Effectiveness-NTU method

The actual heat transfer may be computed by calculating either the energy lost by the hot fluid or the energy gained by the cold fluid. Consider the parallel-flow and counterlow heat exchangers shown in Fig. 10-7. For the parallel-flow exchanger 

The minimum fluid may be either the hot or cold fluid, depending on the mass-flow rates and specific heats. For the parallel-flow exchanger 

The subscripts on the effectiveness symbols designate the fluid which has the minimum value of me. For the counterflow exchanger  

We may derive an expression for the effectiveness in parallel flow as follows. Rewriting Eq. (10-10), we have 

Inserting this relation back in Eq. (10-23) gives for the effectiveness 

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The effectiveness—NTU method is a procedure for evaluating the performance of heat exchangers, which has the advantage that it does not require the evaluation of the mean temperature differences. NTU stands for the Number of Transfer Units, and is analogous with the use of transfer units in mass transfer see Chapter 11. 

ESDU 93018 (2001) Forced convection heat transfer in straight tubes. Part 2 laminar and transitional flow. ESDU 98003-98007 (1998) Design and performance evaluation of heat exchangers the effectiveness-NTU method. 

Kays and London [3] have presented effectiveness ratios for various heat-exchanger arrangements, and some of the results of their analyses are available in chart form in Figs. 10-12 to 10-17. Examples 10-9 to 10-14 illustrate the use of the effectiveness-NTU method in heat-exchanger analysis. 

What advantage does the effectiveness-NTU method have over the LMTD method ... 

Hot exhaust gases are used in a finned-tube cross-flow heat exchanger to heat 2.5 kg/s of water from 35 to 85°C. The gases [cp = 1.09 kJ/kg °C] enter at 200 and leave at 93°C. The overall heat-transfer coefficient is 180 W/m2 °C. Calculate the area of the heat exchanger using (a) the LMTD approach and (b) the effectiveness-NTU method. 

The effectiveness-NTU method will not be covered in this book, as it is more useful for rating than design. The method is covered in books by Incropera and Dewitt (1996), Ozisik (1985) and Hewitt et al. (1994). The method is also covered in the Engineering Sciences Data Unit, ESDU 86018 (1986). This reference gives large clear plots of effectiveness versus NTU and is recommend for accurate work. 

We mentioned earlier that when all the inlet and outlet temperatures are specified, the size of the heat exchanger can easily be determined using the LMTD method. Alternatively, it can also be determined from the effectiveness-NTU method by first evaluating the effectiveness e from its definition (Hq. 11-29) and then the NTU from the appropriate NTU relation in Table 11-5. 

Analj is In the effectiveness-NTU method, we first determine the heat ca-pacify rates of the hot and cold fluids and Identify the smaller one ... 

ESDU 98003-98007 (1998) Design and performance evaluation of heat exchangers the effectiveness-NTU method. 

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