Some peculiarities of the asymmetric Graetz problem

A numerical simulation and an analysis of the steady state forced convection heat transfer with plane laminar flow confined by two parallel plates that are kept at constant but different temperatures are presented. We name this heat transfer configuration shortly the asymmetric Graetz problem. The essential features of the asymmetric in comparison to the symmetric Graetz problem are the reversal of the heat flux and the jump of the Nusselt number from positive to negative region at the plate having the temperature closer to the fluid inlet temperature. These phenomena occur at different axial positions, which depend on the thermal asymmetry and the fluid inlet conditions. The numerical results agree excellently with an analytical solution obtained in terms of Kummer confluent hypergeometric function and Hermite polynomials.