Performance. NTU Method

The thermal design of heat exchangers discussed in the preceding sections rests usually on the following first key problem  

The outlet temperatures can be determined by trial and error using the LMTD method. IT one of the outlet temperatures is guessed, then the problem is reduced to the first type. However, because this would not be the actual exit temperature, the heat transfer values given by Eqs. (7.12) and (7.31) will not match. As the assumed value of the outlet temperature approaches its actual value (through successive guesses), the difference between Eqs. (7.12) and (7.31) diminishes. This is a tedious trial-and-error procedure, and a new method different from the LMTD method is needed. The so-called NTU method14 eliminates the foregoing trial-and-error and is the topic of this section. 

Return to Eq. (7.12) and let this equation be equal to a product eCA7 where the proportionality constant e is the so-called heat-exchanger effectiveness and AT is a temperature difference. Since the inlet temperatures are given, let AT = Tm — Tci, which is the largest temperature difference in a heat exchanger. Ch or Cc are two possibilities for C. Consider the smaller of the two and designate it as Cjnin. Then, for any heat exchanger, we have 

This definition accepts an interpretation in terms of a counter-flow heat exchanger as 

To demonstrate that C iThi — TCi) is the maximum attainable heat transfer with a counter-flow heat exchanger, consider Eq. (7.11) for a counter-flow heat exchanger, 

---

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. 

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

It is important to note that the NTU method, although devised for performance under different conditions, equally applies to the design of heat exchangers. Therefore, it is a more general method than the LMTD method. Here we recapitulate both methods for a ready reference in heat-exchanger calculations ... 

The principal use of this method is in the rating of an existing exchanger. It can be used to determine the performance of the exchanger when the heat transfer area and construction details are known. The method has an advantage over the use of the design procedure outlined above, as an unknown stream outlet temperature can be determined directly, without the need for iterative calculations. It makes use of plots of the exchanger effectiveness versus NTU. The effectiveness is the ratio of the actual rate of heat transfer, to the maximum possible rate. 

---