Natural convection along a vertical isothermal plate with linear and non-linear Rosseland thermal radiation

The steady laminar natural convection along a vertical isothermal plate with linear or non-linear Rosseland radiation is investigated in this paper. The problem is self-similar and the results are obtained with the direct numerical solution of the governing equations. This problem is governed by the Prandtl number, the temperature parameter as well as the radiation parameter, and the influence of these parameters on the results are presented in tables and figures. A new radiation parameter is introduced which leads to an asymptotic state. It is found that the temperature profiles take a special S-shape form with an inflection point. Moreover, it is shown that when the wall shear stress increases the wall heat transfer decreases and vice versa.