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BOOKCOMP, Inc. — John Wiley & Sons / Page 845 / 2nd Proofs / Heat Transfer Handbook / Bejan COMPACT HEAT EXCHANGERS 845 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 [845], (49) Lines: 2283 to 2283 ——— -0.903pt PgVar ——— Normal Page PgEnds: T E X [845], (49) Header Air fin Air fin Tube Tube Tube plates ( ) Round tube and fina ( ) Bar and plated ( ) Formed plate fing ( ) Flat tube and finb ( ) Bar and platee ( ) Formed plate finh ( ) Dimpled strut tubei ( ) Tube and centerc ( ) Bar and platef Tube Tube Tube Tube plates Tube plates Spacer bar Heating fins Louvered air fins Header Header Header Header Side bar Side bar Header bar Louvered air fins Louvered air fins Louvered air fins Louvered air fins Turbulator strip Turbulator dimples Turbulator strip Reinforcement rod Header bar Corrugated air fins Side bar Figure 11.16 Some compact heat exchanger elements. (Courtesy of Harrison Radiator Division.) 3. Surfaces with flow normal to banks of smooth tubes. Unlike the radial low fin tubes, smooth round tubes are expanded into fins that can accept a number of tube rows, as shown in Fig. 11.16a. Holes may be stamped in the fin with a drawn hub or foot to improve contact resistance or as a spacer between successive fins, as shown, or brazed directly to the fin with or without a hub. Other types reduce the flow resistance outside the tubes by using flattened tubes and brazing, as indicated in Fig. 11.16b and c. Flat tubing is made from strips similar to the manufacture of welded circular tubing but is much thinner and is joined by soldering or brazing rather than welding. BOOKCOMP, Inc. — John Wiley & Sons / Page 846 / 2nd Proofs / Heat Transfer Handbook / Bejan 846 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 [846], (50) Lines: 2283 to 2322 ——— 1.17004pt PgVar ——— Short Page PgEnds: T E X [846], (50) The designation considers staggered (S) and in-line (I) arrangements of tubes and identifies transverse and longitudinal pitch ratios. The suffix (s) indicates data correla- tion from steady-state tests. All other data were correlated from a transient technique. Examples include the surface S1.50-1.25(s), which is a staggered arrangement with data obtained via steady-state tests with transverse pitch-to-diameter ratio of 1.50 and longitudinal pitch-to-diameter ratio of 1.25. The surface I1.25-1.25 has an in- line arrangement with data obtained from transient tests with both transverse and longitudinal pitch-to-diameter ratios of 1.25. 4. Plate fin surfaces. These are shown in Figs. 11.16d through i. (a) The plain fin is characterized by long uninterrupted flow passages and is designated by a numeral that indicates the number of fins per inch. The suffix T is appended when the passages are of definite triangular shape. Examples are the surfaces 19.86, 15.08, and 46.45T. (b) The louvered fin is characterized by fins that are cut and bent into the flow stream at frequent intervals and is designated by a fraction which indicates the length of the fin in the flow direction (inches) followed by a numeral that indicates the number of fins per inch. For example, the designation 1 2 − 6.06 indicates 6.06 1 2 -in long fins per inch. (c) The strip fin is designated in the same manner as the louvered fin. The suffixes (D) and (T) indicate double and triple stacks. The strip fins are frequently referred to as offset fins because they are offset at frequent intervals and the exchanger is essentially a series of plate fins with alternate lengths offset. (d) The wavy fin is characterized by a continuous curvature. The change in flow direction introduced by the waves in the surface tends to interrupt the boundary layer, as in the case of louvered and strip fins. Wavy fin designations are always followed by the letter W. For example, the 11.44 − 3 8 W is a wavy fin with 11.44 fins per inch and a 3 8 -in. wave. (e) The pin fin surface is constructed from small-diameter wires. This surface yields very high heat transfer coefficients because the effective flow length is very small. The designation of the pin fin surfaces is nondescriptive. (f) The perforated fin surface has holes cut in the fins to provide boundary layer interruption. These fins are designated by the number of fins per inch followed by the letter P. 5. Finned-tube surfaces. Circular tubes with spiral radial fins are designated by the letters CF followed by one or two numerals. The first numeral designates the number of fins per inch, and the second (if one is used) refers to the nominal tube size. With circular tubes with continuous fins, no letter prefix is employed and the BOOKCOMP, Inc. — John Wiley & Sons / Page 847 / 2nd Proofs / Heat Transfer Handbook / Bejan COMPACT HEAT EXCHANGERS 847 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 [847], (51) Lines: 2322 to 2430 ——— 6.0pt PgVar ——— Short Page PgEnds: T E X [847], (51) two numerals have the same meaning as those used for circular tubes with spiral radial fins. For finned flat tubes, no letter prefix is used; the first numeral indicates the fins per inch and the second numeral indicates the largest tube dimension. When CF does not appear in the designation of the circular tube with spiral radial fins, the surface may be presumed to have continuous fins. 6. Matrix surfaces. These are surfaces that are used in rotating, regenerative equip- ment such as combustion flue gas–air preheaters for conventional fossil furnaces. In this application, metal is deployed for its ability to absorb heat with minimal fluid friction while exposed to hot flue gas and to give up this heat to incoming cold com- bustion air when it is rotated into the incoming cold airstream. No designation is employed. 11.5.3 Geometrical Factors and Physical Data Compact heat exchanger surfaces are described in the literature by geometric factors that have been standardized largely through the extensive work of Kays and London (1984). These factors and the relationships between them are essential for application of the basic heat transfer and flow friction data to a particular design problem. They are listed and defined in Table 11.1. Physical data for a number of compact heat exchanger surfaces are given in Table 11.2. Relationships between the geometric factors in Table 11.1 will now be established. Consider an exchanger composed of n 1 layers of one type of plate fin surface and n 2 layers of a second type, as shown in Fig. 11.13. The separation plate thickness is established by the pressure differential to which it is exposed or through designer discretion. Retaining the subscripts 1 and 2 for the respective types of surface, the overall exchanger height H is H = n 1 (b 1 + a) + n 2 (b 2 + a) (11.119) where b 1 and b 2 are separation distances between the plates for the two kinds of surface. With the width W and depth D selected, the overall volume V is V = WDH (11.120) In Fig. 11.15, the length L 1 is along the depth of the exchanger (L 1 = D) and the length L 2 is along the width (L 2 = W ). The frontal areas are also established. Again referring to Fig. 11.13, we have A fr,1 = HW (11.121a) A fr,2 = HD (11.121b) If the entire exchanger consisted of a single exchanger surface, surface 1 or surface 2, the total surface area would be the product of the ratio of total surface to total BOOKCOMP, Inc. — John Wiley & Sons / Page 848 / 2nd Proofs / Heat Transfer Handbook / Bejan 848 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 [848], (52) Lines: 2430 to 2430 ——— 7.34407pt PgVar ——— Normal Page PgEnds: T E X [848], (52) TABLE 11.1 Compact Heat Exchanger Geometric Factors Factor and Symbol Descriptive Comments A Free flow area on one side of the exchanger. To distinguish hot and cold sides, the free flow areas are frequently designated by A h and A c . A fr Frontal area on one side of the exchanger. This is merely the product of the overall exchanger width and height or depth and height. a Separation plate thickness. This applies only to plate fin surfaces and its value is at the designer’s discretion. b Separation plate spacing. This dimension is an approximation of the fin height. Applies to plate fin surfaces only. d e Equivalent diameter used to correlate flow friction and heat transfer; four times the hydraulic radius, r h . L Flow length on one side of the exchanger. Note that this factor always concerns the flow length of a single side of the exchanger, although two sides may be present, and that the ambiguity is avoided with the overall exchanger dimensions, which are designated width, depth, and height. It is therefore reasonable to have the overall exchanger depth be the length on one side of the exchanger and the overall width the length on the other side. P Perimeter of the passage. p Porosity, the ratio of the exchanger void volume to the total exchanger volume. Applies to matrix surfaces only. r h Hydraulic radius; the ratio of the passage flow area to its wetted perimeter. S Heat transfer surface on one side of the exchanger. Subscripts are often appended to distinguish between hot- and cold-side surfaces. S f Surface of the fins, only, on one side of the exchanger. Applies to finned surfaces only. V Total exchanger volume. This applies to both sides of the heat exchanger and is merely the product of the overall heat exchanger width, depth, and height. α Ratio of the total surface area on one side of the exchanger to the total volume on both sides of the exchanger. Applies to tubular, plate fin surfaces, and crossed-rod matrices only. β Ratio of the total surface area to the total volume on one side of the exchanger. The surface alone is S. The total volume includes the overall exchanger dimensions. Applies to plate fin surfaces only. δ f Fin thickness. η f Fin efficiency. η ov Overall passage efficiency. σ Ratio of the free flow area to the frontal area on one side of the exchanger. BOOKCOMP, Inc. — John Wiley & Sons / Page 849 / 2nd Proofs / Heat Transfer Handbook / Bejan COMPACT HEAT EXCHANGERS 849 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 [849], (53) Lines: 2430 to 2438 ——— 0.00925pt PgVar ——— Normal Page * PgEnds: Eject [849], (53) TABLE 11.2 Surface Geometry of Some Plate Fin Surfaces Plain Plate Fins 11.1 15.08 19.86 46.45T b(×10 −3 m) 6.35 10.62 6.35 2.54 Fins per inch 11.1 15.08 19.86 46.45 d e (×10 −3 m) 3.08 2.67 1.875 0.805 δ f (×10 −3 m) 0.152 0.152 0.152 0.051 β(m 2 /m 3 ) 1204 1358.3 1840.6 4371.7 S f /S 0.756 0.870 0.849 0.837 Louvered Fins 3 8 -6.06 1 2 -6.06 3 16 -11.1 3 4 -11.1 b(×10 −3 m) 6.35 6.35 6.35 6.35 Fins per inch 6.06 6.06 11.1 11.1 d e (×10 −3 m) 4.453 4.453 3.084 3.084 δ f (×10 −3 m) 0.152 0.152 0.152 0.152 β(m 2 /m 3 ) 840 840 1204 1204 S f /S 0.640 0.640 0.756 0.756 Strip Fins 1 8 -13.95 1 8 -16.00D 1 8 -19.82D 1 8 -20.06 b(×10 −3 m) 9.54 6.48 5.21 5.11 Fins per inch 13.95 16.00 19.82 20.06 d e (×10 −3 m) 2.68 1.86 1.54 1.49 δ f (×10 −3 m) 0.254 0.152 0.102 0.102 β(m 2 /m 3 ) 1250 1804 2231 2290 S f /S 0.840 0.845 0.841 0.843 Wavy and Pin Fins 11.5- 3 8 W 17.8- 3 8 W AP-1 PF-3 b(×10 −3 m) 9.53 10.49 6.10 19.1 Fins per inch or fin pattern 11.5 17.8 In-line In-line d e (×10 −3 m) 3.02 2.12 4.40 1.636 δ f or pin diameter (×10 −3 m) 0.254 0.152 1.02 0.79 β(m 2 /m 3 ) 1138 1686 617 1112 S f /S 0.822 0.892 0.512 0.834 volume β(m 2 /m 3 ) and the total volume V . However, where there are two surfaces, it is necessary to employ the factor α, which is the ratio of the total surface on one side to the total surface on both sides of the exchanger. By taking simple proportions, α 1 = b 1 b 1 + b 2 + a β 1 (11.122a) α 2 = b 2 b 1 + b 2 + a β 2 (11.122b) BOOKCOMP, Inc. — John Wiley & Sons / Page 850 / 2nd Proofs / Heat Transfer Handbook / Bejan 850 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 [850], (54) Lines: 2438 to 2511 ——— 1.12427pt PgVar ——— Short Page PgEnds: T E X [850], (54) and the total surfaces will be S 1 = α 1 V (11.123a) S 2 = α 2 V (11.123b) The hydraulic radius is defined as the flow area divided by the wetted perimeter of the passage: r h = A P = AL S (11.124) and the ratio of the flow area to the frontal area is designated as σ: σ = A A fr (11.125) For all but matrix surfaces, because eq. (11.124) leads to A = Sr h /L, σ = Sr h A fr L = Sr h V = αr h (11.126) Thus, the flow areas are given by A 1 = σ 1 A fr,1 (11.127a) A 2 = σ 2 A fr,2 (11.127b) 11.5.4 Heat Transfer and Flow Friction Data HeatTransfer Data Heat transfer data for compact heat exchangers are correlated on an individual surface basis using a Colburn type of representation. This represen- tation plots the heat transfer factor j h : j h = St · Pr 2/3 = h Gc p  c p µ k  2/3 (11.128) as a function of the Reynolds number, which is obtained by employing the equivalent diameter d e = 4r h : Re = 4r h G µ = d e G µ (11.129) The Stanton number St is the ratio of the Nusselt number Nu to the product of the Reynolds and Prandtl numbers, with the specific heat c taken as the value for constant pressure, BOOKCOMP, Inc. — John Wiley & Sons / Page 851 / 2nd Proofs / Heat Transfer Handbook / Bejan COMPACT HEAT EXCHANGERS 851 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 [851], (55) Lines: 2511 to 2516 ——— * 20.227pt PgVar ——— Short Page PgEnds: T E X [851], (55) Fin pitch = 46.45 per in. Plate spacing, = 0.100 in. Fin length flow direction = 2.63 in. Flow passage hydraulic diameter, 4 = 0.002643 ft. Fin metal thickness = 0.002 in., stainless steel Total heat transfer area/volume between plates, = 1332.5 ft /ft Fin area/total area = 0.837 b r h ␤ 23 Fin pitch = 15.08 per in. Plate spacing, = 0.418 in. Flow passage hydraulic diameter, 4 = 0.00876 ft. Fin metal thickness = 0.006 in., aluminum Total heat transfer area/volume between plates, = 414 ft /ft Fin area/total area = 0.870 b r h ␤ 23 Fin pitch = 11.1 per in. Plate spacing, = 0.250 in. Flow passage hydraulic diameter, 4 = 0.01012 ft. Fin metal thickness = 0.006 in., aluminum Total transfer area/volume between plate, = 367 ft /ft Fin area/total area = 0.756 b r h ␤ 23 Fin pitch = 19.86 per in. Plate spacing, = 0.250 in. Flow passage hydraulic diameter, 4 = 0.00615 ft. Fin metal thickness = 0.006 in., aluminum Total heat transfer area/volume between plates, = 561 ft /ft Fin area/total area = 0.849 b r h ␤ 23 0.18Љ Lr/4 = 20.6 h Lr/4 = 83.0 h Lr/4 = 65 h Lr/4 = 35.0 h 0.25Љ 0.0431Љ 0.1326Љ 0.1006Љ 0.25Љ 0.418Љ ()a ()c ()b ()d 10 2 10 3 10 4 Re = , dimensionless dG e ␮ 0.001 0.01 0.1 f, dimensionless j hG c c k h = , dimensionless ␮ 2/3 ( ( ()c ()d ()b ()a 46.45T 11.1 15.08 19.86 .0100Љ Figure 11.17 Heat transfer and flow friction characteristics of some plain plate fin compact heat exchanger surfaces. (From Kays and London, 1984.) BOOKCOMP, Inc. — John Wiley & Sons / Page 852 / 2nd Proofs / Heat Transfer Handbook / Bejan 852 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 [852], (56) Lines: 2516 to 2516 ——— -2.773pt PgVar ——— Normal Page PgEnds: T E X [852], (56) Fin pitch = 11.1 per in. Plate spacing, = 0.250 in. Louver spacing = 0.1875 in. Fin gap = 0.035 in. Louver gap = 0.055 in. Flow passage hydraulic diameter, 4 = 0.01012 ft. Fin metal thickness = 0.006 in., aluminum Total heat transfer area/volume between plates, = 367 ft /ft Fin area/total area = 0.756 b r h ␤ 23 Fin pitch = 6.06 per in. Plate spacing, = 0.250 in. Louver spacing = 0.375 in. Fin gap = 0.110 in. Louver gap = 0.055 in. Flow passage hydraulic diameter, 4 = 0.01460 ft. Fin metal thickness = 0.006 in., aluminum Total transfer area/volume between plates, = 256 ft /ft Fin area/total area = 0.640 b r h ␤ 23 Fin pitch = 11.1 per in. Plate spacing, = 0.250 in. Louver spacing = 0.75 in. Fin gap = 0.05 in. Louver gap = 0.04 in. Flow passage hydraulic diameter, 4 = 0.01012 ft. Fin metal thickness = 0.006 in., aluminum Total heat transfer area/volume between plates, = 367 ft /ft Fin area/total area = 0.756 b r h ␤ 23 Fin pitch = 6.06 per in. Plate spacing, = 0.250 in. Louver spacing = 0.50 in. Fin gap = 0.110 in. Louver gap = 0.055 in. Flow passage hydraulic diameter, 4 = 0.01460 ft. Fin metal thickness = 0.006 in., aluminum Total heat transfer area/volume between plates, = 256 ft /ft Fin area/total area = 0.640 b r h ␤ 23 .25Љ 0.04Љ .180Љ 0.75Љ 0.05Љ .035Љ .055Љ .1875Љ 0.110Љ .055Љ .110Љ .25Љ .50Љ .330Љ 0.055Љ 0.25Љ 0.375Љ 3/8-6.06 0.330Љ ()a ()c ()b ()d 10 2 10 3 10 4 Re = , dimensionless dG e ␮ 0.001 0.01 0.1 f, dimensionless ( ( ()c ()d ()b ()a 3/16-11.1 3/4-11.1 3/8-6.06 1/2-6.06 .25Љ j hG c c k h = , dimensionless ␮ 2/3 Figure 11.18 Heat transfer and flow friction characteristics of some louvered fin compact heat exchanger surfaces. (From Kays and London, 1984.) BOOKCOMP, Inc. — John Wiley & Sons / Page 853 / 2nd Proofs / Heat Transfer Handbook / Bejan COMPACT HEAT EXCHANGERS 853 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 [853], (57) Lines: 2516 to 2521 ——— -0.073pt PgVar ——— Normal Page PgEnds: T E X [853], (57) Fin pitch = 20.06 per in. Plate spacing, = 0.201 in. Splitter symmetrically located Fin length flow direction = 0.125 in. Flow passage hydraulic diameter, 4 = 0.004892 ft. Fin metal thickness = 0.004 in., aluminum Splitter metal thickness = 0.006 in. Total heat transfer area/volume between plates, = 698 ft /ft Fin area (including splitter)/total area = 0.843 b r h ␤ 23 Fin pitch = 16.00 per in. Plate spacing, = 0.255 in. Splitter symmetrically located Fin length flow direction = 0.125 in. Flow passage hydraulic diameter, 4 = 0.006112 ft. Fin metal thickness = 0.006 in., aluminum Splitter metal thickness = 0.006 in. Total heat transfer area/volume between plates, = 550 ft /ft Fin area (including splitter)/total area = 0.845 b r h ␤ 23 Fin pitch = 19.82 per in. Plate spacing, = 0.205 in. Splitter symmetrically located Fin length flow direction = 0.125 in. Flow passage hydraulic diameter, 4 = 0.005049 ft. Fin metal thickness = 0.004 in., nickel Splitter metal thickness = 0.006 in. Total heat transfer area/volume between plates, = 680 ft /ft Fin area (including splitter)/total area = 0.841 b r h ␤ 23 Fin pitch = 13.95 per in. Plate spacing, = 0.375 in. Fin length = 0.125 in. Flow passage hydraulic diameter, 4 = 0.00879 ft Fin metal thickness = 0.010 in., aluminum Total heat transfer area/volume between plates, = 381 ft /ft Fin area/total area = 0.840 Note: The fin surface area on the leading and trailing edges of the fins have not been included in area computations. b r h ␤ 23 .205Љ .125Љ .0505Љ .201Љ .125Љ .0499Љ .125Љ .072Љ 1 – 8 Љ .375Љ .255Љ .0625Љ ()a ()c ()b ()d 10 2 10 3 10 4 Re = , dimensionless dG e ␮ 0.001 0.01 0.1 f, dimensionless j h Gc c k h = , dimensionless ␮ 2/3 ( ( ()c ()d ()b ()a 1/8-20.06( )D 1/8-19.82( )D 1/8-16.00( )D 1/8-13.95 Figure 11.19 Heat transfer and flow friction characteristics of some strip fin compact heat exchanger surfaces. (From Kays and London, 1984.) BOOKCOMP, Inc. — John Wiley & Sons / Page 854 / 2nd Proofs / Heat Transfer Handbook / Bejan 854 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 [854], (58) Lines: 2521 to 2526 ——— -13.073pt PgVar ——— Normal Page PgEnds: T E X [854], (58) Pin diameter = 0.031 in., aluminum Pin pitch parallel to flow = 0.062 in. Pin pitch perpendicular to flow = 0.062 in. Plate spacing, = 0.750 in. Flow passage hydraulic diameter, 4 = 0.00536 ft Total heat transfer area/volume between plates, = 339 ft /ft Fin area/total area = 0.834 b r h ␤ 23 Pin diameter = 0.04 in., copper Pin pitch parallel to flow = 0.125 in. Pin pitch perpendicular to flow = 0.125 in. Plate spacing, = 0.24 in. Flow passage hydraulic diameter, 4 = 0.01444 ft Total heat transfer area/volume between plates, = 188 ft /ft Fin area/total area = 0.512 b r h ␤ 23 Fin pitch = 17.8 per in. Plate spacing, = 0.413 in. Flow passage hydraulic diameter, 4 = 0.00696 ft Fin metal thickness = 0.006 in., aluminum Total heat transfer area/volume between plates, = 514 ft /ft Fin area/total area = 0.892 Note: Hydraulic diameter based on free-flow area normal to mean flow direction. b r h ␤ 23 Fin pitch = 11.5 per in. Plate spacing, = 0.375 in. Flow passage hydraulic diameter, 4 = 0.00993 ft Fin metal thickness = 0.010 in., aluminum Total heat transfer area/volume between plates, = 347 ft /ft Fin area/total area = 0.822 Note: Hydraulic diameter based on free-flow area normal to mean flow direction. b r h ␤ 23 .094Љ .413Љ 3/8Љ .0775 Approx.Љ .0562Љ .718Љ .062Љ .062Љ .031Љ .750Љ .375Љ .125Љ 0.125Љ .24Љ .04 dia. Min free flow area .375Љ .078Љ .087Љ ()a ()c ()b ()d 10 2 10 3 10 4 Re = , dimensionless dG e ␮ 0.0001 0.001 0.01 f, dimensionless j h Gc c k h = , dimensionless ␮ 2/3 ( ( ()c ()d ()b ()a 11.5-3/8W 17.8-3/8W AP-1 PF-3 Figure 11.20 Heat transfer and flow friction characteristics of some wavy andpin fin compact heat exchanger surfaces. (From Kays and London, 1984.) . σ 1 A fr,1 (11.127a) A 2 = σ 2 A fr,2 (11.127b) 11.5.4 Heat Transfer and Flow Friction Data HeatTransfer Data Heat transfer data for compact heat exchangers are correlated on an individual surface. numbers, with the specific heat c taken as the value for constant pressure, BOOKCOMP, Inc. — John Wiley & Sons / Page 851 / 2nd Proofs / Heat Transfer Handbook / Bejan COMPACT HEAT EXCHANGERS 851 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 [851],. employed and the BOOKCOMP, Inc. — John Wiley & Sons / Page 847 / 2nd Proofs / Heat Transfer Handbook / Bejan COMPACT HEAT EXCHANGERS 847 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 [847],

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