A numerical study of mixed convection in a vertical channel flow impinging on a horizontal surface

In this study, mixed convection in a vertical channel flow discharging over a horizontal isotherm surface is investigated numerically using a finite difference method based on projection algorithm. The governing equations are discretized by a second order central difference in space and first order in time. The average Nusselt number is calculated on the horizontal surface in various vertical channels of varying areas considering non-dimensional parameters consisting of Reynolds and Richardson (or Grashof) numbers. Analysis of the results shows that there is an optimum gap to have a maximum heat transfer rate over the surface. The optimum gap value varies with Grashof and Reynolds numbers and inlet length of the channel but for high Richardson numbers, Nu has an increasing trend with reduction of gap size. By increasing the Re, Gr and Ri numbers, Nu number increases but in Ri of 0.1 and 0.01 the variations are approximately similar to each other. In addition, a divergent channel is usually more efficient than convergent one concerning heat transfer over the horizontal surface. Effects of Prandtl number and asymmetricity in channel are investigated in detail too.