Unsteady MHD double-diffusive convection boundary-layer flow past a radiate hot vertical surface in porous media in the presence of chemical reaction and heat sink

This paper presents an analytical study of the unsteady MHD free convective heat and mass transfer flow of a viscous, incompressible, gray, absorbing-emitting but non-scattering, optically-thick and electrically conducting fluid occupying a semi-infinite porous regime adjacent to an infinite moving hot vertical plate with constant velocity. We employ a Darcian viscous flow model for the porous medium the Rosseland diffusion approximation is used to describe the radiative heat flux in the energy equation. The homogeneous chemical reaction of first order is accounted in mass diffusion equation. The governing equations are solved in closed form by Laplace-transform technique. A parametric study of all involved parameters is conducted and representative set of numerical results for the velocity, temperature, concentration, shear stress function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\frac{\partial u}{\partial y} \vert_{y=0}$\end{document}, temperature gradient \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\frac{\partial \theta }{ \partial y}\vert_{y=0}$\end{document}, and concentration gradient \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\frac{ \partial \phi }{\partial y}\vert_{y=0}$\end{document} is illustrated graphically and physical aspects of the problem are discussed.