Thermal Efficiency of the Cross Flow Heat Exchangers

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 an ideal balanced counter flow heat exchanger. It has been 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. The function defining the efficiency of these heat exchangers is identical to that of a constant area fin with an insulated tip. This paper presents exact expressions for the efficiencies of the different cross flow heat exchangers. It is shown that by generalizing the definition of Fa, very accurate results can be obtained by using the same algebraic expression, or a single algebraic expression can be used to assess the performance of a variety of commonly used heat exchangers.