BOOKCOMP, Inc. — John Wiley & Sons / Page 795 / 2nd Proofs / Heat Transfer Handbook / Bejan REFERENCES 795 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 [795], (77) Lines: 2173 to 2214 ——— 3.0pt PgVar ——— Custom Page (-7.0pt) PgEnds: T E X [795], (77) Royal, J. H., and Bergles, A. E. (1978). Augmentation of Horizontal In-Tube Condensation by Means of Twisted-Tape Inserts and Internally Finned Tubes, J. Heat Transfer, 100, 17–24. Rudy, T. M., and Webb, R. L. (1981). Condensate Retention on Horizontal Integral-Fin Tubing, in Advances in Enhanced Heat Transfer, 20th National Heat Transfer Conference, ASME- HTD-18, ASME, New York, pp. 35–41. Saunders, E. A. D. (1988). Heat Exchangers Selection, Design and Construction, Wiley, New York. Schlager, L. M., Pate, M. B., and Bergles, A. E. (1990). Performance Predictions of Refrigerant–Oil Mixtures in Smooth and Internally Finned Tubes, ASHRAE Trans., 96(1), 161–182. Shah, M. M. (1979). A General Correlation for Heat Transfer during Film Condensation inside Pipes, Int. J. Heat Mass Transfer, 22, 547–556. Sklover, G. G. (1990). Generalized Data of Steam Condensation Computation in Horizontal Tube Bundles, Proc. 2nd International Symposium on Condensers and Condensation, Uni- versity of Bath, Bath, Somersetshire, England, pp. 203–212. Sklover, G. G., and Grigor’ev, V. G. (1975). Calculating the Heat Transfer Coefficient in Steam Turbine Condensers, Teploenergetika, 22(1), 86–91. Soliman, H. M. (1982). On the Annular-to-Wavy Flow Pattern Transition during Condensation inside Horizontal Tubes, Can. J. Chem. Eng., 60, 475–481. Soliman, H. M. (1983). Correlation of Mist-to-Annular Transition during Condensation, Can. J. Chem. Eng., 61, 178–182. Soliman, H. M. (1986). The Mist–Annular Transition during Condensation and Its Influence on the Heat Transfer Mechanism, Int. J. Multiphase Flow, 12(2), 277–288. Soliman, H. M.,Schuster, J. R.,and Berenson, P. J. (1968).A General HeatTransfer Correlation for Annular Flow Condensation, J. Heat Transfer, Trans. ASME, 90, 267–276. Souza, A. L., and Pimenta, M. M. (1995). Prediction of Pressure Drop during Horizontal Two-Phase Flow of Pure and Mixed Refrigerants, ASME Conference on Cavitation and Multiphase Flow, ASME-HTD-210, ASME, New York, pp. 161–171. Souza, A. L., Chato, J. C., Jabardo, J. M. S., Wattelet, J. P., Panek, J., Christoffersen, B., and Rhines, N. (1992). Pressure Drop during Two-Phase Flow of Refrigerants in Horizontal Smooth Tubes, ACRC Technical Report 25, University of Illinois, Urbana-Champaign, IL. Souza, A. L., Chato, J. C., Wattelet, J. P., and Christoffersen, B. R. (1993). Pressure Drop during Two-Phase Flow of Pure Refrigerants and Refrigerant–Oil Mixtures in Horizontal Smooth Tubes, ASME-HTD-243, ASME, New York, pp. 35–41. Spencer, E., and Hewitt, E. W. (1990). Analysis of an Earlier Geothermal Surface Condenser Design with Current Knowledge and Practice, Proc. 2nd International Symposium on Con- densers and Condensation, University of Bath, Bath, Somerset, England, pp. 135–146. Sweeney, K. A. (1996). The Heat Transfer and Pressure Drop Behavior of a Zeotropic Refrig- erant Mixture in a Microfinned Tube, M.S. thesis, Department of Mechanical and Industrial Engineering, University of Illinois, Urbana-Champaign, IL. Sweeney, K. A., and Chato, J. C. (1996). The Heat Transfer and Pressure Drop Behavior of a Zeotropic Refrigerant Mixture in a Microfinned Tube, ACRC Technical Report 95, University of Illinois, Urbana-Champaign, IL. Taitel, Y., and Dukler, A. E. (1976). A Model for Predicting Flow Regime Transitions in Horizontal and Near Horizontal Gas–Liquid Flow, AIChE J., 22(1), 47–55. BOOKCOMP, Inc. — John Wiley & Sons / Page 796 / 2nd Proofs / Heat Transfer Handbook / Bejan 796 CONDENSATION 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 [Last Page] [796], (78) Lines: 2214 to 2251 ——— 63.04701pt PgVar ——— Normal Page PgEnds: T E X [796], (78) Tien, C. L., Chen, S. L., and Peterson, P. F. (1988). Condensation inside Tubes, EPRI Project 1160-3 Final Report. Tinker, T. (1933). Surface Condenser Design and Operating Characteristics, paper contributed by the Central Power Station Committee of the Power Division for the Semi-annual Meet- ing, Chicago, June 25 to July 1, of the American Society of Mechanical Engineers. Traviss, D. P., Rohsenow, W. M., and Baron, A. B. (1973). Forced-Convective Condensation in Tubes: A Heat Transfer Correlation for Condenser Design, ASHRAE Trans., 79(1), 157– 165. Wang, Z Z., and Zhao, Z N. (1993). Analysis of Performance of Steam Condensation Heat Transfer and Pressure Drop in Plate Condensers, Heat Transfer Eng., 14(4), 32–41. Wang, S P., and Chato, J. C. (1995). Review of Recent Research on Heat Transfer with Mixtures, 1: Condensation, ASHRAE Trans., 101(1), 1376–1386. Wattelet, J. P. (1994). Heat Transfer Flow Regimes ofRefrigerants in a Horizontal-Tube Evapo- rator, Ph.D. dissertation, Department of Mechanical and Industrial Engineering, University of Illinois, Urbana-Champaign, IL. Wattelet, J. P., Chato, J. C., Christofferson, B. R., Gaibel, J. A., Ponchner, M., Shimon, R. L., Villaneuva, T. C., Rhines, N. L., Sweeney, K. A., Allen, D. G., and Hershberger, T. T. (1994). Heat Transfer Flow Regimes of Refrigerants in a Horizontal-Tube Evaporator, ACRC Technical Report 55, University of Illinois, Urbana-Champaign, IL. Webb, R. L. (1994). Principles of Enhanced Heat Transfer, Wiley-Interscience, New York. Webb, R. L., Rudy, T. M., and Kedzierski, M. A. (1985). Prediction of the Condensation Coefficient on Horizontal Integral-Fin Tubes, ASME J. Heat Transfer, 107, 369–376. Yabe, A. (1991). Active Heat Transfer Enhancement by Applying Electric Field, Proc. 3rd ASME/JSME Thermal Engineering Conference, Vol. 3, pp. xv–xxiii. Yang, C. Y., and Webb, R. L. (1997). A Predictive Model for Condensation in Small Hydraulic Diameter Tubes Having Axial Micro-fins, J. Heat Transfer, 119, 776–782. Yu, J., and Koyama, S. (1998). Condensation Heat Transfer of Pure Refrigerants in Microfin Tubes, Proc. 1998 International Refrigeration Conference at Purdue, pp. 325–330. Zener, C., and Lavi, A. (1974). Drainage Systems for Condensation, J. Eng. Power, 96, 209– 215. Zhang, C. (1994). Numerical Modeling Using a Quasi-Three Dimensional Procedure for Large Power Plant Condensers, J. Heat Transfer, 116, 180–188. Zhang, C. (1996). Local and Overall Condensation Heat Transfer Behavior in Horizontal Tube Bundles, Heat Transfer Eng., 17(1), 19–30. Zhang, C., and Zhang,Y. (1994). Sensitivity Analysis of Heat Transfer Coefficient Correlations on the Predictions of Steam Surface Condensers, Heat Transfer Eng., 15(2), 54–63. Zhang, C., Sousa, A. C. M., and Venart, J. E. S. (1993). TheNumerical and Experimental Study of a Power Plant Condenser, J. Heat Transfer, 115, 435–444. Zivi, S. M. (1964). Estimation of Steady-State Steam Void-Fraction by Means of the Principle of Minimum Entropy Production, J. Heat Transfer, Trans. ASME, 86, 247–252. BOOKCOMP, Inc. — John Wiley & Sons / Page 797 / 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] [797], (1) Lines: 0 to 89 ——— * 17.2201pt PgVar ——— Normal Page * PgEnds: PageBreak [797], (1) CHAPTER 11 Heat Exchangers ALLAN D. KRAUS University of Akron Akron, Ohio 11.1 Introduction 11.2 Governing relationships 11.2.1 Introduction 11.2.2 Exchanger surface area 11.2.3 Overall heat transfer coefficient 11.2.4 Logarithmic mean temperature difference 11.3 Heat exchanger analysis methods 11.3.1 Logarithmic mean temperature difference correction factor method 11.3.2 –N tu method Specific –N tu relationships 11.3.3 P –N tu,c method 11.3.4 ψ–P method 11.3.5 Heat transfer and pressure loss 11.3.6 Summary of working relationships 11.4 Shell-and-tube heat exchanger 11.4.1 Construction 11.4.2 Physical data Tube side Shell side 11.4.3 Heat transfer data Tube side Shell side 11.4.4 Pressure loss data Tube side Shell side 11.5 Compact heat exchangers 11.5.1 Introduction 11.5.2 Classification of compact heat exchangers 11.5.3 Geometrical factors and physical data 11.5.4 Heat transfer and flow friction data Heat transfer data Flow friction data 11.6 Longitudinal finned double-pipe exchangers 11.6.1 Introduction 797 BOOKCOMP, Inc. — John Wiley & Sons / Page 798 / 2nd Proofs / Heat Transfer Handbook / Bejan 798 HEAT EXCHANGERS 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 [798], (2) Lines: 89 to 168 ——— 0.97pt PgVar ——— Normal Page PgEnds: T E X [798], (2) 11.6.2 Physical data for annuli Extruded fins Welded U-fins 11.6.3 Overall heat transfer coefficient revisited 11.6.4 Heat transfer coefficients in pipes and annuli 11.6.5 Pressure loss in pipes and annuli 11.6.6 Wall temperature and further remarks 11.6.7 Series–parallel arrangements 11.6.8 Multiple finned double-pipe exchangers 11.7 Transverse high-fin exchangers 11.7.1 Introduction 11.7.2 Bond or contact resistance of high-fin tubes 11.7.3 Fin efficiency approximation 11.7.4 Air-fin coolers Physical data Heat transfer correlations 11.7.5 Pressure loss correlations for staggered tubes 11.7.6 Overall heat transfer coefficient 11.8 Plate and frame heat exchanger 11.8.1 Introduction 11.8.2 Physical data 11.8.3 Heat transfer and pressure loss 11.9 Regenerators 11.9.1 Introduction 11.9.2 Heat capacity and related parameters Governing differential equations 11.9.3 –N tu method 11.9.4 Heat transfer and pressure loss Heat transfer coefficients Pressure loss 11.10 Fouling 11.10.1 Fouling mechanisms 11.10.2 Fouling factors Nomenclature References 11.1 INTRODUCTION A heat exchanger can be defined as any device that transfers heat from one fluid to another or from or to a fluid and the environment. Whereas in direct contact heat exchangers, there is no intervening surface between fluids, in indirect contact heat exchangers, the customary definition pertains to a device that is employed in the trans- fer of heat between two fluids or between a surface and a fluid. Heat exchangers may be classified (Shah, 1981, or Mayinger, 1988) according to (1) transfer processes, BOOKCOMP, Inc. — John Wiley & Sons / Page 799 / 2nd Proofs / Heat Transfer Handbook / Bejan GOVERNING RELATIONSHIPS 799 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 [799], (3) Lines: 168 to 199 ——— 1.7pt PgVar ——— Normal Page PgEnds: T E X [799], (3) (2) number of fluids, (3) construction, (4) heat transfer mechanisms, (5) surface com- pactness, (6) flow arrangement, (7) number of fluid passes, and (8) type of surface. Recuperators are direct-transfer heat exchangers in which heat transfer occurs between two fluid streams at different temperature levels in a space that is separated by a thin solid wall (a parting sheet or tube wall). Heat is transferred by convection from the hot (hotter) fluid to the wall surface and by convection from the wall surface to the cold (cooler) fluid. The recuperator is a surface heat exchanger. Regenerators are heat exchangers in which a hot fluid and a cold fluid flow al- ternately through the same surface at prescribed time intervals. The surface of the regenerator receives heat by convection from the hot fluid and then releases it by convection to the cold fluid. The process is transient; that is, the temperature of the surface (and of the fluids themselves) varies with time during the heating and cooling of the common surface. The regenerator is a also surface heat exchanger. In direct-contact heat exchangers, heat is transferred by partial or complete mix- ing of the hot and cold fluid streams. Hot and cold fluids that enter this type of ex- changer separately leave together as a single mixed stream. The temptation to refer to the direct-contact heat exchanger as a mixer should be resisted. Direct contact is discussed in Chapter 19. In the present chapter we discuss the shell-and-tube heat exchanger, the compact heat exchanger, the longitudinal high-fin exchanger, the trans- verse high-fin exchanger including the air-fin cooler, the plate-and-frame heat ex- changer, the regenerator, and fouling. 11.2 GOVERNING RELATIONSHIPS 11.2.1 Introduction Assume that there are two process streams in a heat exchanger, a hot stream flowing with a capacity rate C h =˙m h C ph and a cooler (or cold stream) flowing with a capacity rate C c =˙m c c ph . Then, conservation of energy demands that the heat transferred between the streams be described by the enthalpy balance q = C h (T 1 − T 2 ) = C c (t 2 − t 1 ) (11.1) where the subscripts 1 and 2 refer to the inlet and outlet of the exchanger and where the T ’s and t’s are employed to indicate hot- and cold-fluid temperatures, respectively. Equation (11.1) represents an ideal that must hold in the absence of losses, and while it describes the heat that will be transferred (the duty of the heat exchanger) for the case of prescribed flow and temperature conditions, it does not provide an indication of the size of the heat exchanger necessary to perform this duty. The size of the exchanger derives from a statement of the rate equation: q = U ηSθ m = U h η ov,h S h θ m = U c η ov,c S c θ m (11.2) where S h and S c are the surface areas on the hot and cold sides of the exchanger, U h and U c are the overall heat transfer coefficients referred to the hot and cold sides of BOOKCOMP, Inc. — John Wiley & Sons / Page 800 / 2nd Proofs / Heat Transfer Handbook / Bejan 800 HEAT EXCHANGERS 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 [800], (4) Lines: 199 to 273 ——— 0.60005pt PgVar ——— Short Page PgEnds: T E X [800], (4) the exchanger and θ m is some driving temperature difference. The quantities η ov,h and η ov,c are the respective overall fin efficiencies and in the case of an unfinned exchanger, η ov,h = η ov,c = 1. The entire heat exchange process can be represented by q = U h η ov,h S h θ m = U c η ov,c S c θ m = C h (T 1 − T 2 ) = C c (t 2 − t 1 ) (11.3) which is merely a combination of eqs. (11.1) and (11.2). 11.2.2 Exchanger Surface Area Consider the unfinned tube of length L shown in Fig. 11.1a and observe that because of the tube wall thickness δ w , the inner diameter will be smaller than the outer diameter and the surface areas will be different: S i = πd i L (11.4a) S o = πd o L (11.4b) In the case of the finned tube, shown with one fin on the inside and outside of the tube wall in Fig. 11.1b, the fin surface areas will be S fi = 2n i b i L (11.5a) S fo = 2n o b o L (11.5b) where n i and n o are the number of fins on the inside and outside of the tube wall, respectively, and it is presumed that no heat is transferred through the tip of either of the inner or outer fins. In this case, the prime or base surface areas S bi = (πd i − n i δ fi )L (11.6a) S bo = (πd o − n o δ fo )L (11.6b) The total surface will then be S i = S bi + S fi = (πd i − n i δ fi + 2n i b i )L or S i = πd i + n i (2b i − δ fi ) L (11.7a) S o = πd o + n o (2b o − δ fo ) L (11.7b) The ratio of the finned surface to the total surface will be S fi S i = 2n i b i L πd i + n i (2b i − δ fi ) L = 2n i b i πd i + n i (2b i − δ fi ) (11.8a) BOOKCOMP, Inc. — John Wiley & Sons / Page 801 / 2nd Proofs / Heat Transfer Handbook / Bejan GOVERNING RELATIONSHIPS 801 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 [801], (5) Lines: 273 to 308 ——— 8.11423pt PgVar ——— Short Page PgEnds: T E X [801], (5) S fo S o = 2n o b o L πd o + n o (2b o − δ fi ) L = 2n o b o πd o + n o (2b o − δ fo ) (11.8b) The overall surface efficiencies η ov,h and η ov,c are based on the base surface operating at an efficiency of unity and the finned surface operating at fin efficiencies of η fi and η fo . Hence η ov,i S i = S bi + η fi S fi = S i − S fi + η fi S fi or η ov,i = 1 − S fi S i 1 − η fi (11.9a) and in a similar manner, η ov,o = 1 − S fo S o 1 − η fo (11.9b) Figure 11.1 End view of (a) a bare tube and (b) a small central angle of a tube with both internal and external fins of length, L. BOOKCOMP, Inc. — John Wiley & Sons / Page 802 / 2nd Proofs / Heat Transfer Handbook / Bejan 802 HEAT EXCHANGERS 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 [802], (6) Lines: 308 to 363 ——— 0.07822pt PgVar ——— Normal Page * PgEnds: Eject [802], (6) Notice that when there is no finned surface, S fi = S fo = 0 and eqs. (11.9) reduce to η ov,i = η ov,o = 1 and that with little effort, the subscripts in eqs. (11.4) through (11.9) can be changed to reflect the hot and cold fluids. 11.2.3 Overall Heat Transfer Coefficient In a heat exchanger containing hot and cold streams, the heat must flow, in turn, from the hot fluid to the cold fluid through as many as five thermal resistances: 1. Hot-side convective layer resistance: R h = 1 h h η ov,h S h (K/W) (11.10) 2. Hot-side fouling resistance due to an accumulation of foreign (and undesirable) material on the hot-fluid exchanger surface: R dh = 1 h dh η ov,h S h (K/W) (11.11) Fouling is discussed in a subsequent section. 3. Resistance of the exchanger material, which has a finite thermal conductivity and which may take on a value that is a function of the type of exchanger: R m = δ w k m S m (K/W) plane walls ln(d o )(d i ) 2πk m Ln t (K/W) circular tubes (11.12) where δ m is the thickness of the metal, S m the surface area of the metal, and n t the number of tubes. 4. Cold-side fouling resistance: R dc = 1 h dc η ov,c S c (K/W) (11.13) 5. Cold-side convective layer resistance: R h = 1 h c η ov,c S c (K/W) (11.14) The resistances listed in eqs. (11.10)–(11.14) are in series and the total resistance can be represented by BOOKCOMP, Inc. — John Wiley & Sons / Page 803 / 2nd Proofs / Heat Transfer Handbook / Bejan GOVERNING RELATIONSHIPS 803 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 [803], (7) Lines: 363 to 423 ——— 2.78242pt PgVar ——— Normal Page * PgEnds: Eject [803], (7) 1 US = 1 h h η ov,h S h + 1 h dh η ov,h S h + R m + 1 h dc η ov,c S c + 1 h c η ov,c S c (11.15) where, for the moment, U and S on the left side of eq. (11.16) are not assigned any subscript. Equation (11.16) is perfectly general and may be put into specific terms depending on the selection of the reference surface, whether or not fouling is present and whether or not the metal resistance needs to be considered. If eq. (11.16) is solved for U , the result is U = 1 S h h η ov,h S h + S h dh η ov,h S h + SR m + S h dc η ov,c S c + S h c η ov,c S c (11.16) and if the thickness of the metal is small and thermal conductivity of the metal is high, the metal resistance becomes negligible and U = 1 S h h η ov,h S h + S h dh η ov,h S h + S h dc η ov,c S c + S h c η ov,c S c (11.17) Several forms of eq. (11.17) are: • For a hot-side reference with fouling, U h = 1 1 h h η ov,h + 1 h dh η ov,h + 1 h dc η ov,c S h S c + 1 h c η ov,c S h S c (11.18) • For a cold-side reference with fouling, U c = 1 1 h h η ov,h S c S h + 1 h dh η ov,h S c S h + 1 h dc η ov,c + 1 h c η ov,c (11.19) • For a hot-side reference without fouling, U h = 1 1 h h η ov,h + 1 h c η ov,c S h S c (11.20) • For a cold-side reference without fouling, U c = 1 1 h h η ov,h S c S h + 1 h c η ov,c (11.21) BOOKCOMP, Inc. — John Wiley & Sons / Page 804 / 2nd Proofs / Heat Transfer Handbook / Bejan 804 HEAT EXCHANGERS 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 [804], (8) Lines: 423 to 465 ——— 7.63702pt PgVar ——— Normal Page PgEnds: T E X [804], (8) • For an unfinned exchanger where η ov,h = η ov,c = 1 and a hot-side reference without fouling, U h = 1 1 h h + 1 h c S h S c (11.22) • For an unfinned exchanger and a cold-side reference without fouling, U c = 1 1 h h S h S c + 1 h c (11.23) 11.2.4 Logarithmic Mean Temperature Difference For the four basic simple arrangements indicated in Fig. 11.2, θ m in eqs. (11.2) and (11.3) is the logarithmic mean temperature difference, which can be written as θ m = LMTD = ∆T 1 − ∆T 2 ln(∆T 1 /∆T 2 ) = ∆T 2 − ∆T 1 ln(∆T 2 /∆T 1 ) (11.24) TT T 2 T s T 2 T 2 T 1 T 1 T 1 t 2 t 2 t 2 t 1 t 1 t 1 t s L L L L ()a ()c ()b ()d T 1 T 1 T 1 T 2 T 2 T 2 t 2 t 2 t 2 t 2 t 1 t 1 t 1 t 1 Figure 11.2 Four basic arrangements for which the logarithmic mean temperature differ- ence may be determined from eq. (11.23): (a) counterflow; (b) co-current or parallel flow; (c) constant-temperature source and rising-temperature receiver; (d) constant-temperature re- ceiver and falling-temperature source. . Tubes, J. Heat Transfer, 100, 17–24. Rudy, T. M., and Webb, R. L. (1 981) . Condensate Retention on Horizontal Integral-Fin Tubing, in Advances in Enhanced Heat Transfer, 20th National Heat Transfer. Large Power Plant Condensers, J. Heat Transfer, 116, 180–188. Zhang, C. (1996). Local and Overall Condensation Heat Transfer Behavior in Horizontal Tube Bundles, Heat Transfer Eng., 17(1), 19–30. Zhang,. Compact heat exchangers 11.5.1 Introduction 11.5.2 Classification of compact heat exchangers 11.5.3 Geometrical factors and physical data 11.5.4 Heat transfer and flow friction data Heat transfer