To apply a conventional design method (say, the MTD method;Section 3.7) a mean value of the overall heat transfer coefficient should be defined (seeSection 4.2.3.1).Analysis: The heat transfer surface area can be calculated from A¼ q U ÁTlm. (4.97) at x ¼ ‘, ‘ ¼ cosh m‘ 1 sinh m‘ ð4:100Þ 0 þBwhere B ¼ he ¼ 2 Bi* ¼ *f Bi* Bi* ¼ he *f ¼ 2‘ ð4:101Þ mkf m m‘ 2kf, 268 ADDITIONAL CONSIDERATIONS FOR THERMAL DESIGN OF RECUPERATORSHere Bi* is the Biot number at the fin tip; it is the ratio of conduction resistance withinthe fin ½1=fkf =ð=2ÞgŠ to convection resistance at the fin tip ð1=heÞ. However, when it varies significantly as in a cryogenic heatexchanger, the third point calculated for the Cmax and Cmin fluid by Eq. I hope that the above rules of our Project would help us to get success in our scientific work ... , every one of us would like that His work would be noted, read, recommended, commented, discussed, and cited ... , but somebody should do that ... evaporators; and fouling of heat exchangers, Heat Exchangers: Selection, Rating, and Thermal Design, Second Edition, Heating, ventilating, and air conditioning: analysis and design. (4.42) becomes 1/2. Thus long-itudinal heat conduction increases the NTU required by 92%, a significant penalty inrequired surface area due to longitudinal conduction. For example, consider a very simplifiedproblem with the heat transfer coefficient on each fluid side of a counterflow exchanger, 250 ADDITIONAL CONSIDERATIONS FOR THERMAL DESIGN OF RECUPERATORSFIGURE 4.5 Length effect correction factor for one and both laminar streams based onequations in Table 4.3 (From Roetzel, 1974).varying from 80 to 40 W=m2 Á K from entrance to exit and A1 ¼ A2, Rw ¼ 0,o;1 ¼ o;2 ¼ 1, and there is no temperature effect. (b) Determine the true mean temperature difference ÁTm for heat transfer. The book is intended for use in two regular semester courses, following which the student should be capable of participating in the design of all types of HVAC systems. d!Per�����n^s��i,���tT�i﷛� ���_}�Zs*ft��x�Rܐ����z�4Nf4�G�3��nW����3�{W��5.��>[���{�N�D��W�P��m�f�?Ҹ���1�S�� 11�����M����MF��gE����(�N�� ���(�Eq7�t����~�]�q��+�+�⯵98�ݷ���Ц�{��I� c!�����.`����g�f0��(p�5+^��7U0�_x>k����f��>Ae�4t5Q�=O�[�K����b/�$Z{��:�^g">�i endstream endobj 571 0 obj 308 endobj 537 0 obj << /Type /Page /Parent 531 0 R /Resources 538 0 R /Contents [ 543 0 R 545 0 R 547 0 R 549 0 R 551 0 R 564 0 R 566 0 R 569 0 R ] /MediaBox [ 0 0 612 792 ] /CropBox [ 0 0 612 792 ] /Rotate 0 >> endobj 538 0 obj << /ProcSet [ /PDF /Text ] /Font << /F2 557 0 R /TT2 539 0 R /TT4 554 0 R /TT6 562 0 R /TT8 559 0 R /TT10 560 0 R >> /ExtGState << /GS1 568 0 R >> /ColorSpace << /Cs5 541 0 R >> >> endobj 539 0 obj << /Type /Font /Subtype /TrueType /FirstChar 32 /LastChar 121 /Widths [ 278 0 0 0 0 0 0 0 333 333 389 0 278 333 278 278 556 556 556 556 556 556 556 556 556 556 278 0 0 584 0 0 0 667 0 722 722 667 611 0 722 278 0 0 556 833 0 778 667 0 722 667 611 722 667 944 0 0 0 0 0 0 0 0 0 556 556 500 556 556 278 556 556 222 222 500 222 833 556 556 556 556 333 500 278 556 500 722 500 500 ] /Encoding /WinAnsiEncoding /BaseFont /Arial /FontDescriptor 540 0 R >> endobj 540 0 obj << /Type /FontDescriptor /Ascent 905 /CapHeight 0 /Descent -211 /Flags 32 /FontBBox [ -665 -325 2028 1037 ] /FontName /Arial /ItalicAngle 0 /StemV 0 >> endobj 541 0 obj [ /CalRGB << /WhitePoint [ 0.9505 1 1.089 ] /Gamma [ 2.22221 2.22221 2.22221 ] /Matrix [ 0.4124 0.2126 0.0193 0.3576 0.71519 0.1192 0.1805 0.0722 0.9505 ] >> ] endobj 542 0 obj 2560 endobj 543 0 obj << /Filter /FlateDecode /Length 542 0 R >> stream 4.11dand b, respectively. 220 BASIC THERMAL DESIGN THEORY FOR RECUPERATORSRoetzel, W., and B. Spang, 1990, Verbessertes Diagramm zur Berechnung von Wa¨ rmeu¨ bertragern, Wa¨rme-und Stoffu¨bertragung, Vol. For NTU ! 0000018380 00000 n Thus, if the indivi-dual h values vary across the exchanger surface area, it is highly likely that U will notremain constant and uniform in the exchanger. For the straight fin ofFig. 0000002916 00000 n 4.5 and Table 4.3.Example 4.2 In a liquid-to-steam two-fluid heat exchanger, the controlling thermalresistance fluid side is the liquid side. The heat transfer coefficient h for the fin surface is uniform over the surface (except at the fin tip in some cases) and constant with time. Equation (4.64)reduces to d2 À m2 ¼ 0 ð4:66Þ dx2This is a second-order, linear, homogeneous ordinary differential equation. Longitudinal wall conduction has a significant influence on thecounterflow exchanger size (NTU) for a given \" when NTU > 10 and > 0:005.4.1.3 Single-Pass Parallelflow ExchangerIn the case of a parallelflow exchanger, the wall temperature distribution is always almostclose to constant regardless of the values of C* and NTU. The corresponding F value will be:(a) 0.98 (b) 0.88 (c) 1.00 (d) 0.013.52 Consider a clean counterflow heat exchanger with desired \" ¼ 85% at C* ¼ 1. The water and oil flow rates are 1 and 4 kg/s, respectively. �v�褸T%���ƥ1L.�Q�ڂ�_\)沥�c��G��!o�&�z�ZG�C�m`��� endstream endobj 271 0 obj <>stream (LEW), Selection Criteria Based on Operating Parameters General Selection Guidelines for Major Exchanger Types Some Quantitative Considerations Summary References Review Questions Problems. (4.67) has C1 ¼ 0 C2 ¼ 0 ð4:86Þand ¼ eÀmx ð4:87Þ 0 As noted before, the total fin heat transfer rate can be obtained by integrating thistemperature profile as indicated by Eq.

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