Natural convection near an isothermal wall far downstream from a source

Abstract

Steady, two-dimensional, free convection flows near an isothermal wall are considered downstream from a heat source at large Grashof numbers for cases when the temperature of the wall is maintained the same as that of the fluid far from the wall. The analyses are given for two cases: (A) for a vertical wall and (B) for a horizontal wall, when the thermal plume spreads along the wall horizontally. The study is based on the Boussinesq boundary layer equations. The solutions have been found in the self-similar form of the second kind. The asymptotic solutions for very large and small Prandtl numbers in the case of the vertical wall, and for very large Prandtl numbers in the case of the horizontal wall are presented. It was found that in the case of the horizontal wall the self-similar solution does not exist in the specific low Prandtl-number regime, σ<0.04218.