The Shell and Tube Heat Exchanger Efficiency and Its Relation to Effectiveness

Abstract

The heat exchanger efficiency is defined as the ratio of the actual heat transfer in a heat exchanger to the optimum heat transfer rate. The optimum heat transfer rate, qopt, is given by the product of UA and the Arithmetic Mean Temperature Difference, which is the difference between the average temperatures of hot and cold fluids. The actual rate of heat transfer in a heat exchanger is always less than this optimum value, which takes place in a balanced counter flow heat exchanger. It is shown that for parallel flow, counter flow, and shell and tube heat exchanger the efficiency is only a function of a single nondimensional parameter called Fin Analogy Number. Remarkably, the functional dependence of the efficiency of these heat exchangers on this parameter is identical to that of a constant area fin with an insulated tip. Also a general algebraic expression as well as a generalized chart is presented for the determination of the efficiency of shell and tube heat exchangers with any number of shells and even number of tube passes per shell, when the Number of Transfer Units (NTU) and the capacity ratio are known. Although this general expression is a function of the number of shells and another nondimensional group, it turns out to be almost independent of the number of shells over a wide range of practical interest. The same general expression is also applicable to parallel and counter flow heat exchangers.