On the Reynolds-number independence of mixed convection in a vertical channel subjected to asymmetric wall temperatures with and without flow reversal

Abstract

The problem of mixed convection in a vertical channel with asymmetric wall temperatures including situations of flow reversal is studied numerically. The SIMPLER algorithm with a staggered grid system is employed to solve the corresponding numerical equations formulated by the finite-volume method. A second-order upwind scheme is used to model the convective term, and a suitable grid distribution is introduced. The ranges of the parameters studied are 0 ⩽ r t ⩽ 1, 1 ⩽ Re ⩽ 1000, and 0 ⩽ Gr/Re ⩽ 500. The numerical results, with the streamwise coordinate scaled by the Reynolds number (Re), show that solutions for the velocity and temperature fields are independent of the Reynolds number when Re ⩾ 50, even in the presence of flow reversal. These solutions, however, are dependent on r t and Gr/Re. Subsequently, correlations are proposed for the bulk temperature distribution and the local Nusselt numbers along the hot wall and the cold wall.