Flow reversal symmetry in a convective heat exchange model

Under some simplifying assumptions often used in the thermal design of heat exchangers, a system of two coupled linear homogeneous first‐order partial differential equations with variable coefficients is used to describe a steady‐state convective heat exchange process. Using an integral representation for the outlet temperatures as functions of the inlet ones, a symmetry property is proved for the transformation that inverts the velocity fields of both fluids. In particular, the average thermal effectiveness is shown to coincide for the direct and reversed processes.