51 - Heat Exchangers - LMTD Method

In most shell and tube exchangers the flow will be a mixture of co-current, counter-current and cross flow. The usual practice in the design of shell and tube exchangers is to estimate the “true temperature difference” from the logarithmic mean temperature by applying a correction factor (\(F\); or \(F_t, F_T\)) to allow for the departure from true counter-current flow: \[\Delta T_{\text{corr}} = F\; \Delta T_{\text{lm}}\] \(F\) depends on the geometry of the heat exchanger and the inlet and outlet temperatures of the hot and cold fluid streams.

Charts for correction factor (\(F\)) are available for commonly used heat exchanger configurations. In these figures, the abscissa is a dimensionless ratio \(P\), defined as \[P = \frac{t_2-t_1}{T_1-t_1}\] where \(T\) represents the shell-side temperature, \(t\) to the tube-side temperature, and subscripts 1 and 2, respectively to the inlet and outlet conditions. The parameter \(R\) appearing on the curves is defined as \[R = \frac{T_1-T_2}{t_2-t_1} = \frac{(\dot{m}C_P)_{\text{tube side}}}{(\dot{m}C_P)_{\text{shell side}}}\]