Heat transfer engineering an international journal, tập 31, số 1, 2010 1 2

Heat Transfer Engineering, 31(1):1–2, 2010 Copyright C Taylor and Francis Group, LLC ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457630903263176 editorial The New 3rd Edition of the ALPEMA Plate-Fin Heat Exchanger Standards JOHN R THOME Laboratory of Heat and Mass Transfer, Ecole Polytechnique F´ed´erale de Lausanne, Lausanne, Switzerland As the Chairman of ALPEMA (Aluminum Plate-Fin Heat Exchanger Manufacturers’ Association) since May 2008, I wish to announce the new third edition of the ALPEMA Standards for the construction of brazed aluminum plate-fin heat exchangers The development of the new third edition of the ALPEMA Standards has involved a significant effort by the former chairman of ALPEMA, David Butterworth, the current secretariat (Simon Pugh of IHS, London), and the five ALPEMA member companies [Chart Energy and Chemicals Inc (USA), Fives Cryo (France), Kobe Steel, Ltd (Japan), Linde AG (Germany), and Sumitomo Precision Products Co., Ltd (Japan)] I wish to acknowledge their many contributions to help me update and extend this industrial standard for the safe construction and operation of brazed aluminum plate-fin heat exchangers In brief, brazed aluminum plate-fin exchangers are the most effective and energy-efficient heat exchangers for handling a wide range of services, noted particularly for their compactness and low weight This class of heat exchangers nearly always provides the lowest capital, installation, and operating cost whenever the application is within the operating range of these units, in particular over a wide range of cryogenic and non-cryogenic applications Where it is feasible to use a brazed aluminum platefin heat exchanger, it is usually the most cost-effective solution, often by a significant margin These units enjoy a very large heat transfer surface area per unit volume of heat exchanger They provide a total surface area of 1000 to 1500 m2 /m3 of vol- ume; this compares very well with the approximate range of 40 to 70 m2 /m3 for shell-and-tube units Plate-fin heat exchangers with surface area per unit volume of 2000 m2 /m3 are sometimes employed in the process industry! Plate-fin heat exchangers find applications in aircraft, automobiles, rail transport, offshore platforms, etc However, the main applications are in the industrial gas processing, natural gas processing, LNG (liquefied natural gas) facilities, refining of petrochemicals, and refrigeration services Their ability to carry multiple streams, occasionally up to 12 or more (as opposed to typically only two streams in a shell-and-tube heat exchanger), allows process integration all in one unit The very large surface area per unit volume is particularly advantageous when operating at low temperature differences between the hot and cold streams Such applications are typically found in cryogenic systems and hydrocarbon dewpoint control systems where temperature difference is linked to compressor power consumption The first edition of the ALPEMA Standards was published in 1994, and it was extremely successful and popular The second edition was published in 2000 New industrial developments and applications, experience with using the ALPEMA Standards, and feedback from users have indicated that the time was right for a third edition The new third edition is expected to appear early in 2010 The most significant additions and amendments that have been made are summarized here: Address correspondence to Prof John Thome, Laboratory of Heat and Mass Transfer, EPFL-STI-IGM-LTCM, Mail 9, CH-1015 Lausanne, Switzerland E-mail: john.thome@epfl.ch A new Chapter has been added to cover cold boxes and block-in-shell heat exchangers J R THORNE Many figures have been redrawn to make them easier to understand Photographs of the most common types of fin geometries have been added Information has been provided on two-phase distributors with diagrams Guidance on flange design and transition joints is included Guidance on acceptable mercury levels is given Allowable nozzle loadings have been updated Many small changes have been made to improve clarity The new third edition can be purchased and downloaded from the following website: http://engineers.ihs.com/products/ standards/petrochemical-standards.ht heat transfer engineering John R Thome has been professor of heat and mass transfer at the Swiss Federal Institute of Technology in Lausanne (EPFL), Switzerland, since 1998, where his primary interests of research are two-phase flow and heat transfer, covering both macro-scale and micro-scale heat transfer and enhanced heat transfer He directs the Laboratory of Heat and Mass Transfer (LTCM) at the EPFL with a research staff of about 18–20 and is also director of the Doctoral School in Energy He received his Ph.D at Oxford University, England, in 1978 He is the author of four books: Enhanced Boiling Heat Transfer (1990), Convective Boiling and Condensation, third edition (1994), Wolverine Engineering Databook III (2004), and Nucleate Boiling on MicroStructured Surfaces (2008) He received the ASME Heat Transfer Division’s Best Paper Award in 1998 for a three-part paper on two-phase flow and flow boiling heat transfer published in the Journal of Heat Transfer He has received the J&E Hall Gold Medal from the UK Institute of Refrigeration in February, 2008 for his extensive research contributions on refrigeration heat transfer Since 2008, he has been chairman of ALPEMA (the plate-fin heat exchanger manufacturers association) He has published widely on the fundamental aspects of micro-scale two-phase flow and heat transfer He is an associate editor of Heat Transfer Engineering vol 31 no 2010 Heat Transfer Engineering, 31(1):3–16, 2010 Copyright C Taylor and Francis Group, LLC ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457630903263200 Single-Phase Flow in Meso-Channel Compact Heat Exchangers for Air Conditioning Applications AMIR JOKAR,1 STEVEN J ECKELS,2 and MOHAMMAD H HOSNI2 School of Engineering and Computer Science, Washington State University–Vancouver, Vancouver, Washington, USA Mechanical and Nuclear Engineering Department, Kansas State University, Manhattan, Kansas, USA Experimental study of the single-phase heat transfer and fluid flow in meso-channels, i.e., between micro-channels and minichannels, has received continued interest in recent years The studies have resulted in empirical correlations for various geometries ranging from simple circular pipes to complicated enhanced noncircular channels However, it is still unclear whether the correlations developed for conventional macro-channels are directly applicable for use in micro-/mini-channels, i.e., hydraulic diameter less than mm, with heat exchanger applications A few researchers have agreed that similar results may be obtained for the laminar flow regime regardless of the channel size, but no general agreement has been reached for the transitional and turbulent flow regimes yet In this study, different meso-channel air–liquid compact heat exchangers were evaluated and the experimental results were compared with published empirical correlations A modified Wilson plot technique was applied to obtain the heat transfer coefficients, and the Fanning equation was used to calculate the pressure drop friction factors The uncertainty estimates for the measured and calculated parameters were also calculated The results of this study showed that the well-established heat transfer and pressure drop correlations for the macro-channels are not directly applicable for use in the compact heat exchangers with meso-channels INTRODUCTION adequately predict the single-phase heat transfer and pressure drop in multiport circular and rectangular mini-channels with hydraulic diameter ranging from 0.96 to 2.13 mm However, they mentioned their findings were in contrast to the results and conclusions that Wang and Peng [4] obtained in a similar study Steinke and Kandlikar [5, 6] recently made extensive reviews of single-phase heat transfer and pressure drop in microchannels They generated a database from the available literature and compared the results obtained by different researchers in order to answer this fundamental question of whether the classical macro-scale theories can be applied to micro- and minichannels Subsequently, they concluded these theories are in good agreement with smaller channel size provided all the flow factors, such as development of flow, efficiency of fins, and experimental uncertainties, are accurately taken into consideration We believe more applied research on micro- and minichannel heat transfer and fluid flow with different industry applications can further clarify the answers to this question, and may result in a set of general correlations for each scale and regime The co-authors previously obtained heat transfer and pressure drop for different type of air–liquid meso-channel compact heat exchangers and published the results in conference proceedings There have been many experimental studies conducted on single-phase fluid flow within compact heat exchangers with micro- and mini-channels, and new findings have been reported for different applications However, the researchers offer differing opinion on the role of channel size, as classified by Kandlikar and Grande [1], in correlating heat transfer and pressure drop, especially at the transitional and turbulent regimes This issue becomes more complicated when the heat exchanger channel geometries are compact and enhanced, such as in automotive compact heat exchangers, as described by Webb and Kim [2] Some researchers reported the possibility of significant differences between the macro- and micro-scale theories and correlations, while others believe the differences are not significant and that the same correlations can provide results that are generally in good agreement For example, Webb and Zhang [3] found the existing correlations for conventional macro-channels can Address correspondence to Dr Amir Jokar, School of Engineering and Computer Science, Washington State University Vancouver, 14204 NE Salmon Creek Ave, Vancouver, WA 98686, USA E-mail: Jokar@vancouver.wsu.edu A JOKAR ET AL [7–9] The objective of this article is to review the previous results and offer a conclusion on the single-phase flow in mesochannel compact heat exchangers of this sort The air–liquid heat exchangers under study were analyzed on both air and water sides A 50% glycol–water mixture was pumped into the enhanced circular and noncircular channels of these heat exchangers while, on the other side, air was pushed through the fin passages with louvered surfaces The goal was to obtain semi-empirical heat transfer correlations for the flow of the glycol–water mixture in the meso-channels and the flow of air through the louvered fin surfaces For this purpose, a modified version of the Wilson plot technique presented by Briggs and Young [10] was applied to find the single-phase heat transfer correlations The glycol–water pressure drop was also analyzed and the Fanning equation was used to calculate the friction factor The compact heat exchangers in this study were operated as components of a refrigeration system They were in turn installed within the secondary fluid loops connected to the main refrigeration loop of a custom automotive air conditioning system The main refrigeration loop included a compressor, condenser, evaporator, and expansion valve The secondary fluid system included two loops that exchanged energy with the main refrigeration loop In air conditioning (AC) mode, one of these loops was formed between the evaporator and the cooler-core compact heat exchanger to absorb thermal energy from the passenger cabin and transfer it to the evaporator during summer conditions The other loop was formed between the condenser and the radiator of compact heat exchanger to transfer thermal energy from the condenser to the surroundings In heat pump (HP) mode, the two secondary loops were switched using a fourway valve, so that one loop was formed between the condenser and the heat-core compact heat exchanger, and the other loop between the evaporator and radiator By changing the glycol– water mixture flow rates through the secondary fluid loops and controlling the temperatures, the required energy was transferred to/from the compact heat exchangers The experimental data were used to calculate the heat transfer rate and pressure drop of the heat exchangers In this article, the experimental test facilities are first described, followed by the geometry and size of the compact heat exchangers The calculation method and data analysis to determine heat transfer and pressure drop correlations from the measured data are then explained The resulting single-phase correlations are finally presented, discussed, and compared with the relevant previous studies EXPERIMENTAL TEST FACILITY The air conditioning system under study consisted of a main refrigeration loop using R-134a as the working fluid and two secondary fluid loops using a 50% glycol–water mixture as the secondary cooling/heating fluid Figure shows a schematic heat transfer engineering Figure Schematic of the test facility diagram of the test facility, and the following subsections give a brief description of the system components Secondary Fluid Loops Secondary glycol–water mixture loops were designed to exchange energy with the evaporator and condenser The temperatures at the inlet/outlet ports of each device were measured using 0.2 m long type-K thermocouples probes The thermocouple probes were inserted a minimum of 0.1 m into the flow longitudinally and fixed in the center of the 0.02 m inner diameter tubes such that the bulk temperature could be measured The pressure drop of the glycol–water mixture passing through the compact heat exchangers was measured by differential pressure transducers installed between the inlet and outlet ports The glycol–water mixture flow rates in each loop were measured by a turbine-type flow meter Conditioned Air Two environmental chambers were used in this study In each chamber, the air temperature and humidity were controlled using conditioned air from external heating/cooling and humidifying/dehumidifying systems In one of the environmental chambers, conditioned air was circulating through either the cooler-core (AC mode) or heater-core (HP mode) compact heat exchanger to simulate cabin conditions In the other chamber, either hot (AC mode) or cold (HP mode) air was circulating through the radiator compact heat exchanger to simulate ambient conditions Two ducts were designed and built for metering air flow through the compact heat exchangers The heat exchangers were installed in the middle of the air ducts during each test Induction fans installed at the ducts’ entrance were used to push air through the heat exchanger, while calibrated ASME standard nozzles were used to measure the air flow rate The mean inlet and outlet air temperatures were measured using several type-K thermocouples distributed on imaginary vertical vol 31 no 2010 A JOKAR ET AL THE COMPACT HEAT EXCHANGERS Five different meso-channel compact heat exchangers, as parts of the secondary fluid system, were tested and analyzed in this study Theses heat exchangers, which were used as the cooler-core, heater-core, or radiator of the automotive air conditioning system, are described next Cooler-Core Figure Thermocouples installation on the front and back of the mesochannel compact heat exchangers plains both in the front and back of the heat exchangers, as typically shown in Figure A chilled-mirror dew-point sensor measured the dew-point temperature at the ducts’ inlets The wet bulb temperature was calculated from psychrometrics using the measured dry bulb and dew-point temperatures Refrigeration Loop The refrigeration loop included an evaporator, a condenser, a compressor, and an expansion valve Thermocouples and pressure transducers were installed at the inlet and outlet ports of all components for temperature and pressure measurements A Coriolis-effect flow meter was used to measure the refrigerant mass flow rate, which was controlled by varying the compressor speed using a frequency-controlled AC motor The refrigerant charge was varied for each test condition to control the subcooled and superheated temperatures at the condenser and evaporator exits, respectively These temperatures were controlled at about 5◦ C for a stable system operation This heat exchanger is installed in cars to cool the cabin in warm conditions (AC mode) Three compact heat exchangers, which were manufactured in different sizes and internal flow-passage configurations, were tested as cooler-cores in this study Air flowed over the fin passages and the glycol–water mixture passed through the rectangular meso-channels, as shown in Figure The glycol–water rectangular channels had small enhancements (bumps) on the top and bottom surfaces These enhancements contacted each other in the middle of channels creating two-dimensional flow passages The geometry and size of the glycol–water flow rectangular channels and their internal enhancements are presented in Figure This figure showed that the glycol–water was flowing, perpendicular to the page, through cavities separated by these enhancements The enhancements created a pattern, as shown in Figure 4, and this pattern was repeated along the length of rectangular tube On the air side, the three meso-channel compact heat exchangers had louvered thin-plate fins, as described by Kays and London [11] The interconnecting thin-plate fins were sandwiched between the two parallel rectangular glycol–water channels, as shown in Figure The louvers on the thin-plate fin surfaces were used to promote turbulence and reduce the boundary Test Procedure A range of test conditions was used to obtain adequate data for analyzing the performance of the heat exchangers All the system variables such as temperatures, pressures, and flow rates were recorded every 10 s as raw data Once the fluctuations in glycol–water mean temperature within the heat exchangers became stable (within ±1◦ C), the system was considered to be at a steady-state condition The data collection then began and continued for at least 10 for each test condition The timeaveraged data were then used to analyze the heat exchangers’ performance heat transfer engineering Figure Cutaways of the three meso-channel compact heat exchangers used as the cooler-core vol 31 no 2010 A JOKAR ET AL Figure Geometry and size of the louvered thin-plate fins in the three mesochannel compact heat exchangers used as the cooler-core The flow of glycol–water mixture within the heater-core was analyzed in the same way as the circular tubes For the air side, an analysis similar to the air flow across a compact heat exchanger with continuous parallel fins was applied Figure Geometry and size of the glycol–water flow channels in the three meso-channel compact heat exchangers used as the cooler-core Radiator layer thickness of the air flowing across the compact heat exchangers The geometry and size of these thin-plate fins are presented in Figure Heater-Core This heat exchanger is installed in cars to warm the cabin in cold conditions (HP mode) The heater-core used in this study was a finned-tube cross-flow compact heat exchanger, which was run in heat pump mode to heat the passenger cabin A cutaway of this heat exchanger is shown in Figure Air flowed through the finned passages, while the mixture of glycol–water passed through the circular tubes Figure showed the cross-sectional area of the circular tubes through which the glycol–water mixture flowed This figure also showed the helical springs that were inserted into the circular tubes to promote turbulent flow and increase heat transfer This finned-tube compact heat exchanger included eight circular tubes (two-passes) with continuous fins, as described by Kays and London [11] The fin surfaces were parallel continuous thin plates with 16 holes through which 16 circular tubes were inserted and fitted to the plates tightly, as shown in Figure The parallel continuous thin plates were not simply flat plates In fact, part of the fin surfaces between the circular tubes was sliced vertically along the air flow passages creating louvers These louvers between the fin surfaces promote the flow turbulence even at low air flow rates The geometry and size of the circular tubes with the helical-spring inserts and the fin surfaces is shown in Figure heat transfer engineering This heat exchanger is installed in cars to exchange thermal energy between the air conditioning system and ambient in either warm (AC mode) or cold (HP mode) conditions The radiator in this study was a cross-flow compact heat exchangers in which the glycol–water mixture flowed through its rectangular enhanced meso-channels, and on the other side, air flowed through the fin passages with louvered surfaces, as shown in Figure Figure A cutaway of the meso-channel compact heat exchanger used as the heater-core vol 31 no 2010 A JOKAR ET AL Figure Geometry and size of the glycol–water flow channels and the louvered thin-plate fins in the meso-channel compact heat exchanger used as the heater-core The rectangular meso-channels had small enhancements, i.e., bumps, which were raised from the bottom and top surfaces to promote flow transition from laminar to turbulent and to increase the heat transfer effectiveness, as shown in Figure The interconnecting thin-plate fins were sandwiched between two neighboring meso-channels, as shown in Figure These fins were not simply flat plates, and in fact, the fin surfaces were louvered along the flow passes These louvers promoted turbulence and reduced the boundary layer thickness of the air flowing through the radiator The geometry and size of the louvered thin-plate fins on the radiator are shown in Figure Figure Geometry and size of the glycol–water flow channels and the louvered thin-plate fins in the meso-channel compact heat exchanger used as the radiator DATA REDUCTION AND CALCULATION METHOD A multi-channel data acquisition system allowed continuous data collection and monitoring of the experimental test facility Heat transfer and pressure drop correlations within the mesochannel compact heat exchangers were obtained from extensive data sets gathered from multiple experimental test runs This section reviews in detail the equations used for the heat exchanger analysis Heat Transfer Calculation Method Figure A cutaway of the meso-channel compact heat exchanger used as the radiator heat transfer engineering A set of experiments was performed to analyze the thermohydrodynamic performance of each heat exchanger The Wilson plot technique was then applied to find the heat transfer correlations for both the glycol–water mixture and air The first step vol 31 no 2010 A JOKAR ET AL was to calculate the overall heat transfer coefficient for each data point The experimental data and measured dimensions of the heat exchangers were used to obtain the overall heat transfer coefficient based on the glycol–water side This coefficient was calculated from the following heat transfer equations: Q˙ g = Ug Ag TLM F (1) ˙ g,tot CP,g (Tg,out – Tg,in ) Q˙ g = m (2) (3) where the log-mean temperature difference was defined as: TLM = T1 − T2 Ln( T1 / T2 ) T1 = Ta,out – Tg,in T2 = Ta,in – Tg,out (4) The fin surfaces on the compact heat exchangers were effective in transferring heat between glycol–water mixture and air This effect was taken into account by adding the fin thermal efficiency to the energy balance equation The fin thermal efficiency, presented in Incropera and DeWitt [12], is shown as: ηfin = ˙ fin ˙ fin Q Q = ˙ max hAfin (Ta – Tb ) Q (5) where “b” denotes the fin base This equation implies the maximum heat transfer rate is attainable only if the entire fin surface is at the base temperature, which is generally not the case The fin efficiencies for different fin geometries have been presented graphically in many references as a function of the heat transfer coefficient One simple case is the straight fin with a uniform cross-sectional area As shown in Incropera and DeWitt [12], the fin efficiency in this case is analytically calculated as ηfin = tanh(mL) mL (6) where L is the fin length and parameter “m” is defined as m2 = hP kfin Ac (7) Since the fin plates on the compact heat exchangers in this study had a uniform cross-sectional area, Eq (6) was applied to approximate the fin efficiency The fin overall surface efficiency to characterize an array of fins, as presented in Incropera and DeWitt [12], is defined as: ηo = ˙ tot ˙ tot Q Q Afin =1− = (1 − ηfin ) ˙ hAtot (Ta − Tb ) Atot Qmax Atot = Afin + Ab (8) heat transfer engineering (9) Applying an energy balance between the glycol–water mixture and air for the compact heat exchangers yielded: hg Ag,tot (Twall – Tg ) = ηo Aa,tot (Ta – Twall ) where F is a correction factor for multipass cross-flow heat exchangers This factor was empirically estimated using the inlet/outlet temperatures of fluids passing through the heat exchanger, as described in Incropera and DeWitt [12] The correction factor was estimated as 0.9 for most conditions in this study Combining Eqs (1) and (2), the overall heat transfer coefficient was calculated as: ˙ g,tot CP,g (Tg,out – Tg,in ) / Ag TLM F Ug = m where the subscript “tot” denotes the total exposed area of the finned and un-finned surfaces The total area was calculated by: (10) Knowing the overall heat transfer coefficient and overall fin surface efficiency, the modified Wilson plot technique, introduced by Briggs and Young [10], was applied to find a heat transfer correlation for both sides of the heat exchangers Assuming the areas on both sides of the channel are not the same, and neglecting the wall thermal resistance due to the small wall thickness and high thermal conductivity of the wall’s material, the overall heat transfer coefficient was calculated as: 1 = + Ug Ag hg A g h a A a ηo (11) The heat transfer coefficient in this study was assumed to be in the form of the Dittus-Boelter equation, as described in Incropera and DeWitt [12], and presented as: h=C kfluid Dh Rep Prn = Ch (12) Equation (11) is then rearranged as: hg h g Ag 1 + = U Cg Ca h a Aa ηo (13) It should be noted that the Dittus–Boelter equation is valid for a single-phase fluid with the Prandtl number greater than 0.7; however, that correlation was not exactly used in this study Equation (12) was applied to both glycol–water and air flows in the heat exchangers knowing the Prandtl numbers of air and the glycol–water mixture were greater than 0.7 The parameters of the Wilson plot technique were then defined as: ⎧ 1 ⎪ ⎪ ⎨b = C ,m = C g a (14) Y = b + mX ⎪ h h g g Ag ⎪ ⎩Y = ,X = U h a Aa ηo To obtain more accurate results, all the thermophysical properties were calculated as a function of temperature The properties for the glycol–water mixture were obtained from the ASHRAE Handbook of Fundamentals [13] It was necessary to evaluate the heat exchangers’ fin characteristics to complete the Wilson plot technique Based on the heat exchanger geometries presented in previous section, the characteristics of the fin surfaces of the five meso-channel compact heat exchangers are summarized in Table In order to apply the Wilson plot technique, Eq (14), it was necessary to calculate the hydraulic diameter on both glycol– water and air sides The hydraulic diameter on the glycol–water side was calculated based on the flow cross-sectional area and vol 31 no 2010 A JOKAR ET AL Table Measured and calculated parameters for the five meso-channel compact heat exchangers Parameter Fin pitch (number of fin plates/m) Hydraulic diameter (air side), Dh (m) Fin thickness, t (m) Frontal area, Afr (m2 ) Minimum free-flow area, Amin (m2 ) σ = Amin /Afr Area of single fin plate, Asingle−fin (m2 ) Total fins area, Afin,tot (m2 ) Total unfinned area (pipe base), Ab,tot (m2 ) Total heat transfer area (air side), Aa,tot (m2 ) Total glycol–water heat transfer area (based on the internal wall projected area), Ag,tot (m2 ) Aa,tot /Afin,tot Aa,tot /Ag,tot Cooler-core (42 mm) Cooler-core (58 mm) Cooler-core (78 mm) Heater-core Radiator 620 2.27E-3 0.08E-3 5.17E-2 3.68E-2 0.712 2.62E-4 540 2.67E-3 0.10E-3 5.28E-2 3.89E-2 0.736 4.35E-4 540 2.81E-3 0.10E-3 5.79E-2 4.29E-2 0.741 6.86E-4 1100 1.45E-3 0.10E-3 3.88E-2 2.01E-2 0.519 5.61E-3 860 3.62E-3 0.10E-3 1.96E-1 1.57E-1 0.802 2.47E-2 0.959 0.403 1.218 0.462 1.805 0.587 1.544 0.095 3.715 0.805 1.362 1.680 2.392 1.638 4.520 0.424 0.488 0.620 0.094 0.848 1.420 3.211 1.379 3.746 1.325 3.857 1.061 17.4 1.217 5.330 wetted perimeter The hydraulic diameter on the air side was calculated from the following equation, as defined by Kays and London [11]: AC Dh =4 L A (15) where Ac is the minimum cross-sectional area of the air flow (i.e., Amin in Table 1), and A is the total heat transfer area on the air side (i.e., Aa,tot in Table 1) In Eq (15), “L” is an equivalent flow length measured from the leading edge of the first channel to the leading edge of the second channel The Reynolds number in Eq (12) was defined as a function of mass flux: ReD = GDh µ (16) The mass flux of the glycol–water mixture was calculated based on the measured flow rate and the minimum free-flow area of the meso-channels The mass flux of the air flowing through the compact heat exchangers was also calculated based on the measured air flow rate and the minimum free-flow area of the fin plates, as presented in Table The parameters X and Y used in the Wilson plot technique were calculated for each single experiment These data points were then curve-fitted linearly using the least-squares method The slope and intercept of the fitted line would thus be the inverse of coefficients Ca and Cg , respectively, as presented in Eq (14) The heat transfer coefficients of the glycol–water mixture (hg ) and air (ha ) were then obtained by Eq (12) For the air side, the new value of “ha ” was used to recalculate the parameter “m” in Eq (7) The fin efficiency and overall surface efficiency were then calculated from Eqs (6) and (8), respectively, based on the calculated parameter “m.” These calculations created a trial–error loop between “m” and in the Wilson plot technique The procedure was repeated until the heat transfer engineering difference between the new and old value of became less than 0.1% Friction Factor Calculation Method The frictional pressure drop for the glycol–water mixture within the meso-channel compact heat exchangers was calculated by subtracting the pressure drop across the inlet/outlet manifolds and gravitational pressure drop from the total pressure drop: Pf = Ptot − Pgr − Pman (17) The pressure drop from the inlet port to the outlet port was measured by a differential pressure transducer The gravitational pressure drop was considered to be zero for this analysis since the inlet and outlet ports were at the same height The inlet/outlet manifolds pressure drop was approximated as a function of the inlet head velocity as: Pman = K ρu2m (18) in where K is obtained empirically This constant was approximated as 1.5 for the compact heat exchangers in this study, as described by Shah and Wanniarachchi [14] It was found that the frictional pressure drop was the largest component of the total pressure drop, being over 90% of the total pressure drop for the glycol–water mixture in the meso-channel compact heat exchangers The Fanning friction factor for the glycol–water flow was then defined as: Cf,g = vol 31 no 2010 f = Pf Dh ρm L 2G2 (19) g Heat Transfer Engineering, 31(1):83–89, 2010 Copyright C Taylor and Francis Group, LLC ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457630903263549 Temperature Difference Error Determination for Heat Meter Validation TADEUSZ GOSZCZYNSKI Industrial Research Institute for Automation and Measurements (PIAP), Warsaw, Poland A method to calculate the maximum value of temperature difference error in heat meters is presented It is designed for heat meters used for measuring the volume of heat provided to buildings by heating systems using hot water Validation offices generally use computer-based numerical methods for the calculation of the error over the full temperature range and temperature difference range Use of these methods is time-consuming due to taking in succession the temperature and temperature difference with a constant gradient as well as selecting the maximum value of error The author has developed a method that allows the practicing engineer to calculate the maximum error in a short time with his or her own program This method can also be used for heat meters not conforming to any standard or pairs of temperature sensors not dedicated for heat meters INTRODUCTION calculations evaluating the worst-case error of the pair (maximum ratio of error to maximum permissible error, MPE) in full measurement range of the heat meter This worst-case error must be calculated precisely; therefore, the graphical methods normally used are not acceptable The standard method requires sensor pair calculations for every point of area demonstrated in Figure For example, if the gradient of 0.1◦ C is used for the calculation it results in more than 106 calculations of quadratic equations Even if this takes only to minutes for every pair, it is irritating for personnel and lowers efficiency The proposed method requires calculating a much smaller number of equations At first, the parameters (t, t) of extremum points are determined In the next step the error values in those points only are calculated, and the worst-case error is selected Heat meters are instruments intended for measuring the heat that, in a heat-exchange circuit, is absorbed or given up by a heat conveying liquid Typically, heat meters that are regulated by legal metrology services in Europe must comply with the requirements formulated in standard EN 1434 [1] Heat meters are manufactured either as complete instruments or as combined instruments A combined heat meter consists of a flow sensor, a temperature sensor pair, and a calculator The flow sensor is a subassembly through which the heat-conveying liquid flows, at either the flow or return of a heat-exchange circuit, and that emits a signal that is a function of the volume of the flowing liquid The temperature sensor pair is a subassembly that senses the temperatures of the heat-conveying liquid at the flow and return of a heat-exchange circuit The calculator receives signals from the flow sensor and the temperature sensors, and calculates the quantity of heat exchanged In a combined heat meter, the subassemblies can be verified separately When validating the temperature sensor pair, both sensors must be inserted into a temperature-controlled bath and their resistance should be measured at three temperature points The standard [1] requires ERROR ANALYSIS Standard EN 60751 [2] defines resistance / temperature relation as r = R0 (1 + At + Bt ) (1) where R0 , A, and B are the standard values The measured resistance values are used in the system of three equations to calculate the three constants R01 , A1 , B1 for one sensor and R02 , A2 , B2 for the second sensor Address correspondence to Mr Tadeusz Goszczynski, Industrial Research Institute for Automation and Measurements (PIAP), Al Jerozolimskie 202, 02-486 Warsaw, Poland E-mail: tgoszczynski@piap.pl 83 84 T GOSZCZYNSKI and from these, rsp − rst = (R01 − R02 ) + (R01 A1 − R02 A2 )t + (R01 A1 − R0 A) t + (R01 B1 − R02 B2 )t + (R01 B1 − R0 B)2t t + (R01 B1 − R0 B) t (10) where t = t1 − t2 Figure Limit lines of temperature and temperature difference range for heat meters as defined by standard EN 1434 [1] where t2 + t = t1 In the procedure according to the standard [1], for every pair of temperature values t2 and t1 = t2 + t, from the range given for the heat meter, the following resistances are calculated: Rt1 = R01 + A1 t1 + B1 t12 (2) Rt2 = R02 + A2 t2 + B2 t22 (3) After substituting the results into two quadratic equations Rt1 = R0 + At1M + Bt1M (4) Rt2 = R0 + At2M + Bt222M (5) their roots are calculated and the relative error is determined from et = (t1M − t2M ) − t t (6) where the error relates the indicated value to the conventional true value of the relationship between the temperature sensor pair output and temperature difference This method of calculation is mandatory for the calculation of error to comply with the requirements formulated in the standard [1] But it need not be done for every point in full temperature range and full temperature difference range if the analysis of extremum points location is carried out Korytkowski et al [3] used resistance difference value as an output signal of the temperature sensor pair and calculated the relative error: er = rsp − rst rst (7) where t = t2 and These equations can be used in numerical methods of calculating maximum error using resistance instead of temperature This method of calculating the maximum error was presented by Korytkowski et al [3, 4] It used Eq (10) and multiple temperature and temperature difference values with a constant gradient of 0.1◦ C and then selected the maximum value of error Tegeler et al [5] present a mathematical model for the calculation of the temperature difference uncertainty of calibration of paired temperature sensors It provides requirements for apparatus used for the calibration but cannot be used for calculation of maximum error of the controlled pairs Analysis presented in [3] and [4] is expanded in this article to determine extremum points of the equation by calculating derivatives over temperature and over temperature difference, which simplifies determination of the maximum error during validation of the heat meter The analysis determines the worstcase relative error of the temperature pair over the temperature range and over the temperature difference range specified for the heat meter and shown in Figure The range of evaluating the error is limited by standard [1]: for temperature, tmin ≤ t2 ≤ tmax − t rsp = R01 + A1 t1 + − R02 + A2 t2 + B2 t22 (8) tmax ≥ t≥ tmin and t≥ t EN for t2 ≥ tmin EN tmin EN = 10◦ C and tmin EN = 80◦ C where rst = R0 + At1 + Bt12 − R0 + At2 + Bt22 R01 − R02 = w1 ; R01 A1 − R02 A2 =w2 ; R01 A1 − R0 A = w3 ; (14) Consequently, the equation for further analysis has the form rst = w1 + w2 t + w3 t + w4 t (9) heat transfer engineering (13) The manufacturer of the heat meter defines tmin , tmax , tmin , and tmax In order to make further calculations simpler, some substitutions were required Expressions in parentheses in Eq (10) are replaced with w1 to w5 : rsp − and (12) and for temperature difference, R01 B1 − R02 B2 = w4 ; R01 B1 − R0 B = w5 B1 t12 (11) + 2w5 t t + w5 t vol 31 no 2010 (15) T GOSZCZYNSKI and the ratio of a relative error divided by the maximum permissible error (MPE), ErMPE , is er (16) err = |ErMPE | From [1] we have EMPE tmin = ± 0.5 + t 85 and temperature extremum points are determined as √ −4w4 (6 rmin + R0 A t + R0 B t ) ± del1 (23) t= 8w4 R0 B t where del = 16w42 (6 rmin + R0 A t + R0 B t )2 − 16w4 R0 B t (17) × (2w2 + 4w5 t)(6 rmin + R0 A t + R0 B t ) and since we have resistance values in Eq (16) ErMPE rmin = ±(0.5 + ) rst (18) rst + rmin rst (19) |ErMPE | = 0.5 2w1 + 2w2 t + 2w3 t + 2w4 t + 4w5 t t + 2w5 t rmin + R0 + At1 + Bt12 − R0 + At2 + Bt22 (20) At this point we have the equation from which derivatives can be calculated In order to find points of extremum of Eq (20) the derivatives over temperature and over temperature difference are determined and compared to zero The derivative over temperature is − − t) = 4w5 t + 2(w3 + 2w5 t) rmin + R0 A t + R0 B t + 2R0 B tt (2w5 t + 2(w3 + 2w5 t) t + 2(w1 + w2 t + w4 t )(R0 A + 2R0 Bt + 2R0 B t) (6 rmin + R0 A t + R0 B t + 2R0 B tt)2 (25) and for t) =0 (26) √ −4w5 rmin + 4R0 B(w1 + w2 t + w4 t ) ± del2 t= 2(2w5 (R0 A + 2R0 Bt) − 2R0 B(w3 + 2w5 t)) (27) where del = (4w5 rmin − 4R0 B(w1 + w2 t + w4 t ))2 4w4 t + 2(w2 + 2w5 t) = rmin + R0 A t + R0 B t + 2R0 B tt − 4(2w5 (R0 A + 2R0 Bt) − 2R0 B(w3 + 2w5 t))(2(w3 + 2w5 t) 2R0 B t(2w4 t + 2(w2 + 2w5 t)t + 2(w1 + w3 t + w5 t )) (6 rmin + R0 A t + R0 B t + 2R0 B tt)2 err ,( err ,( DETERMINATION OF EXTREMUM err (t) (24) The derivative over temperature difference is where rmin = 0.385 tmin Substituting Eqs (7), (9), (15), and (19) into Eq (16) we obtain err = − 4R0 B t(w1 + w3 t + w5 t ) (21) For points of extremum err (t) = (22) ×6 rmin − 2(w1 + w2 t + w4 t )(R0 A + 2R0 Bt)) (28) These equations can be used to determine points of maximum or minimum error values on the horizontal line of Eq (23) and vertical line of Eq (27) limiting the range of heat meter’s measurements But there is also another limit line, the slanted line, defined from Eq (12) as t = tmax − t (29) Inserting Eq (29) to Eq (20) we obtain errs = 2(w4 − w5 ) t + 2(−w2 + w3 − 2w4 tmax + 2w5 tmax ) t + 2(w1 + w2 tmax + w4 tmax ) −R0 B t + (R0 A + 2R0 Btmax ) t + rmin (30) Derivative over temperature difference is errs ( t) = 4w5 t + 2(w3 + 2w5 t) rmin + R0 A t + R0 B t + 2R0 B tt − (2w5 t + 2(w3 + 2w5 t) t + 2(w1 + w2 t + w4 t )(R0 A + 2R0 Bt + 2R0 B t) (6 rmin + R0 A t + R0 B t + 2R0 B tt)2 heat transfer engineering vol 31 no 2010 (31) 86 T GOSZCZYNSKI For errs ,( t) =0 (32) points of extremum are calculated as demonstrated in Figure should be eliminated Points lying inside should be now recalculated using values of t1 and t2 with Eq (11) Since some extremum points on the limit lines can lie outside the area, all crossing points of the limiting lines must be √ −2w4 rmin + 2w5 rmin − 4R0 B(w1 + w2 tmax + w4 tmax ) ± del3 t= 2((w4 − w5 )(R0 A + 2R0 Btmax ) + 2R0 B(−w2 + w3 − 2w4 tmax + 2w5 tmax )) where (33) also considered as potential points of maximum error value for a sensor pair Parameters t1 and t2 of the points are: del = (2w4 rmin − 2w5 rmin + 4R0 B(w1 + w2 tmax + w4 tmax ))2 (tmin + − 4((w4 − w5 )(R0 A + 2R0 Btmax ) (tmin EN + + 2R0 B(−w2 + w3 − 2w4 tmax + 2w5 tmax )) (tmax , tmax − ·(12 rmin (−w2 + w3 − 2w4 tmax + 2w5 tmax ) − 2(w1 + w2 tmax + w4 tmax )(R0 A + 2R0 Btmax )) (34) DETERMINATION OF EXTREMUM ON THE LIMIT LINES The equations derived in the previous section can be used for determining points of extremum on limit lines In order to find the points, the conditions for these lines should be taken into consideration For vertical limit lines t = constant, and therefore only the derivative over temperature difference should be determined and compared to zero Points of extremum are calculated from Eqs (27) and (28) with consecutive substitutions of t = tmin and t = tmin EN For horizontal limit lines t = constant, and therefore only the derivative over temperature should be determined and compared to zero Equations (23) and (24) give parameters of extremum points for three horizontal lines after consecutive substitutions of t = tmin , t = tmax and t = tmin EN For the slanted line, the extremum point should be determined using Eqs (33) and (34) and Eq (29) tmin , tmin ), (tmin EN + tmin , tmin EN ), tmin EN , tmin EN ), (tmax , tmax − tmax ), (tmin + tmax , tmin ) tmin EN ), (35) Next, the ratio of a relative error to the maximum permissible error should be calculated for all extremum points as er/MPE = 100 | rsp − rst | rst | ErMPE | (36) using Eqs (8), (9), and (19) Finally, the one absolute maximum value from all calculated from Eq (36) should be determined as the worst-case error of the sensor pair To conform to maximum permissible error determined for the temperature sensor pair, the error calculated as just described should be less than The order of calculations is presented in Table To demonstrate the difference in results from calculations of errors using resistance characteristics of sensors and from calculations using temperature characteristics (in accordance with the standard), the ratio of relative errors et /er calculated from Eqs (6) and (7) for different values of sensor parameters are presented in Figures and DETERMINATION OF THE WORST-CASE ERROR After calculating values of constants using Eqs (13) and (14), all extremum points are determined The simplest way to determine the worst-case error is to find the absolute maximum value of error relative to the maximum permissible error (MPE) from all values calculated at extremum points lying on the limit lines of Figure Since in the next steps the absolute maximum value from all the extremum values will be chosen, there is no need to determine whether the extremum is a maximum or a minimum Next, all the extremum points lying outside the area heat transfer engineering Figure Ratio of relative errors et /er calculated for the pair of sensors: R01 = 100.0; A1 = 3.9383 × 10−3 ; B1 = −5.8250 × 10−7 ; R02 = 100.0; A2 = 3.8783 × 10−3 ; B2 = −5.715 × 10−7 vol 31 no 2010 T GOSZCZYNSKI 87 Table Order of calculations of the worst-case error Number 10 11 12 Calculations Symbols Give manufacturer-defined values to these constants Calculate constants using manufacturer defined values Determine extremum points on horizontal lines for t = tmin , t = tmax and t = tmin EN Determine extremum points on vertical lines for t = tmin and t = tmin EN Determine extremum points on slanted line Calculate temperature values of liquid on flow and on return for first pair of values t and t determined in line of this table For calculated t1 and t2 , calculate resistance differences For calculated rsp and rst , calculate maximum permissible error For calculated |ErMP E |, calculate relative error to the MPE ratio Make calculations given in lines to of this table for other pairs of values t and t determined in lines 3, 4, and of this table Make calculations given in lines to of this table for pairs of values t1 and t2 given in Eq (35) Determine absolute maximum value from all calculated er/MP E values Equations tmin , tmax , tmin , tmax , tmin EN , tmin EN w1 ; w2 ; w3 ; w4 ; w5 rmin = 0.385 tmin del1, t 13 14 23, 24 del2, t 27, 28 del3, t1 , t2 t, t rsp , rst |ErMP E | er/MP E er/MP E 33, 34, 29 11 8, 19 36 er/MP E er/MP E max Note When determining roots of quadratic equation in lines 3, 4, and 5, reject the root with value out of range for resistance temperature sensor CONFORMING TO THE STANDARD This method can also be useful for validation of heat meters and their subassemblies in conformity with the standard [1] It can be used to determine whether the worst-case point lies inside the area of measurement The only case when a worstcase point can lie inside the area of measurement is when the minimum point of extremum in the range of heat meter measurements is on one of the vertical lines and the minimum point of extremum in the range of heat meter measurements is on one of the horizontal lines In other cases a worst-case point lies on limit lines of the area Simulation of error characteristics, with many different sets of parameters, for pairs of temperature sensors displays the shape of rows or ridge, descending or ascending in a continuous way (see Figures and 5) In all these cases, only for one type of line (horizontal or vertical) was an extremum point detected Therefore after calculations according to points 1, 2, 3, and of Table (and verifying that the worst-case point lies on limit lines of the area of measurement), calculations of errors are made on a limited number of points instead of on nearly 106 points of the full range Errors are calculated in conformity with the standard [1] using Eqs (2) to (6) and comparing to the value given in Eq (17) This method of calculation is used in the apparatus KAL-LEG-7 developed by the Industrial Research Institute for Automation and Measurements (PIAP) located in Warsaw, Poland The method is used for verification of the heat meters with temperature sensor pairs as a subassembly This method of calculation determines the extremum points as described earlier, and if it proves that a worst-case point lies on limit lines, it makes calculation of Figure Ratio of relative errors et /er calculated for the pair of sensors:R01 = 100.4; A1 = 3.9383 × 10−3 ; B1 = −5.8250 × 10−7 ; R02 = 99.6; A2 = 3.8783 × 10−3 ; B2 = −5.715 × 10−7 Figure Results of calculations for “vertical” lines (t2 = constant) for an example sensor pair heat transfer engineering vol 31 no 2010 88 T GOSZCZYNSKI Table Values of error relative to the maximum permissible error calculated with new method R0 = 100.0 R01 = 100.0 R02 = 100.7 tmin = 20◦ C A = 3.9083 × 10−3 B = −5.775 × 10−7 −3 A1 = 3.9663 × 10 B1 = −5.7985 × 10−7 A2 = 3.9383 × 10−3 B2 = −5.8250 × 10−7 ◦ ◦ tmax = 150 C tmin = C tmax = 100◦ C t (◦ C) 100 10 t2 (◦ C) = −0.5404 (6) −16.837 (1) 20.00 −11.859 −0.5405 −0.53885 (5) 26.033 50.00 22.297 −11.818 (3) −16.719 (2) 80.00 −11.685 (4) 140.00 Note Numbers in parentheses designate crossing points of the limiting lines with reference to Figure Values in bold type are extremum points on horizontal lines The worst-case value is underlined errors only for a limited number of points lying on all limit lines The Central Office of Measures in Poland has certified the apparatus and the method The apparatus is presently used for validation of heat meters (required by Polish law every years) by small enterprises, which validate a few dozen meters a day A short program using this method for computers or calculators is attached to the mobile testing device for heat meters TEC400 and to the validation apparatus TEC-LEG-8H for hybrid heat meters developed by PIAP under Project C/06316 founded by the Polish Ministry of Science and presented by Goszczynski et al [6] The presented method has not been previously published for commercial reasons EXAMPLES The sensor pair with parameters R01 = 100.0; A1 = 3.9663∗ 10−3 ; B1 = −5.7985∗ 10−7 ; R02 = 100.7; A2 = 3.9703∗ 10−3 ; B2 = −5.9725∗ 10−7 is used as an example for calculations These values were chosen in order to present error characteristics with extremum points lying in the range of measurement determined by the standard [1] In most of practical cases, errors calculated in the range are smaller but extremum points are far away from the measurement range or there are no extremum points According to the procedure described in this article, the extremum points on horizontal, vertical, and slanted limit lines given in Figure were calculated and are presented in Table All crossing points of the limiting lines given in Eq (35) are marked with numbers in parentheses in Figure and in Table Only extremum points on horizontal lines are presented in Table since no extremum points are present on vertical limit lines (value of del2 is negative) and on slanted lines the point is far out of range Values of relative error to the MPE ratio calculated from Eq (36) in extremum points are presented in boldface type Values of the ratio for all crossing points on the limit lines were also calculated and presented Maximum error in the range is –16.837 for t = and t= 20 (underlined in Table 2) Results of calculations are also presented in Figure for “vertical” lines (t2 = constant) with few different values of t2 and in Figure for “horizontal” lines ( t = constant) with a few different values of t In Figure the curves presented have extremum points in accordance with data in Table Curves in Figure are ascending with rising values of t with no extremum visible, confirming calculations using Eqs (27) and (28), since values of del2 are negative CONCLUSIONS Figure Results of calculations for “horizontal” lines ( t = constant) for an example sensor pair heat transfer engineering The presented method of calculation allows the determination of the value of error in a very short time This method of calculation is much more convenient than the numerical method used in other (known to the author) equipment, by calculating multiple values of error using a large number of temperature and temperature difference values with a constant gradient and then selecting the maximum value This method can also be used for pairs of sensors not dedicated for heat meters and then appropriate values can be used for values limiting the range of measurements and for definition of maximum permissible error vol 31 no 2010 T GOSZCZYNSKI NOMENCLATURE A; A1 ; A2 B; B1 ; B2 del1; del2; del3 EMPE ErMPE er err err (t) err ( t) errs (t) errs ( t) er/MPE er/MPE max et r R0 ; R01 ; R02 Rt1 Rt2 t t1 t2 t1M t2M tmin , tmax tmin EN w1 ; w2 ; w3 ; w4 ; w5 rsp rst t tmin , tmax constants constants discriminants of quadratic equations maximum permissible error (%) maximum permissible error for resistance characteristics (%) relative error ratio of relative error to maximum permissible error derivative over temperature derivative over temperature difference derivative over temperature for slant line derivative over temperature difference for slant line relative error to the MPE ratio worst-case error relative error resistance of temperature sensor, resistance of temperature sensor at 0◦ C, resistance value in temperature t1 , resistance value in temperature t2 , temperature, ◦ C temperature of liquid on flow, ◦ C temperature of liquid on return, ◦ C temperature calculated from Rt1 , ◦ C temperature calculated from Rt2 , ◦ C minimum and maximum values of temperature, ◦ C value of temperature defined by [1] for calculation of error, ◦ C constants for substitutions resistance difference for temperature sensor pair at any temperature difference taken from calculated parameters of characteristics of sensors, resistance difference for temperature sensor pair at any temperature difference taken from standard characteristics of sensors, heat transfer engineering tmin EN 89 temperature difference, ◦ C minimum and maximum values of temperature difference defined by manufacturer of heat meter, ◦ C value of temperature difference defined by [1] for calculation of error, ◦ C REFERENCES [1] European Standard BS EN 1434-5:2007 Heat Meters, Initial Verification Tests May 31, 2007, London, United Kingdom [2] European Standard BS EN 60751 Industrial Platinum Resistance Thermometer Sensors March 15, 1996, London, United Kingdom [3] Korytkowski, J., Goszczynski, T., and Jachczyk, E., Computer Testing System for Examining the Accuracy of Pairs of Temperature Probes, Pomiary Automatyka Robotyka, vol 10, pp 17–19, 1997 [4] Korytkowski, J., Goszczynski, T., and Jachczyk, E., Methods of Automatic Computer Testing System for Examining the Accuracy of Pairs of Temperature Probes and Heat Meter Calculators, Automation’98 Conf., March 11–12, 1998, Warsaw, Poland, pp 335–342 [5] Tegeler, E., Heyer, D., and Siebert, B., Uncertainty of the Calibration of Paired Temperature Sensors for Heat Meters, Tempmeko 2007 Conf., www.tempmeko2007.org [6] Goszczynski, T., and Korytkowski, J., Apparatus TEC-LEG-8H for Validation of Hybrid Heat Meters, Pomiary Automatyka Robotyka, vol 9, pp 11–12, 2006 Tadeusz Goszczynski is Project Leader at the Industrial Institute of Automation and Measurement, Warsaw, Poland He received his Master’s and Eng degrees from Warsaw University of Technology, Poland in 1970 His main research and design interests are testing equipments and devices, especially for validation of heat meters and their sub-assemblies and mobile testing devices for heat meters He is a recipient of Polish Association of Engineering Organizations Master of Technology Award He has published more than 30 articles in Polish technical journals and one book He has authored 10 patents and 14 patent applications to the Polish Patent Office vol 31 no 2010 Heat Transfer Engineering, 31(1):90–97, 2010 Copyright C Taylor and Francis Group, LLC ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457630902976000 Research Regarding Heat Exchange Through Nanometric Polysynthetic Thermal Compound to Cooler–CPU Interface ˆ IOAN MIHAI, CRISTIAN PIRGHIE, and VLAD ZEGREAN Department of Management, Mechatronics, and Mechanical Engineering, “Stefan cel Mare” University, Suceava, Romania This article documents some of the factors that influence the heat transfer through polysynthetic thermal compounds at the central processing unit (CPU)/heat sink interface First, special attention is paid to assessing the effect of mechanical and thermal properties of the contacting bodies, applied contact pressures, and surface roughness characteristics, as well as the use of different thermal interface materials on the maximum temperature experienced by the CPU Second, it can be appreciated that good wetting of the mating surfaces and the retention of asperity micro-contacts can become critical elements in effectively removing the heat generated by the CPU This study uses the Holman model for calculating the heat transfer, indicating the role of thermal contact resistance The mathematical results clearly indicate that any strain in the interface material leads to a change in thermal contact resistance, with an effect on CPU overheating Experimentally obtained images with an atomic force microscope clearly revealed that eliminating micro-gaps using thermal interface materials can facilitate the heat transfer by significantly lowering the thermal contact resistance of the CPU/heat sink assembly This effect is amplified by the plastic deformation of micro-contacts due to high contact pressures and lower micro-hardness levels INTRODUCTION made of a copper plate to which are fitted a series of bars that are set in the shape of a grid, made of aluminum and fixed with a steel bracket As time went on, a temperature sensor has been incorporated in radiators, inside the copper plate Another step in the processor cooling is based on the usage of heat pipes [4], which implies passive cooling (the fan is not used), reaching performances that are at least equal to the classical systems Still, these systems are significantly more expensive than the usual coolers A final stage in the CPU cooling systems’ modifications consisted of research regarding agents such as liquid water and Freon [1, 4] Simultaneously with the CPU cooling systems’ development, different interface materials were tested, which can allow a maximum of heat flow transfer between the CPU and the radiator [1, 5–8] A number of thermal transfer materials have also been tried, designed for the interface between the cooling system and the processor core It was assumed that the roughness and blisters prevent more than half of the contact surface between the processor core and the radiator forming a good, heat-conducting surface even when they are in direct contact This problem can be alleviated by The silent and stable functioning of the central processing unit (CPU) [1, 2] represents a desideratum that involves more profound research in the field Until now, specific classical cooling systems based on coolers have been used exclusively Over the years, processors evolved so the dissipated energy manifested as heat became increasingly larger, a fact that leads to the development of new cooling systems So, during a first phase, mono-bloc radiators were built, on which were mounted large fans that assured an increased air flow [2] If the first radiators were made of aluminum, a next step in raising the efficiency consisted in using a copper insertion inside the aluminum radiator [1] In this respect, proper materials were used to assure good thermal conductivity, often including copper or ceramic materials A series of new ideas regarding the size and configuration of such cooling systems was developed [3] Thus, the radiator was Address correspondence to Dr Ioan Mihai, Department of Management, Mechatronics and Mechanical Engineering, “Stefan cel Mare” University, Str Universitatii nr 13, 720229, Suceava, Romania E-mail: mihai.i@fim.usv.ro 90 I MIHAI ET AL filling the space between the cooler and CPU with a material that provides good heat conductivity Several kinds of thermal transfer materials have been developed They should be capable of being compressed to within 25% of their total thickness This is necessary due to the tolerance variation of large gap situations The next section discusses in detail the technical elements of three classes of materials that are used in this architecture ELASTOMERIC THERMAL PADS This class of materials [8] (also known as gap-filler pads) is used to improve heat dissipation across large gaps, by establishing a conductive heat-transfer path between the mating surfaces Thermal pads [8] are typically 200 µm to 1000 µm thick and are used for cooling low-power devices, such as chipsets and mobile processors The pad consists [8] of a filled elastomer, with filler materials ranging from ceramic to boron nitride for varying thermal performance Metal particles are seldom used due to the risk of dislodged particles resulting in electrical shorts Typical failure mechanisms [8] have increased thermal resistance due to loss of contact at one or more surfaces or inadequate pressure The thermal performance is also sensitive to the contact pressure at the mated surfaces PHASE-CHANGE FILMS (PCFs) A first category uses the “phase-change” phenomenon Phase-change films (PCFs) [8] are a class of materials that undergoes a transition from a solid to semi-solid phase when heat is applied The material is in a liquid phase under die-operating conditions The thermal materials melted when the heat reached the level of 55◦ C and tried to fill the blisters situated between the two devices involved in the cooling system Although theoretically the process works, several undesired aspects can appear: • The larger blisters are not filled with this kind of material, so performances are limited • The thermal compound layer layout is not regular • A large amount of force between the processor and the radiator is needed • In the process of disassembling the processor, the interface is destroyed THERMAL GREASE The second kind of thermal transfer materials is called “thermal grease.” It is made of thermal conductive ceramic mixed with silicone or hydrocarbon oils in order to make a paste [8] The stronger the contact between the two surfaces, the better heat transfer engineering 91 the thermal transfer paste that fills the blisters and eliminates air Thermal grease ensures a very low thermal resistance and it is also an electricity conductor One of its disadvantages is that it gets dry over time, thermal resistance grows, and thermal transfer becomes increasingly poor after a period of time The “thermal compound” is an augmented thermal transfer paste, which becomes liquid and fills the blisters Unlike “thermal grease,” after the interface is obtained and a certain temperature level is reached, the paste becomes similar to rubber Two kinds of paste can be found on the market: those containing silicone and those without silicone The ones based on silicone are used more frequently and offer a good performance The other ones are designed for the professional market sector and use aluminum, nitrates, or other substances that conduct heat One of the thermal transfer paste advantages is the recycling of the amalgam after the processor has been changed, and the other is the fact that it can fill large blisters inaccessible to thermal grease Continued development in this area is necessary to satisfy the insatiable performance demands of the next generation of processors EXPERIMENTAL RESEARCH REGARDING THE NANOMETRIC FILM THERMAL COMPOUND With the help of an atomic force microscope AFM-Universal SPM, processing unit module SPC 400, and electronic control unit SFM 220A, Park Scientific Instruments firm, the interface layer was scanned for different processors Multiple images were obtained, out of which this article presents the most suggestive ones for an AMD CPU AFM leads to determination of the parameters of a scanned section through tracing of a histogram in the zone under surveillance In the first stage, an overall layout (scale ì àm) was obtained, one that includes an adequate zone for cooling and a damaged area (with void spaces) This can be easily noticed in Figure and Table Tables 1–4 contain the technical parameters corresponding to Figures 1–4, obtained by means of the atomic force microscope Analysis of the image and of the obtained parameters reveals the following: • The surface is adequate for thermal exchange, when the material layer has the same height, does not present holes or clefts in the structure Table The AFM technical parameters for the transition zone Parameter Value Parameter Value X scale Y scale Force Image Scan Rate Mode 3.00 µ 3.00 µ nN Z CH0 1.00 Hz AIR SFM1 Median height Average height Peak to valley RMS roughness AVE roughness Data points 171.60A˚ 171,81A˚ 2843.10A˚ 338.68A˚ 244.88A˚ 16,384 vol 31 no 2010 92 I MIHAI ET AL Table The AFM technical parameters, for a surface with incipient fault appearance Parameter Value Parameter Value X scale Y scale Force Image Scan rate Mode 1.00 µ 1.00 µ nN Z CH0 1.00 Hz AIR SFM1 Median height Average height Peak to valley RMS roughness AVE roughness Data points 117.00A˚ 114.95A˚ 2039.75A˚ 218.62A˚ 112.14A˚ 16,384 Table The AFM technical parameters, when the imperfections advance in the surface Figure An overall image of the interface layer Parameter Value Parameter Value X scale Y scale Force Image Scan rate Mode 1.00 µ 1.00 µ nN Z CH0 1.00 Hz AIR SFM1 Median height Average height Peak to valley RMS roughness AVE roughness Data points 93.60A˚ 72.91A˚ 2051.40A˚ 237.50A˚ 151.99A˚ 16,384 Table The AFM technical parameters for a damaged surface Figure ance Parameter Value Parameter Value X scale Y scale Force Image Scan rate Mode 1.00 µ 1.00 µ nN Z CH0 1.00 Hz AIR SFM1 Median height Average height Peak to valley RMS roughness AVE roughness Data points −50.70A˚ −78.59A˚ 2554.50A˚ 432.58A˚ 347.36A˚ 16,384 Adequate surface for heat conductance with incipient fault appear- Figure Advance of the transition zone heat transfer engineering Figure Inadequate surface for heat conductance vol 31 no 2010 I MIHAI ET AL • A transition zone appears, simultaneously with small holes or accentuated clefts • The surface is inadequate for thermal exchange when the layer height is maintained only on limited sections, and there appear quasi-total deformations of the thermal transfer surface marked by holes and deep clefts In order to study the surface appearance in detail, the AFM scanned surface was reduced to × µm; thus, Figures and were obtained Details of the zone (scale ì àm) that does not display faults on a large surface section are revealed in Figure Figure clearly shows that the surface is largely uniform, with small holes that can have a medium depth according to ˚ In comparison to the the AFM obtained graphs of about 20A ˚ depth (peak to valley) of the clefts, i.e., a maximum of 2039.75A (see Table 2), it immediately becomes apparent that, for a surface with holes, heat exchange is not entirely compromised Figure (scale ì àm) demonstrates the transition beginning with gradual damage that reveals the developing of blisters in comparison with the previous situation This figure presents basically the same aspects as in the previous case, evidencing a ˚ (see Table 3) cleft depth evolution to only 2051.40A A fully damaged thermal compound material surface (scale 1.4 ì 1.4 àm) appears in Figure The inadequate heat exchange surface shown in Figure clearly reveals in-depth damage of ˚ (see Table 4) A maximum of 3564.60A ˚ has been 2554.50A obtained on a different scanned surface of the same type The ˚ holes in Figure have a medium depth of 150A Based on the experimental research, the assumption is correct that situations could occur in which the thermal transfer surface can be damaged on several sections From the presented images, a fact clearly emerges, namely, that larger or smaller penetrations can appear in the depth of the thermal transfer layer Our assertions are also confirmed by [8]: “Under hightemperature bake, the formulation chemistries utilized in typical thermal greases result in separation of the polymer and filler matrix due to the migration of the polymer component The separation and loss of polymeric material could result in poor wetability at the interfaces, resulting in an increase in thermal resistance, also known as “dry-out” (shown in Figure 5).” This phenomenon [8] is strongly dependent on the temperature of the material, with higher temperatures resulting in accelerated degradation The failure mechanisms that can be encountered are strongly related to the thermal grease operating temperature and the number of on/off cycles that the processor assembly has been subjected to The rate of thermal degradation [8] is also dependent on the surface finish of the mating surfaces The pump-out mechanism and phase separation mechanisms [8] “have an exponential dependence on temperature, with a twofold increase in degradation for every 10◦ C increase in average operating temperature of the interface material.” Thus, it is imperative to make performance calculations in order to establish to what extent thermal transfer is affected HEAT EXCHANGE CALCULATION AT THE COOLER–CPU INTERFACE IN THE HYPOTHESIS OF THE ADEQUATE OR INADEQUATE THERMAL TRANSFER SURFACES Heat exchange at the CPU–cooler interface can be interpreted as conductive, unidirectional with linear heat sources [9, 10] It is obvious that the heat source is the core of the CPU [11], a case in which the conducted heat flow depends on the processor type, the emanation power, and the efficiency of the cooling system As we have previously shown, it is desirable that a major quantity of CPU heat emission be absorbed The desired heat is achieved with a thermal compound paste Examination of various packaging techniques reveal that the junction-to-coolant thermal resistance is [11–19], in fact, composed largely of an internal (Rjc ) conductive resistance and primarily of an external (Rex ) convective resistance (see Figure 6) Figure Typical illustration of thermal grease phase separation and dry-out heat transfer engineering 93 vol 31 no 2010 94 I MIHAI ET AL Figure Primary thermal resistances in a single-chip package The total thermal spreading resistance for single-chip packages is: RT = Rjc + Rsp + Rex + Rfl K W (1) where: The internal resistance Rjc is encountered in the flow of dissipated heat from the active chip surface through the material used to support and bond the chip and on to the case of the integrated-circuit package Spreading resistance Rsp arises from the three-dimensional nature of heat flow in the heat spreader and heat sink base External resistance Rex is for convective cooling; Flow resistance Rfl : The transfer of heat to a flowing gas or liquid that does not undergo phase change is an increase in the coolant temperature from the inlet temperature to an outlet temperature For each type of radiator, the values of thermal resistivity can be obtained from straight-line charts for natural or forced convection In the case of the chosen radiator, the manufacturer indicates, for natural and forced convection, the values of thermal resistivity relative to the air speed Using the Holman model [20] one can appraise the heat exchange in a CPU–radiator assembly depicted in Figure In this particular case it is interesting to find out whether a temperature rise occurs at the interface layer when it has nanometric imperfections If this assumption can be proved by calculation, then it can be presumed that the interface material imperfections may be one factor that causes the CPU failure Consider an aluminum heat sink with base-plate dimensions of 60 × 60 × 1.3 mm thick Related values are: thermal conductivity of aluminum and air kAl = 170.00 W/m-K, kair = 0.026 W/m-K, kinematic viscosity of air ν = 1.5 × 10−5 m2 /s, air density ρ = 1.2 kg/m3 , heat capacity of air Cp = 1.0 kJ/kg-K, Prandtl number for air Pr = 0.7, loss coefficient K = 0.9, ambient temperature Ta = 316 K, power dissipation P = 22.5 W, heat sink width w = 0.06 m, heat sink height hhs = 0.037 m, number of fins Nf = 28, height of fins hf = 0.0355 m, thickness of fins tf = 0.0013 m, and shroud spacing hb = 0.003 m In the following relations, Eqs (2)–(11), we made use of the model from [20] and [21] Calculate hydraulic diameter of heat sink/shroud passage area from: Dh = · Area [m] Perimeter (2) Holman [20] indicates the initial use of a certain “guess value,” marked as Vel The authors of this paper gave this Vel an initial value of 0.2 Holman [20] also indicates the use of the relation given next here, which he obtained by solving a threeequation system (pressure due to density difference, pressure drop due to friction, temperature rise due to power dissipation): V = root − 2· Vel g · P · hhs Ta · Area · Cp · ρ 64·ν Vel·Dh · hhs Dh +K · Vel (3) Calculate Reynolds number from: Re = V · Dh ν (4) According to Re, one can establish the type of flow (laminar, transitory or turbulent) One can calculate the friction factor between two reciprocating parts in contact: f= Figure Parallel flat walls with internal heat sources heat transfer engineering vol 31 no 2010 64 Re (5) I MIHAI ET AL One then obtains Reynolds number value on the direction of air flow in the radiator: V · hhs ν Rex = (6) Wall heat flux is give by: Qw = W m2 P (Nf · · hf + w) · hhs (7) Calculate the heat sink temperature rise from: δT = Qw · hhs kair 1 (0.6795 · Rex ) · Pr (8) [K] In order to observe the thermal convection data, ref [9] recommends for Nusselt number: Nu = 0.453 · Rex · Pr (9) Calculate the heat transfer coefficient: hhs h= Nu · · dx kair x hhs W m2 K (10) Calculate the fin efficiency: ηfin tf = hf + · h kAl · tf · hf (11) In order to determine the temperature field we use the general heat conductance equation [9, 10]: ∂T qv = α∇ T + ∂τ ρcp (12) Ts,2 = T∞,2 + 95 T∞,1 − T∞,2 + · δ · qv 1+ h2 h1 + hk2 δ h1 + δ k [K] (16) The maximum amount of heat generated by the CPU was deduced by calculations and represented as a matrix Using the data obtained from the Holman model and Eq (14), it was possible to calculate the temperature field along the x direction The variation of the thermal conduction coefficient, induced by the presence of air gaps, was taken into account RESULTS OBTAINED THROUGH CALCULATION The mathematic model achieved in MathCad allows the calculation of the temperature field at the CPU surface, toward the interface and radiator The authors considered the internal source of heat as being directly proportional to the energy generated by each kind of processor Figure shows the field of isotherms that corresponds to the CPU interface, for the same thermal conductivity coefficient Figure presents a calculation simulation to the effect that a part of the interface shows imperfections, in which case the coefficient of thermal conduction is altered Easily noticeable is a significant temperature rise for the second case, which can affect the CPU’s progress This is borne out by ref [8]: “It is a well-known fact that the reliability of circuits (transistors) is exponentially dependent on the operating temperature of the junction As such, small differences in operating temperature (order of 10–15◦ C) can result in a ∼2X difference in the lifespan of the devices The other factor is the speed of the microprocessor At lower operating temperatures, where qv represents the CPU-generated source density [W/m3 ] Generally qv is a time-variable function For short spacing it can be considered constant A study of heat exchange will be conducted, based on the following hypotheses: The walls are infinite parallel plates, qv = constant, and heat conductance occurs unidirectionally If we assume that heat conductance occurs in the x direction, the heat exchange general equation becomes: qv d2 T =− dx k (13) If one operates the integration, one obtains the temperature field equation, in the case of the infinite parallel flat walls with inside heat sources: T(x) = −qv x2 + 2k Ts,2 − Ts,1 qv δ + 2δ k · x + Ts,1 [K] (14) Ts,1 and Ts,2 are the temperatures of the exterior parts of the wall (see Figure 7): Ts,1 = T∞,1 + T∞,2 − T∞,1 + · δ · qv 1+ h1 h2 + hk1 δ h2 + δ k [K] (15) heat transfer engineering Figure The temperature field in the interface layer, for the same thermal conductivity coefficient vol 31 no 2010 96 I MIHAI ET AL • In time, a thermal compound layer fatigue appears, which leads to the CPU “drying” phenomenon (confirmed by [8] and [22]) • The CPU is wrongly assembled, added to which there occurs full or partial damage of the thermal compound layer (confirmed by [8]) • The cooler capacity for undertaking the heat flow generated by the CPU is insufficient, because of the convective phenomenon or to the wrong choice (confirmed by [23]) • The temperature does not present a sufficiently fast diminishing degree if the thermal compound layer does not have a sufficient conductive coefficient (confirmed by [7] and [18]) Consequently, irrespective of the cooling method, it is vital to use thermal compound materials that have an adequate conductive coefficient [24, 25] that does not deteriorate with time Figure The temperature field in the interface, flawed layer due to reduced gate delay, microprocessors can operate at higher speeds A secondary effect of lower temperatures is related to a reduction in leakage power dissipation of the devices, which manifests itself as reduction in overall power dissipation These two factors combined dictate the operating temperature of devices as a function of the speed of the device.” CONCLUSIONS In this article, only a few issues regarding the influence of cooling at the CPU–cooler interface, separated by nanometric polysynthetic thermal compound film, have been presented In a first stage we noticed from the AFM obtained Figures 1–4 that there are cases in which blisters appear in the thermal compound material We showed that in this case the structure will be inhomogeneous and the thermal compound material can be breached In this situation the heat conduction coefficient is not prompted by the thermal compound material but rather by air Thus, faults appear that we can associate to a semi-sphere or a semi-ellipsoid The fact remains definitive that in these volumes appear “stagnant circulation areas,” in which the presence of air blocks heat transfer In this case, there appears a cooling fault, characterized by the impossibility of diminishing the CPU temperature, which initially leads to a global superheating and finally to irreversible damage In order to verify the assumptions that were made, we proposed a mathematical model, in the hypothesis of a homogeneous or inhomogeneous material structure Based on the experimentally obtained results (CPU interface) and on the mathematical models, we can uphold that in certain well-defined situations a CPU can be destroyed if: • The thermal compound film thickness is irregular on a sufficiently large area (confirmed by [8]) heat transfer engineering NOMENCLATURE Area Cp cp Dh f g h h1 , h2 hb hhs hf k K kair kAl Nf Nu P Perimeter Pr qv Qw Re Rex Rex Rfl Rjc Rsp RT T Ta area of the radiator, m2 heat capacity of air, J/kg-K specific heat of CPU material at constant pressure, J/kg-K hydraulic diameter of heat sink/shroud passage area, m friction factor acceleration due to gravity, m/s2 heat transfer coefficient, W/m2 -K heat transfer coefficient, on each side of the parallel flat walls with internal heat sources, W/m2 -K shroud spacing, m heat sink height, m height of fins, m thermal conductivity, W/m-K loss coefficient thermal conductivity of air, W/m-K thermal conductivity of aluminum, W/m-K number of fins Nusselt number power dissipation, W perimeter of the radiator, m Prandtl number for air CPU generated source density, W/m3 wall heat flux, W/m2 Reynolds number Reynolds number on the direction of air flow in the radiator external resistance, W/K flow resistance, W/K the internal resistance, W/K spreading resistance, W/K total thermal spreading resistance, W/K temperature, K ambient temperature, K vol 31 no 2010 I MIHAI ET AL tf Tmax Ts,1 ,Ts,2 T(x) T∞,1 , T∞,2 V Vel w x xm thickness of fins, m the maximum wall temperature, K surface temperatures, K temperature field equation, K coolant temperature, K velocity, m/s guess value heat sink width, m heat spread direction, m neutral plan equation, m [15] [16] [17] [18] Greek Symbols [19] α δ δT ηfin ν ρ τ ∇ 2T thermal diffusivity, m /s characteristic length in the x direction, m heat sink temperature rise, K fin efficiency, % kinematic viscosity of air, m2 /s air density, kg/m3 time, s the Laplacian of temperature [20] [21] [22] REFERENCES [23] [1] Loyd, C., A Silent PC, PC Magazine, pp 91–96, 2006 [2] Azar, K., and Tavassoli, B., How Much Heat Can Be Extracted From a Heat Sink?, Electronics Cooling, vol 9, no 2, pp 30–36, 2003 [3] Matei, S., Methods for CPU cooling, Xtrem PC, no 78, pp 46–57, 2006 [4] Wilson, J R., The Great Cooling Dilemma, Military & Aerospace Electronics, pp 34–40, 2006 [5] Thermal Management—Solutions for Electronics, Saint–Gobain Performance Plastics Corporation, AFF-1549-250-0107-SGCS, New York, 2004 [6] Mahajan, R., Chiu, C P., and Prasher, R., Thermal Interface Materials: A Brief Review of Design Characteristics and Materials, Electronics Cooling, vol 10, no 1, pp 10–19, 2004 [7] Blazej, D., Thermal Interface Materials, Electronics Cooling, vol 9, no 4, pp 14–20, 2003 [8] Viswanath, R., Wakharkar, V., Watwe, A., and Lebonheur V., Thermal Performance Challenges From Silicon to Systems, Intel Technology Journal Q3, pp 1–16, 2000 [9] Bejan, A., and Kraus, A D., Heat Transfer Handbook, pp 161571 and 947-1006, John Wiley & Sons, Hoboken, NJ, 2003 [10] Lienhard, J H IV, and Lienhard, J H V., A Heat Transfer Textbook, 3rd ed., pp 139166, Cambridge, MA, 2006 [11] Fitch, J S., A One-Dimensional Thermal Model for the VAX 9000TM Multi Chip Units, Western Research Laboratory, CA, July 1990 [12] CPU Thermal Management, AAVID Engineering, Inc., NH, 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Materials, Electronics Cooling, vol 9, no 3, pp 8–9, 2003 Ioan Mihai is a professor of heat transfer at “Stefan cel Mare” University, Suceava, Romania He received his Ph.D in 1996 from “Gh Asachi” Technical University, Iassy, Romania His main research interests are mini and micro heat exchangers, heat transfer, and microelectronic devices cooling He has published more than 90 articles in well-recognized journals, books, and proceedings Cristian Pˆırghie is a lecturer of physics at the Applied Mechanics Department, “Stefan cel Mare” University, Suceava, Romania He received his Ph.D in 2007 from “Al I Cuza” University, Iassy, Romania His main research interests are nanomaterials technologies and magnetic thin films He has published more then 20 articles in well-recognized journals, books and proceedings He is member of the IEEE Magnetics Society Vlad Flaviu Zegrean is a Ph.D student in the Applied Mechanics Department, “Stefan cel Mare” University of Suceava, Romania Currently, he is working on computer hardware technology and mechatronics He is trained in atomic force microscopy vol 31 no 2010