BOOKCOMP, Inc. — John Wiley & Sons / Page 1026 / 2nd Proofs / Heat Transfer Handbook / Bejan 1026 HEAT TRANSFER IN ELECTRONIC EQUIPMENT 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1026], (80) Lines: 2223 to 2266 ——— 0.0pt PgVar ——— Custom Page (3.0pt) PgEnds: T E X [1026], (80) Classes of Interstitial Materials, Proc. NSF/DITAC Workshop, Monash University, Mel- bourne, Victoria, Australia, pp. 103–115. Schl ¨ under, E. U., Krotzsch, P., and Hennecke, F. W. (1970). Gesetzm ¨ abkerten der W ¨ arme-und Stoff ¨ ubertragung bei der Prallstr ¨ omung aus Rung-und Schlitzd ¨ usen, Chem. Ing. Tech., 42, 333–338. Sergent, J., and Krum, A. (1994). Thermal Management Handbook for Electronic Assemblies, McGraw-Hill, New York. Semiconductor Industry Association (1997). National Technology Roadmap for Semiconduc- tors: Technology Needs, Semiconductor Industry Association, Washington, DC. Simons, R. E., Antonetti, V. W., Nakayama, W., and Oktay, S. (1997). Heat Transfer in Elec- tronic Packages, in Microelectronics Packaging Handbook, 2nd ed. Part I, Tummala, R. R., Rymaszewski, E. J., and Kloptenstein, A. G., eds., pp. 1-315 to 1-403, Chapman and Hall, New York, N.Y. Sitharamayya, S., and Raju, K. S. (1969). Heat Transfer between an Axisymmetric Jet and a Plate Hold Normal to the Flow, Can. J. Chem. Eng., 47, 365–368. Solbrekken, G. L., and Chiu, C P. (1998). Single Temperature Calibration Method for Die Level Temperature Sensors. Using a Single Temperature Technique, IEEE Trans. Compo- nents and Packaging Tech., 23(1), 40–46. Song, S., Lee, S., and Au, V. (1994). Closed Form Equation for Thermal Constriction/ Spreading Resistances with Variable Resistance Boundary Condition, Proc. 1994 IEPS Conference, pp. 111–121. Sparrow, E. M., and Bahrami, P. A. (1980). Experiments on Natural Convection from Vertical Parallel Plates with Either Open or Closed Edges, J. Heat Transfer, 102, 221–227. Starner, K. E., and McManus, H. N. (1963). An Experimental Investigation of Free Convection Heat Transfer from Rectangular Fin Arrays, J. Heat Mass Transfer, 85, 273–278. Stevens, J., and Webb, B. W. (1989). Local Heat Transfer Coefficients under an Axisymmetric, Single-Phase Liquid Jet, Proc. National Heat Transfer Conference, Philadelphia, pp. 113– 119. Swartz, E. T., and Pohl,R. O. (1989). Thermal Boundary Resistance, Rev. Modern Phys., 61(3). Tien, C. L., and Chen, G. (1994). Challenges in Microscale Conductive and Radiative Heat Transfer, J. Heat Transfer, 116, 799–807. Van de Pol, D. W., and Tierney, J. K. (1973). Free Convection Nusselt Number for Vertical U-Shaped Channels, J. Heat Transfer, 95, 542–543. Wadsworth, D. C., and Mudawar, I. (1990). Cooling of a Multichip Electronic Module by Means of Confined Two Dimensional Jets of Dielectric Liquid, J. Heat Transfer, 112, 891– 898. Wang, X. S., Dagan, Z., and Jiji, L. M. (1990). Heat Transfer between a Laminar Free-Surface Impinging Jet and a Composite Disk, Proc. 9th International Heat Transfer Conference, Vol. 4, Hemisphere Publishing, New York, p. 137. Watwe, A. A., Bar-Cohen, A., and McNeil, A. (1997). Combined Pressure and Subcooling Effects on Pool Boiling from a PPGA Chip Package, J. Electron. Packag., 119(2), 95–105. Welling, J. R., and Wooldridge, C. B. (1965). Free Convection Heat Transfer Coefficients from Rectangular Vertical Fins, J. Heat Transfer, 87, 439–444. Witzman, S. (1998). Thermal Modelingof Air Cooled Components Mounted on Printed Circuit Boards, in Advances in Thermal Modeling of Electronic Components and Systems, Vol. 4, A. Bar-Cohen and A. D. Kraus, eds., ASME, New York, pp. 179–250. BOOKCOMP, Inc. — John Wiley & Sons / Page 1027 / 2nd Proofs / Heat Transfer Handbook / Bejan REFERENCES 1027 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1027], (81) Lines: 2266 to 2287 ——— * 225.04701pt PgVar ——— Custom Page (3.0pt) * PgEnds: PageBreak [1027], (81) Womac, D. H. (1989). Single-Phase Axisymmetric Liquid Jet Impingement Cooling of Dis- crete Heat Sources, M.S. thesis, Department of Mechanical Engineering, Purdue University, West Lafayette, IN. Womac, D. J., Aharoni, G., Ramadhyani, S., and Incropera, F. P. (1990). Single Phase Liquid Jet Impingement Cooling of Small Heat Sources, in Heat Transfer 1990 (Proc. 9th Interna- tional Heat Transfer Conference), Vol. 4, Hemisphere Publishing, New York, pp. 149–154. Wroblewski, D., and Joshi, Y. (1992). Transient Natural Convection from a Leadless Chip Carrier in a Liquid Filled Enclosure: A Numerical Study, J. Electron. Packag., 114, 271– 279. Xu, Y., Luo, X., and Chung, D. D. L. (2000). Sodium Silicate Based Thermal Interface Material for High Thermal Contact Conductance, J. Electron. Packag., 122, 128–131. You, S. M., Simon, T. W., and Bar-Cohen, A. (1990). Experiments on Boiling Incipience with a Highly-Wetting Dielectric Fluid: Effects of Pressure, Subcooling and Dissolved Gas Content, Proc. 9th International Heat Transfer Conference, Jerusalem, Israel, Vol. 3, pp. 337–342. Yovanovich, M. M. (1990). Personal communication. Yovanovich, M. M., and Antonetti, V. W. (1988). Application of Thermal Contact Resistance Theory to Electronic Packages, in Advances in Thermal Modeling of Electronic Compo- nents and Systems, Vol. 1, A. D. Kraus, and A. Bar-Cohen, eds., Hemisphere Publishing, New York. Zeng, S., Chen, C H., Mikkelsen, J. C., and Santiago, J. G. (2000). Fabrication and Charac- terization of Electrokinetic Micro Pumps, Proc. Itherm, May 23–26, pp. 31–36. Zorbil, V., Stulc, P., and Polase, F. (1988). Enhancement Cooling of Boards with Integrated Circuits by Heat Pipes, Proc. 3rd International Heat Pipe Symposium, Tsukuba, Japan, pp. 273–279. Zuber, N. (1959). Atomic Energy Commission Technical Information Service, Report AECU- 4439, Atomic Energy Commission, Washington, DC. BOOKCOMP, Inc. — John Wiley & Sons / Page 1029 / 2nd Proofs / Heat Transfer Handbook / Bejan 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [First Page] [1029], (1) Lines: 0 to 91 ——— 6.25609pt PgVar ——— Normal Page * PgEnds: PageBreak [1029], (1) CHAPTER 14 Heat Transfer Enhancement R. M. MANGLIK Thermal-Fluids and Thermal Processing Laboratory Department of Mechanical, Industrial and Nuclear Engineering University of Cincinnati, Cincinnati, Ohio 14.1 Introduction 14.1.1 Classification of enhancement techniques 14.1.2 Performance evaluation criteria 14.2 Treated surfaces 14.2.1 Boiling 14.2.2 Condensing 14.3 Rough surfaces 14.3.1 Single-phase flow 14.3.2 Boiling 14.3.3 Condensing 14.4 Extended surfaces 14.4.1 Single-phase flow 14.4.2 Boiling 14.4.3 Condensing 14.5 Displaced enhancement devices 14.5.1 Single-phase flow 14.5.2 Boiling 14.5.3 Condensing 14.6 Swirl flow devices 14.6.1 Single-phase flow 14.6.2 Boiling 14.6.3 Condensing 14.7 Coiled tubes 14.7.1 Single-phase flow 14.7.2 Boiling 14.7.3 Condensing 14.8 Additives for liquids 14.8.1 Single-phase flow 14.8.2 Boiling 14.9 Active techniques 14.10 Compound enhancement Nomenclature References 1029 BOOKCOMP, Inc. — John Wiley & Sons / Page 1030 / 2nd Proofs / Heat Transfer Handbook / Bejan 1030 HEAT TRANSFER ENHANCEMENT 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1030], (2) Lines: 91 to 108 ——— 0.0pt PgVar ——— Normal Page PgEnds: T E X [1030], (2) 14.1 INTRODUCTION The conversion, utilization, and recovery of energy in every industrial, commercial, and domestic application involve a heat exchange process. Some common examples are steam generation and condensation in power and cogeneration plants; sensible heating and cooling of viscous media in thermal processing of chemical, pharma- ceutical, and agricultural products; refrigerant evaporation and condensation in air conditioning and refrigeration; gas flow heating in manufacturing and waste-heat re- covery; air and liquid cooling of engine and turbomachinery systems; and cooling of electrical machines and electronic devices. Improved heat exchange, over and above that in the usual or standard practice, can significantly improve the thermal efficiency in such applications as well as the economics of their design and operation. The engineering cognizance of the need to increase the thermal performance of heat exchangers, thereby effecting energy, material, and cost savings as well as a con- sequential mitigation of environmental degradation had led to the development and use of many heat transfer enhancement techniques. These methods have in the past been referred to variously as augmentation and intensification, among other terms. There is an enormous database of technical literature on the subject, now estimated at over 8000 technical papers and reports, which has been disseminated periodically in numerous bibliographic reports (Bergles et al., 1983, 1991, 1995; Jensen and Shome, 1994), reviews (Webb and Bergles, 1983a; Webb, 1987; Shatto and Peterson, 1996; Bergles, 1998, 1999; Manglik and Bergles, 2002a), and monographs and edited texts (Thome, 1990; Webb, 1994; Manglik and Kraus, 1996; Kakac¸ et al., 1999). This information growth, represented by the typical yearly distribution of technical pub- lications depicted in Fig. 14.1, urgently warrants that a digital library of enhanced heat and mass transfer be established (Bhatnagar and Manglik, 2002). This literature documents the extensive research effort devoted to establishing the conditions under which enhancement techniques will improve the heat or mass transfer in various ap- plications. An effort that began more than 140 years ago, when the first attempt to enhance heat transfer coefficients in condensing steam was reported in the classical study by J. P. Joule (1861), continues to be a major research and development activity (Manglik et al., 2000; Bergles, 2000). Enhancement techniques essentially reduce the thermal resistance in a conven- tional heat exchanger by promoting higher convective heat transfer coefficient with or without surface area increases (as represented by fins or extended surfaces). As a result, the size of a heat exchanger can be reduced, or the heat duty of an existing exchanger can be increased, or the pumping power requirements can be reduced, or the exchanger’s operating approach temperature difference can be decreased. The latter is particularly useful in thermal processing of biochemical, food, plastic, and pharmaceutical media, to avoid thermal degradation of the end product. On the other hand, heat exchange systems in spacecraft, electronic devices, and medical applica- tions, for example, may rely primarily on enhanced thermal performance for their successful operation. The commercialization of enhancement techniques, where the technology has been transferred from the research laboratory to full-scale industrial use of those that are more effective and workable (Bergles et al., 1991; Fletcher and BOOKCOMP, Inc. — John Wiley & Sons / Page 1031 / 2nd Proofs / Heat Transfer Handbook / Bejan INTRODUCTION 1031 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1031], (3) Lines: 108 to 139 ——— 1.097pt PgVar ——— Normal Page PgEnds: T E X [1031], (3) Figure 14.1 Yearly growth of the published technical literature on heat transfer enhancement (citations up to mid-1995). (From Bergles et al., 1995.) Andrews, 1994), has also led to a larger number of patents (Webb et al., 1983; Bergles et al., 1991; Webb et al., 1993, 1994). In this chapter we give an overview of the state of the art in heat transfer enhance- ment in various applications and provide a review of the pertinent literature. The use of many different techniques, their thermal–hydraulic performance (with lists of predictive correlations for the heat transfer and pressure drop, or reference to design databases, wherever available), and some methodologies for design optimization and overall performance evaluation of heat exchangers are outlined. 14.1.1 Classification of Enhancement Techniques Sixteen different enhancement techniques have been identified by Bergles et al. (1983, 1991, 1995), which can be classified broadly as passive and active techniques. A list of the various methods or devices under each of these two categories in given in Table 14.1. The primary distinguishing feature is that unlike active methods, passive techniques do not require direct input of external power. They generally use surface BOOKCOMP, Inc. — John Wiley & Sons / Page 1032 / 2nd Proofs / Heat Transfer Handbook / Bejan 1032 HEAT TRANSFER ENHANCEMENT 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1032], (4) Lines: 139 to 153 ——— 2.78607pt PgVar ——— Short Page PgEnds: T E X [1032], (4) TABLE 14.1 Classification of Various Heat Transfer Enhancement Techniques Passive Techniques Active Techniques Treated surfaces Mechanical aids Rough surfaces Surface vibration Extended surfaces Fluid vibration Displaced enhancement devices Electrostatic fields Swirl flow devices Injection Coiled tubes Suction Surface tension devices Jet impingement Additives for liquids Additives for gases Compound Enhancement Two or more passive and/or active techniques that are employed together or geometrical modifications to the flow channel, or incorporate an insert, material, or additional device. Except for extended surfaces, which increase the effective heat transfer surface area, these passive schemes promote higher heat transfer coefficients by disturbing or altering the existing flow behavior. This, however, is accompanied by an increase in the pressure drop. In the case of active techniques, the addition of ex- ternal power essentially facilitates the desired flow modification and the concomitant improvement in the rate of heat transfer. The use of two or more techniques (passive and/or active) in conjunction constitutes compound enhancement. The effectiveness of any of these methods is strongly dependent on the mode of heat transfer (single-phase free or forced convection, pool boiling, forced convection boiling or condensation, and convective mass transfer), and type and process appli- cation of the heat exchanger. In considering their specific applications, a descriptive characterization of each of the 16 techniques is useful in assessing their potential. The descriptions of passive techniques, as given by Bergles (1998), are as follows: 1. Treated surfaces are heat transfer surfaces that have a fine-scale alteration to their finish or coating. The alteration could be continuous or discontinuous, where the roughness is much smaller than what affects single-phase heat transfer, and they are used primarily for boiling and condensing duties. 2. Rough surfaces are generally surface modifications that promote turbulence in the flow field, primarily in single-phase flows, and do not increase the heat transfer surface area. Their geometric features range from random sand-grain roughness to discrete three-dimensional surface protuberances. 3. Extended surfaces, more commonly referred to as finned surfaces, provide an effective heat transfer surface area enlargement. Plain fins have been used routinely BOOKCOMP, Inc. — John Wiley & Sons / Page 1033 / 2nd Proofs / Heat Transfer Handbook / Bejan INTRODUCTION 1033 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1033], (5) Lines: 153 to 183 ——— 3.94pt PgVar ——— Short Page PgEnds: T E X [1033], (5) in many heat exchangers. The newer developments, however, have led to modified finned surfaces that also tend to improve the heat transfer coefficients by disturbing the flow field in addition to increasing the surface area. 4. Displaced enhancement devices are inserts that are used primarily in confined forced convection, and they improve energy transport indirectly at the heat exchange surface by “displacing” the fluid from the heated or cooled surface of the duct with bulk fluid from the core flow. 5. Swirl flow devices produce and superimpose swirl or secondary recirculation on the axial flow in a channel. They include helical strip or cored screw-type tube inserts, twisted ducts, and various forms of altered (tangential to axial direction) flow arrangements, and they can be used for single-phase as well as two-phase flows. 6. Coiled tubes are what the name suggests, and they lead to relatively more compact heat exchangers. The tube curvature due to coiling produces secondary flows or Dean vortices, which promote higher heat transfer coefficients in single-phase flows as well as in most regions of boiling. 7. Surface tension devices consist of wicking or grooved surfaces, which direct and improve the flow of liquid to boiling surfaces and from condensing surfaces. 8. Additives for liquids include the addition of solid particles, soluble trace ad- ditives, and gas bubbles in single-phase flows, and trace additives, which usually depress the surface tension of the liquid, for boiling systems. 9. Additives for gases include liquid droplets or solid particles, which are intro- duced in single-phase gas flows in either a dilute phase (gas–solid suspensions) or dense phase (fluidized beds). Descriptions for the various active techniques have been given as follows: 1. Mechanical aids are those that stir the fluid by mechanical means or by rotating the surface. The more prominent examples include rotating tube heat exchangers and scraped-surface heat and mass exchangers. 2. Surface vibration has been applied primarily, at either low or high frequency, in single-phase flows to obtain higher convective heat transfer coefficients. 3. Fluid vibration or fluid pulsation, with vibrations ranging from 1.0 Hz to ultra- sound (∼1.0 MHz), used primarily in single-phase flows, is considered to be perhaps the most practical type of vibration enhancement technique. 4. Electrostatic fields, which could be in the form of electric or magnetic fields, or a combination of the two, from dc or ac sources, can be applied in heat exchange systems involving dielectric fluids. Depending on the application, they can promote greater bulk fluid mixing and induce forced convection (corona “wind”) or electro- magnetic pumping to enhance heat transfer. 5. Injection, used only in single-phase flow, pertains to the method of injecting the same or a different fluid into the main bulk fluid either through a porous heat transfer interface or upstream of the heat transfer section. BOOKCOMP, Inc. — John Wiley & Sons / Page 1034 / 2nd Proofs / Heat Transfer Handbook / Bejan 1034 HEAT TRANSFER ENHANCEMENT 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1034], (6) Lines: 183 to 205 ——— -2.0pt PgVar ——— Normal Page PgEnds: T E X [1034], (6) 6. Suction involves either vapor removal through a porous heated surface in nucle- ate or film boiling, or fluid withdrawal through a porous heated surface in single-phase flow. 7. Jet impingement involves the direction of heating or cooling fluid perpendicu- larly or obliquely to the heat transfer surface. Single or multiple jets (in clusters or staged axially along the flow channel) may be used in both single-phase and boiling applications. As acknowledged by Bergles et al. (1983, 1996), there are some difficulties in classifying a few techniques, and the somewhat arbitrarily fuzzy distinctions between them should be recognized. A good example to illustrate this is the classification of some of the newer structured surfaces used in boiling (Bergles, 2000; Webb, 1994; Thome, 1990) as treated, rough, or extended surfaces. Perhaps a future subcatego- rization and/or recategorization of the enhancement techniques might be needed to sort out such issues in the ever-expanding database. Furthermore, as mentioned earlier, any two or more of these techniques (passive and/or active) may be employed simultaneously to obtain enhancement in heat trans- fer that is greater than that produced by only one technique itself. This simultane- ous utilization is termed compound enhancement. Some promising applications, for example, are in heat or mass exchangers where one technique may preexist; this is particularly so when the existing enhancement is from an active method. 14.1.2 Performance Evaluation Criteria The issue of quantifying and evaluating the performance of enhancement devices, with a very broad and universal set of criteria, is complex and difficult. As Bergles (1998) has pointed out in his survey of the subject: “It seems impossible to establish a generally applicable selection criterion. . . .” Besides the relative thermal–hydraulic performance improvements brought about by the enhancement devices, there are many factors that may have to be considered. They include economic (engineer- ing development, capital, installation, operating, maintenance, and other such costs), manufacturability (machining, forming, bonding, and other production processes), reliability (material compatibility, integrity, and long-term performance), and safety, among others. The assessment of these factors, as well as the enhanced convection performance, is usually application driven. The discussion in this chapter, however, will be restricted only to the convective thermal–hydraulic behavior, for which several criteria have been developed to quantify the relative enhancement in different applica- tions (Bergles, 1998; Webb, 1994; Kays and London, 1984; Bergles et al., 1974a,b). The enhanced heat transfer obtained in forced convection is always accompanied by an increase in the pressure drop. This is illustrated in Fig. 14.2 for typical cases of single-phase flows in (a) enhanced plate fin cores, and (b) tubes with structured sur- face roughness. As recommended by Marner et al. (1983), the results for the enhanced geometries are based on an equivalent parallel-plate duct (same plate separation) in the first case, and the “envelope” or “empty” tube diameter in the second case. This allows direct comparison of enhancement data with the “normal” or “smooth tube” BOOKCOMP, Inc. — John Wiley & Sons / Page 1035 / 2nd Proofs / Heat Transfer Handbook / Bejan INTRODUCTION 1035 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1035], (7) Lines: 205 to 212 ——— 0.097pt PgVar ——— Normal Page PgEnds: T E X [1035], (7) Figure 14.2 Typical thermal–hydraulic performance of enhanced surfaces: (a) enhanced plate fin geometries; (continued) performance. It may be noted that in many enhanced duct geometries, particularly with inserts and extended surfaces, the hydraulic diameter is different from their “par- ent” flow channel. The improved heat transfer coefficients due to enhancement are evident from Fig. 14.2, as are the concomitant friction factors. Thus, the problem is essentially one of finding the optimum or net gain after considering the overall energy use of the heat exchanger. In most practical applications of enhancement techniques, the following perfor- mance objectives, along with a set of operating constraints and conditions, are usually considered for optimizing the use of a heat exchanger: BOOKCOMP, Inc. — John Wiley & Sons / Page 1036 / 2nd Proofs / Heat Transfer Handbook / Bejan 1036 HEAT TRANSFER ENHANCEMENT 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1036], (8) Lines: 212 to 227 ——— * 19.097pt PgVar ——— Normal Page PgEnds: T E X [1036], (8) Figure 14.2 (Continued)(b) tubes with different internal roughness. 1. Increase the heat duty of an existing heat exchanger without altering the pump- ing power (or pressure drop) or flow rate requirements. 2. Reduce the approach temperature difference between the two heat-exchanging fluid streams for a specified heat load and size of exchanger. 3. Reduce the size or heat transfer surface area requirements for a specified heat duty and pressure drop. 4. Reduce the process stream’s pumping power requirements for a given heat load and exchanger surface area. . transfer interface or upstream of the heat transfer section. BOOKCOMP, Inc. — John Wiley & Sons / Page 1034 / 2nd Proofs / Heat Transfer Handbook / Bejan 1034 HEAT TRANSFER ENHANCEMENT 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1034],. and Radiative Heat Transfer, J. Heat Transfer, 116, 799–807. Van de Pol, D. W., and Tierney, J. K. (1973). Free Convection Nusselt Number for Vertical U-Shaped Channels, J. Heat Transfer, 95,. J. Heat Transfer, 112, 891– 898. Wang, X. S., Dagan, Z., and Jiji, L. M. (1990). Heat Transfer between a Laminar Free-Surface Impinging Jet and a Composite Disk, Proc. 9th International Heat Transfer