On the Temperature Slip Boundary Condition in a Mixed Convection Boundary-Layer Flow in a Porous Medium

A problem derived previously (Rohni et al., Transp Porous Media 92:1–14, 2012) for unsteady mixed convection flow in a porous medium involving a ‘temperature slip’ boundary condition and fluid transfer through the boundary is considered. It is shown that the solution to this problem can be directly related to the solution of the corresponding problem for a prescribed surface temperature, involving a mixed convection parameter λ, an unsteadiness parameter A and transpiration parameter s. This latter problem is discussed in detail, particular attention being given to the steady analogue, A = 0, allowing for fluid transfer through the surface, and to the unsteady problem, A > 0, for an impermeable surface, s = 0. Asymptotic results are obtained for large fluid transfer rates, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${s \gg 1}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${s <0 , |s| \gg 1}$$\end{document} and for large A. Particular attention is given to deriving asymptotic results for the critical points which determine the range of existence of solutions.