, kg/m3 ρL ρV Subscripts CALC EXP calculated experimental REFERENCES [1] Harms, T M., Groll, E A., and Braun J E., Accurate Charge Inventory Modeling for Unitary Air Conditioners, HVAC&R Research, vol 9, pp 55–78, 2003 vol 31 no 2010 516 D DEL COL ET AL [2] Palm, B., Refrigeration Systems With Minimum Charge of Refrigerant, Applied Thermal Engineering, vol 27, pp 1693–1701, 2007 [3] Fernando, P., Palm, B., Lundqvist, P., and Granryd, E., Propane Heat Pump With Low Refrigerant Charge: Design and Laboratory Tests, International Journal of Refrigeration, vol 27, pp 761– 773, 2004 [4] Hrnjak, P S., and Hoehne, M R., Charge Minimization in Systems and Components Using Hydrocarbons as a Refrigerant, ACRC TR-224, University of Illinois at Urbana-Champaign, 2004 [5] Cavallini, A., Da Riva, E., Del Col, D., and Mantovan, M., Design of an Innovative Low Charge Heat Pump Using Propane, Proc Climamed 2007 Energy, Climate and Indoor Comfort in Mediterranean Countries, Genova, Italy, 2007 [6] Pelletier, O., and Palm, B., Performance of Plate Heat Exchangers and Compressor in a Domestic Heat Pump Using Propane, Proc IIF/IIR Conf Applications for Natural Refrigerants, Aarhus, Denmark, pp 497–505, 1996 [7] Corber´an, J M., Urchuegu´ıa, J., Gonz´alvez, J., Setaro, T., Boccardi, G., and Palm, B., Two Phase Heat Transfer in Brazed Plate Heat Exchangers, Evaporators and Condensers for R22 and Propane, Proc 3rd European Thermal Sciences Conference, Heidelberg, Germany, 10–13 September, 2000 pp 1193–1198, 2000 [8] National Institute of Standard and Technology, Refprop Version 7.0, Boulder CO, 2002 [9] Cavallini, A., Del Col, D., Doretti, L., Matkovic, M., Rossetto, L., and Zillio, C., Condensation in Horizontal Smooth Tubes: A New Heat Transfer Model for Heat Exchanger Design, Heat Transfer Engineering, vol 27, pp 31–38, 2006 [10] Cavallini, A., Rossetto, L., Matkovic, M., and Del Col, D., A model for frictional pressure drop during vapour-liquid flow in minichannels, Proc IIR International Conference Thermophysical Properties and Transfer Processes of Refrigerants, Vicenza, Italy, pp 71–78, 2005 [11] Cavallini, A., Del Col, D., Matkovic M., and Rossetto, L., Frictional Pressure Drop During Vapor–Liquid Flow in Minichannels: Modeling and Experimental Evaluation, International Journal of Heat and Fluid Flow, vol 30, pp 131–139, 2009 [12] Friedel, L., Improved Friction Pressure Drop Correlations for Horizontal and Vertical Two-Phase Pipe Flow, Proc Europ TwoPhase Flow Group Meet., Ispra, Paper E2, 1979 [13] Friedel, L., Pressure Drop During Gas/Vapor-Liquid Flow in Pipes, International Chemical Engineering, vol 20, pp 352–367, 1980 [14] Ni˜no, V G., Jassim, E W., Hrnjak, P S., and Newell, T A., Flow-Regime Based Model for Pressure Drop Predictions in Microchannels, HVAC&R Res., vol 12, pp 17–34, 2006 [15] McAdams, W H., Heat Transmission, 2nd ed., McGraw-Hill, New York, 1942 [16] Blasius, H., Das Ahnlichkeitsgesetz bei reibungsvorgangen, Physik Zeitschr., vol XII, pp 1175–1177, 1911 [17] Rouhani, S Z., Subcooled Void Fraction, AB Atomenergi Sweden, Internal Rep AE-RTV841, 1969 [18] Taborek, J., Shell-and-Tube Heat Exchangers: Single Phase Flow, in Heat Exchanger Design Handbook, Hemisphere Publishing, New York, chap 3.3, 1983 [19] Bell, K J., Final Report of The Cooperative Research Program on Shell-and-Tube Heat Exchangers, University of Delaware Engineering Experimental Station Bulletin 5, 1963 heat transfer engineering [20] Ni˜no, V G., Hrnjak, P S., and Newell, T A., Characteristics of Two-Phase Flow in Microchannels, Ph.D Thesis, ACRC TR-202, University of Illinois at Urbana-Champaign, 2002 [21] Lockhart, R W., and Martinelli, R C., Proposed Correlation of Data for Isothermal Two-Phase, Two-Component Flow in Pipes, Chemical Engineering Progress, vol 45, pp 39–48, 1949 [22] Premoli, A., Francesco, D., and Prina, A., An Empirical Correlation for Evaluating Two Phase Mixture Density Under Adiabatic Conditions, Proc European Two-Phase Flow Group Meet., Milan, Italy, 1970 [23] Zivi, S M., Estimation of Steady-State Steam Void-Fraction by Means of the Principle of Minimum Entropy Production, ASME reprint 63-HT-16,6th National Heat Transfer Conf., AIChEASME, Boston, 1963 [24] Baroczy, C J., Correlation of Liquid Fraction in Two-Phase Flow With Application to Liquid Metals, NAA-SR-8171, 1963 [25] Butterworth, D., A Comparison of Some Void-Fraction Relationships for Co-Current Gas-Liquid Flow, International Journal of Multiphase Flow, vol 1, pp 845–850, 1975 Davide Del Col took his Ph.D at University of Padova, Italy, and was visiting scholar at Pennsylvania State University At present, he is assistant professor in the Faculty of Engineering of the University of Padova, Italy, where he teaches fundamentals of thermodynamics and heat transfer He is a member of the Commission B1 of IIR and a member of the ASME K-13 Committee His research activity deals with heat transfer during condensation and vaporization of new refrigerants, design of condensers and evaporators, and microscale heat transfer He is also active in the field of heat pumps and solar energy conversion He is the co-author of one book and more than 100 papers, most of them published in international journals or presented at international conferences Alberto Cavallini is full professor of energy science at the Engineering Faculty of the University of Padova, Italy He has been director of the Department of Fisica Tecnica of the University of Padova, and of the Refrigeration Institute of the Italian Research Council He is the former president of the Scientific Council of the International Institute of Refrigeration of Paris, an ASHRAE fellow, and former PResident of AICARR, the Italian Society of Air Conditioning, Heating and Refrigerating Engineers His research activity concerns the field of energy management, heat transfer, refrigeration, and air conditioning, with particular reference to problems related to the refrigerant substitution issue He is the author or co-author of about 220 scientific and technical publications and of five textbooks Enrico Da Riva got his Ph.D at the Department of Fisica Tecnica, University of Padova, Italy, in 2009 and was visiting scholar at the Purdue University, Indiana, USA Currently his main research topics refer to heat pump systems using hydrocarbons as refrigerants and computational fluid dynamic of two-phase flow and heat transfer by means of the VOF method vol 31 no 2010 D DEL COL ET AL Simone Mancin took his master’s degree in mechanical engineering at the University of Padova, Italy At the Department of Fisica Tecnica of the same University he gained also his Ph.D His research activities are focused on experimental and analytical twophase and single-phase advanced heat transfer with reference to compact heat exchangers for electronics cooling applications heat transfer engineering 517 Giuseppe Censi obtained his master’s degree in mechanical engineering in 1999 and the Ph.D title in energy science in 2002 He worked at the Dipartimento di Fisica Tecnica, Padova, Italy, studying experimentally and theoretically the two-phase heat transfer processes of refrigerants The main focus of his experimental work was on the features of new fluids and new heat transfer ducts and surfaces and the development of two-phase models for heat transfer, flow categories, and pressure gradients He is now R&D Department Manager at Onda SpA (Lonigo, Italy), a heat exchanger manufacturer, where he coordinates the experimental laboratory activities and deals with heat exchanger modeling and design vol 31 no 2010 Heat Transfer Engineering, 31(6):518–526, 2010 Copyright C Taylor and Francis Group, LLC ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457630903412161 Experimental Investigation of the Effect of Tube-to-Tube Porous Medium Interconnectors on the Thermohydraulics of Confined Tube Banks P V RAMANA, A NARASIMHAN, and D CHATTERJEE Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, India This experimental study investigates the effect of tube-to-tube copper porous interconnectors on the thermohydraulic performance of an in-line and staggered confined tube bank The porous medium, having a transverse thickness equal to that of the diameter of the tube (9 mm), connects longitudinally six successive tubes kept as in-line and staggered arrangements with a square pitch of 2.0 The tubes are subjected to a constant and uniform heat flux and are cooled by forced convection under laminar-transition flow range (200 < Reynolds number < 1500) using air with a Prandtl number of 0.71 as cooling fluid Experimental data presented here establish that by introducing tube-to-tube porous medium interconnectors for the maximum Reynolds number tested here, a reduction in the pressure drop by 18% is observed in the in-line configuration while the heat transfer is enhanced by 100% in the staggered configuration, when compared to their respective configurations without the porous medium Defining an overall energy gain as the ratio of the heat transfer enhancement due to the presence of the porous inserts to the pressure drop incurred, it is seen that fixing the porous inserts in the in-line configuration is advantageous INTRODUCTION Heat exchangers that facilitate exchange of heat between a hot and a cold fluid are widely used in industrial applications They usually employ tube-bank configurations in single or multiple passes To enhance the heat transfer in such heat exchanger configurations, several methods have been followed Use of porous materials made as suitable geometries like fins, metal foam inserts, and as packed beds of sintered media has been extensively investigated in the recent decade The related research literature until year 2000 has been collected and reviewed in [1] A literature survey for the subsequent recent years, presented here culling primarily the experimental investigations, also indicates the continued prominence of use of porous medium as a heat transfer enhancement option Address correspondence to Dr Arunn Narasimhan, Heat Transfer and Thermal Power Laboratory, Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai–600036, India E-mail: arunn@iitm.ac.in Experiments comparing heat sinks with and without metal foam porous extensions for cooling electronics were reported in [2], establishing the superior thermal performance of metal foam-enhanced heat sinks over conventional unfinned heat sinks That work also suggested the existence of an optimum number of such porous fins beyond which the enhancement in heat transfer, due to increased surface area, is offset by the retarding effect of overlapping thermal boundary layers Using experiments and numerical analysis reported in [3] and [4], it has been shown that in a pipe higher heat transfer rates can be achieved using porous inserts at the expense of a reasonable pressure drop Also, compared to fully filling the pipe, partially filling it with the porous material pipe had resulted in comparable Nusselt numbers with a gain in the pressure drop incurred In a related work [5], carbon foam porous medium and aluminum fins were used as attachments in vertical pipes and the experimental investigation showed heat transfer enhancement for both cases to be significant when compared to the plain pipe The aluminum fins performed better than the carbon foam in enhancing the heat transfer but also incurred a higher pressure drop 518 P V RAMANA ET AL 519 Figure Test domain considered for study: (a) in-line, (b) staggered In another recent study, Yucel and Guven [6], laminar forcedconvection cooling of heat-generating obstacles mounted on adiabatic walls in a parallel-plate channel was investigated using numerical simulations It was reported that the mean Nusselt number for the configuration increases with increasing the thickness of the porous layer In another experimental study, Tzeng et al [7], channels filled with sintered porous beads with and without cross baffles were studied, reporting the local and average heat transfer characteristics under asymmetric heating The study found that for channel Re ≈ 1000, with staggered periodic baffles on both walls the heat transfer enhancement was 20 to 30% more than that without the baffles Faghri and Rao [8] numerically investigated and found that by introducing solid fins in the longitudinal direction of flow, heat transfer enhancement is negligible In contrast to this, investigations reported recently by Narasimhan and coworkers [9, 10] presented numerical simulations capturing the thermohydraulic performance of in-line tube banks with tube-to-tube porous inserts under laminar flow (0 < Re < 100) and also studied the effect of variable spatial permeability of such porous inserts on tube bank performance Certain tube bank configurations with the porous inserts were shown to offer lesser pressure drop than that without the porous inserts Heat transfer enhancement was predicted uniformly for all such in-line tube bank configurations with porous connectors In a numerical study, Layeghi [11], forced convection heat transfer from a staggered tube bundle with various lowconductivity wooden porous media inserts at 100 < Re < 300 and for Pr = 0.7 showed that the presence of wooden porous media can augment the heat transfer from a tube bundle significantly but also increases the pressure drop heat transfer engineering Figure (a) Schematic of experimental setup (b) Picture of in-line arrangement with thermocouples before and after brazing the tube-to-tube porous interconnectors No experimental investigation is found for the staggered tube bank arrangement with porous inserts Also, the use of tube-totube porous connectors to reduce pressure drop in the in-line tube bank arrangement as suggested in [9] and [10] requires experimental substantiation The present experimental work investigates the effect of tube-to-tube porous interconnectors on the thermohydraulic performance of both in-line and staggered tube bank arrangements confined in a rectangular channel (see Figure 1) EXPERIMENTAL SETUP AND INSTRUMENTATION Figures 2a and 2b show respectively the schematic of the heat transfer experimental setup and the test domain fitted with tube heaters with and without tube-to-tube porous medium vol 31 no 2010 520 P V RAMANA ET AL interconnectors As shown in Figure 1, the porous medium of transverse thickness t = D connects six successive tubes (D = mm) along the flow direction having square pitch of XT = XL = 2.0 Such a tube bank configuration can be considered to represent a near-compact heat exchanger configuration (NCHX, surface to volume ratio α = 100 to 300 m2 /m3 ) as shown in [12] Rod heaters, having mm diameter and 50 mm length, are placed inside the hollow tubes to simulate the crossflow hot fluid in a NCHX, generating constant and uniform heat flux along their circumference A regulated DC power supply (Aplab, model LD3205) was used to maintain uniform heat input to the tube heaters The electrical power input to the heater was calculated from the measured current and voltage across them using digital multimeter All heater surface temperatures were measured in separate steady-state experiments and the maximum surface temperature differences were checked to be less than 2◦ C to ensure uniformity of surface heat flux This configuration is placed centrally inside an adiabatic rectangular test section (part in Figure 2a) having a size of 150 mm × 50 mm × 30 mm with the tubes exchanging heat under steady state with cross-flowing cooling air under the laminartransition flow range based on the channel hydraulic diameterbased Reynolds number (800 < ReDuct < 6000) The bottom, top, and side walls of the housing are made of an insulating material called Cynthiana (k = 0.04 W/m-K) to ensure adiabatic conditions Further details of the experimental apparatus are as follows: The setup (as shown in Figure 2a) consists of a reciprocating air compressor, desiccant air drier, air filter, pressure regulator, heat transfer test section, data acquisition system, orifice plate, differential pressure transmitter, micro manometers (Furness Controls), thermocouples, and an electrical power input and measuring device Compressed dry air is used as cooling fluid For data acquisition a data logger (Agilent 34970A Bench Link) with 22 + 22 channel multiplexers is used All the measuring parameters are connected to the data logger, and this is interfaced with the computer for monitoring and recording them with respect to time A heavy-duty reciprocating compressor (Kirloskar, model TC 500, capacity to 600 kPa) provides a continuous discharge of compressed air This compressed air is cleaned of contaminants like dust, oil, water, and hydrocarbons by a regenerative-type compressed air drier, (Sanpar, model SHD AA 040, capacity to 15 cfm), which consists of a prefilter, a drier unit, and an after filter Pressure regulator connected next to the drier regulates the pressure from bar to bar throughout the experiments The temperature was monitored and recorded for all tube surfaces by placing four T-type thermocouples on each tube heater as shown in Figure The thermocouple wires of each tube heater were taken out, two from each end of the tube, along with supply terminals The thermocouple wires are threaded through a 50 mm long ceramic sleeve, made up of electrically insulating aluminum oxide The entire heat transfer test section is wrapped with ceramic wool to minimize the heat loss from the test section The inlet air temperature was measured by two heat transfer engineering Figure surface Picture and schematic of thermocouple arrangement on tube heater T-type thermocouples fixed in the crosswise direction at the inlet of the duct Four thermocouples were located on a traverse arrangement, which is kept at the exit of the duct to measure the bulk exit temperature of the fluid The flow rate, input power, and inlet fluid temperature were fixed for each heat transfer test All thermocouples are calibrated before fixing them into the duct at exit T-type thermocouples are used to record the tube wall temperatures The ambient and inlet temperatures are measured by a separate T-type thermocouple kept inside the test section All thermocouples are connected to a PC-interfaced data acquisition system, through compensating wires EXPERIMENTAL PROCEDURE Initially, hydraulic and forced convection experiments were conducted for the row of six cylinders kept in in-line and staggered arrangements inside the test section without the porous medium interconnectors The longitudinal steady-state pressure drop across the test section was measured for several flow rates in the tube diameter-based Re range of 200 < ReD < 1500 Corresponding heat transfer experiments were also conducted to determine the steady state overall Nusselt number (Nu) The ReD and Nu are defined as ReD = Nu = ρUD µ (1) qD AN T¯ w − T¯ bexit kf (2) where all the terminology involved is explained in the Nomenclature section vol 31 no 2010 P V RAMANA ET AL 521 Figure Variation of longitudinal pressure drop with ReD for in-line arrangement without PM interconnectors mated by following the procedure [13] given next: n Figure Photograph of the test section with traverse arrangement and grid for bulk exit temperature measurement A stabilized DC power source was used to heat the tube heaters Constant and uniform 20-W energy was supplied to all six tube heaters by regulating the voltage and current from the DC power source Steady state was reached when the deviations of the tube wall temperatures and the inlet and outlet temperatures were all within ±0.1◦ C for a span of 10 The system typically took to h to reach this steady state, at which point the wall and fluid exit temperatures were measured The mean of the temperatures of the six tube walls (i.e., 24 on all tubes) were used to determine T¯W in Eq (2) The exit bulk temperature T¯b exit of the fluid was measured using a traversing arrangement fitted with thermocouples as shown in Figure Four T-type thermocouples were fixed to the stem at mm distance in the vertical direction The traverse can be moved in both x and y directions As shown in Figure 4, this traverse arrangement was slid using a Vernier scale for five horizontal locations, measuring the temperature in total at 20 locations covering the entire test section exit The corresponding local exit velocities were measured using a pitot type velocity probe Using these data the mass-averaged exit bulk temperature T¯ b exit was calculated using the equation T¯ b exit = UA T(x, y)u(x, y)dA wR = ± i=1 ∂R ∂xi 1/2 w2xi (4) where x stands for the independent variable and wx is the uncertainty associated with x Using this procedure, the uncertainty in the average Nusselt number, pressure drop, and Reynolds number is calculated as ±4.9%, ±3.8%, and ±2.2%, respectively Following the experimental procedure described earlier, the experimental setup was verified for both hydraulic and heat transfer measurements for in-line arrangement of tubes by comparing the obtained pressure drop and Nusselt number data with the established tube bank correlations [14] These experimental setup verification results are presented in Figures and 6, wherein the obtained data is seen to agree well with the correlations in [14] In Figure 5, the pressure drop obtained through experiments is lower when compared to that of the pressure drop estimated from correlation using the average velocity at minimum cross-section area for the in-line tube bank (which is higher than the average velocity for the confined tube banks in the experiments) The pressure drop estimated using the same (3) This procedure was repeated for each flow rate, determining T¯ b exit with fair accuracy The uncertainties in the primary measured quantities are obtained from the calibration of the instruments or the uncertainty prescribed by the manufacturer The uncertainties in the measured physical quantities are 0.02 mm for linear dimensions, ±0.3◦ C for temperature, and ±0.25% for pressure measurement The uncertainty, wR ,in the dependent variable, R, is estiheat transfer engineering Figure Variation of Nu with ReD for in-line arrangement without PM interconnectors vol 31 no 2010 522 P V RAMANA ET AL Figure Longitudinal pressure drop versus average velocity across channel filled with the porous medium to be used as tube-to-tube interconnectors correlation with the average velocity calculated for the confined tube bank is lower than the experimental results, as the pressure drop from the duct walls is not included in the correlation Next in the sequence of experiments is the determination of the hydraulic properties of the porous medium (i.e., its permeability and form coefficient) that is to be used as tube-to-tube interconnectors Separate hydraulic experiments were conducted in a separate rectangular channel filled with the copper mesh porous medium used in this study, determining the longitudinal pressure drop for several flow rates in the identical range of ReDuct These data were curve-fit using the global Hazen– Dupuit–Darcy (HDD) porous medium model, P µ = U + ρCU2 L K (5) Figure shows the experimental results of longitudinal pressure drop versus channel average cross-sectional velocity for copper mesh porous medium (ks = 387 W/m-K) tested in the laminar–turbulent flow regime With the thermophysical properties of the fluid (air) being known, the permeability K and the form coefficient C of the porous medium were determined from the curve-fits coefficients as K = 4.183 × 10−07 m2 , C = Figure Effect of porous inserts on longitudinal pressure drop with ReD in-line arrangement heat transfer engineering Figure Effect of porous inserts on longitudinal pressure drop with ReD for staggered arrangement 43.5836 m−1 , with uncertainties UK /K = ±6.9%, UC /C = ± 3.7% The volumetric porosity of the mesh was determined as ¯ = 0.58 using standard immersion technique φ The in-line and staggered arrangement shown were brazed with this porous medium as shown in Figure 2b, resulting in a final configuration as shown in the schematic of Figure Hydraulic and heat transfer experiments following a similar procedure as explained earlier were conducted for these configurations RESULTS AND DISCUSSION Figure shows the comparison of longitudinal pressure drop for in-line tube arrangement with and without the tubeto-tube porous medium interconnectors As expected for the range of ReD , the pressure-drop increase with increasing ReD is quadratic Interestingly, it can also be observed that the inline configuration with the porous medium interconnectors incurs less pressure drop when compared with the plain in-line configuration This reduction can be attributed to the absence of Figure 10 Variation of cylinder surface temperature for in-line arrangement without porous medium interconnectors vol 31 no 2010 P V RAMANA ET AL Figure 11 Variation of cylinder surface temperature for in-line arrangement with the porous medium interconnectors Figure 12 Variation of cylinder surface temperature for staggered arrangement with the porous medium interconnectors Figure 13 Variation of cylinder surface temperature for staggered arrangement with the porous medium interconnectors heat transfer engineering 523 Figure 14 Effect of porous medium interconnectors on the Nu for in-line configuration the pressure-drop penalty originally caused by the recirculation and vortices behind individual tubes in the in-line configuration without the porous medium This observation was also reported earlier in [9] for a numerical simulation of similar configuration in laminar flow There is a maximum of 18% pressure drop reduction observed for the range of flow considered here For staggered arrangement this advantage doesn’t exist, as observed from the experimental data shown in Figure The pressure drop for the staggered configuration with the porous medium interconnector in place is systematically higher than its corresponding plain staggered configuration Figures 10 and 11 report the variation of the average tube surface temperature along the flow direction for in-line arrangement without and with the porous medium interconnectors As expected, the forced convection effect is less for lower ReD values, resulting in higher temperatures for all the cylinders, irrespective of the presence of porous medium interconnectors Further, by comparing Figures 10 and 11 it can be observed that only a marginal temperature reduction is observed for higher ReD values in the presence of the tube-to-tube porous medium interconnectors It is possible that for higher ReD values, due Figure 15 Effect of porous medium interconnectors on the Nu for staggered configuration vol 31 no 2010 524 P V RAMANA ET AL Figure 16 Comparison of longitudinal pressure drop with and without porous medium interconnectors for in-line and staggered arrangements to high flow rate, the flow is symmetric about the in-line arrangement with the PM in place This arrangement could lead to a stagnation of air inside the PM interconnectors, effectively reducing their convecting capability to only a conduction possibility limited by the insulating effect of stagnant air This results in only the convection by the air flow at the top and bottom as the dominant mechanism of (heat removal) cooling the tubes This convection effect is comparable to the convection possible even without the presence of the PM interconnectors, resulting in only a marginal heat transfer enhancement Figures 12 and 13 plot the average temperatures of six cylinders kept in staggered arrangement without and with the tubeto-tube porous medium interconnectors Again, the strength of forced convection is correctly predicted by the uniformly decreasing temperatures as ReD increases, irrespective of the presence of the porous medium interconnectors Further, it can be observed that the presence of the porous medium interconnectors has reduced the temperature of the tubes by about 10◦ C for the range of ReD reported This average temperature reduction is brought about by the marked reduction in the temperatures of cylinders and 4, in the presence of the porous medium Due to the periodic positioning of the inclined porous medium interconnector, cylinders and experience a possible strong recirculatory and symmetric forced convection cooling on either of their sides Even when the cooling fluid becomes progressively hotter Figure 17 Comparison of Nu with and without porous medium interconnectors for in-line and staggered arrangements heat transfer engineering as it flows over cylinders and 4, the recirculation provides better convection This possible cooling effect is evidently absent for the rest of the cylinders 1, 2, 5, and Further, in the case of cylinders and 2, owing to their staggered location, it is possible that a higher percentage of flow that approaches cylinder is colder than what crosses over cylinder 1, leading to cylinder registering systematically a lower temperature than cylinder for all flow rates The lack of the recirculation shroud downstream results in cylinders and also registering temperatures uniformly higher than cylinders and 4; from the diagonal symmetry of the entire configuration it can be expected that cylinder would register a slightly higher temperature than cylinder Using Eq (2) and the recorded temperatures in Figures 10 through 13, the Nu values for the in-line and staggered configurations without and with the porous medium interconnectors are calculated and plotted in Figures 14 and 15 as a function of ReD No significant heat transfer enhancement is observed in Figure 14 for the in-line case due to the presence of the porous medium interconnectors However, as observed from Figure 15, there is at least a 70% heat transfer enhancement for the staggered case, when the porous medium interconnectors are used Summarizing the hydraulic and heat transfer experimental measurements in Figures 10 and 11 and 14 and 15, respectively, a comparison is shown in Figures 16 and 17 Since the measurements for Figures 10, 11, 14, and 15 were done for different ReD values—although within the range reported—suitable curve fits of the reported data were used to determine the ratios reported in Figures 16 and 17 These curve fits predict the experimental data within 5% deviation, and hence, the comparison values of Figures 16 and 17 also retain this 5% uncertainty It is evident from Figure 16 that the presence of the porous medium interconnector reduces the pressure drop for the in-line case beyond ReD ≈ 800, while in the staggered arrangement it uniformly increases the pressure drop by about three times From Figure 17 the heat transfer enhancement due to the presence of the porous medium interconnector is only marginal in the in-line configuration, while for the staggered case a 70% increase is registered CONCLUSIONS This experimental study investigates the effect of tube-totube copper porous interconnectors on the thermohydraulic performance of an in-line and staggered confined tube bank The tubes are subjected to a constant and uniform heat flux and are cooled by forced convection under laminar-transition flow range (200 < ReD < 1500) using air as cooling fluid The presence of the porous medium interconnector reduces the pressure drop for the in-line case beyond ReD ≈ 800 The recirculation and vortices in the tube gaps that contribute to an additional pressure drop are curtailed by the presence of the PM interconnectors, resulting in this pressure drop gain for the in-line arrangement with the Pm interconnectors However, in the staggered arrangement the presence of the porous medium interconnector uniformly increases the pressure drop vol 31 no 2010 P V RAMANA ET AL by about three times when compared to the corresponding plain staggered arrangement The heat transfer enhancement due to the presence of the porous medium interconnector is only marginal in the in-line configuration, while for the staggered case a uniform 70% increase is registered for the entire range of ReD tested Additional recirculation-driven convection effects around the middle cylinders are expected to be the primary reason for this heat transfer enhancement NOMENCLATURE A Ac cP C D Dh k K L ˙ m N Nu p P PM q ReD ReDuct SL ST t T T¯ U XL XT surface area of the tube, m2 cross sectional area of the duct, m2 specific heat, J/kg-K form coefficient, m−1 diameter of the tube, m hydraulic diameter of the duct, m thermal conductivity, W/m-K permeability, m2 length of the test domain, m mass flow rate of air, kg/s number of rows in tube bank average Nusselt number, Eq (2) pressure, Pa pressure drop across tube bank, Pa porous medium total heat transfer, W Reynolds number based on tube diameter, UD/ν Reynolds number based on hydraulic diameter of the duct, UDh /ν cylinder pitch in direction of flow, m cylinder pitch in normal to flow, m porous medium thickness, m temperature, ◦ C average temperature, ◦ C average flow velocity, m/s dimensionless cylinder pitch in direction of flow, SL /D dimensionless cylinder pitch in normal to flow, ST /D Greek Symbols α µ ν φ ρ thermal diffusivity, m2 dynamic viscosity, N-s/ m2 kinematic viscosity, m2 /s porosity density, kg/m3 REFERENCES [1] Lage, J L., and Narasimhan, A., Porous Media Enhanced Forced Convection: Fundamentals and Applications, in Handbook of Porous Media, Ed K Vafai, Marcel Dekker, New York, pp 357– 394, 2000 [2] Bhattacharya, A., and Mahajan, R L., Metal Foam and Finned Metal Foam Heat Sinks for Electronics Cooling in BuoyancyInduced Convection, ASME Journal of Electronic Packaging, vol 128, pp 259–266, 2006 [3] Bogdan, I P., and Mohamad, A A., Experimental Investigation of the Potential of Metallic Porous Inserts in Enhancing Forced Convective Heat Transfer, ASME Journal of Heat Transfer, vol 126, pp 540–545, 2004 [4] Bogdan, I P., and Mohamad, A A., An Experimental and Numerical Study on Heat Transfer Enhancement for Gas Heat Exchanger Fitted with Porous Media, International Journal of Heat and Mass Transfer, vol 47, pp 4939–4952, 2004 [5] Jamin, Y L., and Mohamad, A A., Enhanced Heat Transfer Using Porous Carbon Foam in Cross Flow—Part I: Forced Convection, ASME Journal of Heat Transfer, vol 129, pp 735–742, 2007 [6] Yucel, N., and Guven, R T., Forced-Convection Cooling Enhancement of Heated Elements in Parallel-Plate Channels Using Porous Inserts, Numerical Heat Transfer, Part A: Applications, vol 51, pp 293–312, 2007 [7] Tzeng, S.-C Jeng, T.-M., and Wang, Y.-C., Experimental study of forced convection in asymmetrically heated sintered porous channels with/without periodic baffles, International Journal of Heat and Mass Transfer, vol 49, pp 78–88, 2006 [8] Faghri, M., and Rao, N., Numerical Computation of Flow and Heat Transfer in Finned and Unfinned Tube Banks, International Journal of Heat and Mass Transfer, vol 30, pp 363–372, 1987 [9] Narasimhan, A., and Sumithra Raju, K., Effect of Variable Permeability Porous Medium Inter-Connectors on Thermo-Hydraulics of Heat Exchanger Modeled as Porous Media, International Journal of Heat and Mass Transfer, vol 50, pp 4052–4062, 2007 [10] Sumithra Raju, K., and Narasimhan, A., Porous Medium InterConnector Effects on the Thermo-Hydraulics of Near-Compact Heat Exchangers Treated as Porous Media, ASME Journal of Heat Transfer, vol 129, pp 273–281, 2007 [11] Layeghi, M., Numerical Analysis of Wooden Porous Media Effects on Heat Transfer From a Staggered Tube Bundle, ASME Journal of Heat Transfer, vol 130, pp 014501-1–014501-6, 2008 [12] Wilson, L., Narasimhan, A., and Venkateshan, S P., Turbulent Flow Hydrodynamic Experiments in Near-Compact Heat Exchanger Models with Aligned Tubes, ASME Journal of Fluids Engineering, vol 126, pp 990–996, 2004 [13] Zukauskas, A.A., Heat Transfer from Tubes in Cross Flow, Advances in Heat Transfer, vol 8, pp 93–169, 1972 [14] Holman, J P., Experimental Methods for Engineers, 7th ed., McGraw-Hill, New York, 2001 P V Ramana is a Ph.D student at the Heat Transfer and Thermal Power Laboratory, Department of Mechanical Engineering, Indian Institute of Technology Madras (IITM), Chennai, India He received his M.Tech in 2002 from IITM Presently, he is investigating hydrodynamics and heat transfer enhancement in heat exchanger models using porous inserts Subscripts b f in s w 525 exit bulk mean at exit fluid property inlet solid property wall heat transfer engineering vol 31 no 2010 526 P V RAMANA ET AL Arunn Narasimhan is an assistant professor at the Heat Transfer and Thermal Power Laboratory, Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, India He received his Ph.D in 2002 from Southern Methodist University, Dallas, TX His research interests involve modeling hydrodynamics and heat transport in porous media, phase change material applications, manufacturing processes in microlithography, and bio-heat transfer heat transfer engineering Dhiman Chatterjee is an assistant professor at the Hydroturbomachines Laboratory, Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, India He received his Ph.D in 2003 from the Indian Institute of Science, Bangalore, India His main areas of research are cavitation, micro-scale fluid flow, and multiphase flows vol 31 no 2010 526 P V RAMANA ET AL Arunn Narasimhan is an assistant professor at the Heat Transfer and Thermal Power Laboratory, Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, India He received his Ph.D in 2002 from Southern Methodist University, Dallas, TX His research interests involve modeling hydrodynamics and heat transport in porous media, phase change material applications, manufacturing processes in microlithography, and bio-heat transfer heat transfer engineering Dhiman Chatterjee is an assistant professor at the Hydroturbomachines Laboratory, Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, India He received his Ph.D in 2003 from the Indian Institute of Science, Bangalore, India His main areas of research are cavitation, micro-scale fluid flow, and multiphase flows vol 31 no 2010