Direct and Inverse Heat Transfer Problems in Dynamics of Plate and Tube Heat Exchangers

Abstract

Cross-flow tube heat exchangers find many practical applications. An example of such an exchanger is a steam superheater, where steam flows inside the tubes while heating flue gas flows across the tube bundles. The mathematical derivation of an expression for the mean temperature difference becomes quite complex for multi-pass cross-flow heat exchangers with many tube rows and complex flow arrangement (Hewitt et al., 1994; Kroger, 2004; Rayaprolu, 2009; Stultz et al., 1992 ; Taler, 2009a). When calculating the heat transfer rate, the usual procedure is to modify the simple counter-flow LMTD (Logarithmic Mean Temperature Difference) method by a correction FT determined for a particular arrangement. The heat flow rate Q$ transferred from the hot to cool fluid is the product of the overall heat transfer coefficient UA, heat transfer area A, correction factor FT and logarithmic mean temperature difference ΔTlm. The heat transfer equation then takes the form: