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Heat Transfer Handbook part 82

Heat Transfer Handbook part 82. The Heat Transfer Handbook provides succinct hard data, formulas, and specifications for the critical aspects of heat transfer, offering a reliable, hands-on resource for solving day-to-day issues across a variety of applications. | HEAT EXCHANGER ANALYSIS METHODS 805 For the counterflow exchanger where the fluids flow in opposite directions through the exchanger Fig. 11.2a LMTD 71 t2 T2 ti ln Ti T2 T2 ti 11.25 For the co-current or parallel flow exchanger where the fluids flow in the same direction through the exchanger Fig. 11.2 LMTD T1 t1 T2 t2 In T1 t1 T2 t2 11.26 For an exchanger that has a constant-temperature source Ts T1 T2 and a rising-temperature receiver Fig. 11.2c 2 ti LMTD -------------2----1-------- 11.27 ln Ts t1 Ts 12 For an exchanger that has a constant-temperature receiver ts t1 t2 and a falling-temperature source Fig. 11.2d LMTD T1 T2 In T1 ts T2 ts 11.28 These simple expressions for the logarithmic mean temperature difference cannot be employed for arrangements other than those shown in Fig. 11.2. The procedure for the case of crossflow and multipass exchangers is given in the next section. 11.3 HEAT EXCHANGER ANALYSIS METHODS 11.3.1 Logarithmic Mean Temperature Difference Correction Factor Method The logarithmic mean temperature difference developed in Section 11.2.4 is not applicable to multipass or crossflow heat exchangers. The temperature parameter Qm in eqs. 11.2 and 11.3 is the true or effective mean temperature difflencm tc and is related to the logarithmic mean temperature difference A T1 A T2 AT2 AT x. LMTD 1------------ 2----------- 11.24 m ln AT1 AT2 ln AT2 AT1 V 7 and the functions t2 t1 P -------- 11.29a T1 t1 806 HEAT EXCHANGERS defined as the cold-side effectiveness and R Ti - T2 C 2 h Ch 11.29b defined as a capacity rate ratio. The true or effective mean temperature difference in multipass or crossflow exchangers em will be related to the counterflow logarithmic mean temperature difference via em F LMTDJ where the correction factor f _ _ LMTDc 11.30 is a function of P R and the flow arrangement. The quest for the logarithmic mean temperature difference correction factor apparently began in the early 1930s Nagle 1933 Underwood 1934 Fischer 1938 Bowman et al.