Influence of Internal Heat Generation on the Natural Convection of Non-Newtonian Fluids over a Vertical Plate in Porous Media with Thermal Radiation and Soret/Dufour Effects: Variable Wall Temperature/Concentration

The heat and mass transfer characteristics of the influence of internal heat generation on the natural convection of non-Newtonian fluids over a vertical plate in porous media with thermal radiation and Soret/Dufour effects are numerically analyzed. The surface of the vertical plate has a variable wall temperature and variable wall concentration (VWT/VWC). The similarity solution is obtained by assuming internal heat generation to be in exponential decaying form. The Rosseland diffusion approximation is employed to describe the radiative heat flux. Similar governing equations are solved by Keller box method. Comparisons showed excellent agreement with the numerical data of previous works. Numerical data for the dimensionless temperature profile, the dimensionless concentration profile, the local Nusselt number and the local Sherwood number are presented for the buoyancy ratio N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ N $$\end{document}, the Lewis number Le\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ Le $$\end{document}, the power-law index of the non-Newtonian fluid n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ n $$\end{document}, the Soret parameter S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ S $$\end{document}, the Dufour parameter D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ D $$\end{document}, the exponent of VWT/VWC λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \lambda $$\end{document}, the internal heat generation coefficient A∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ A^{*} $$\end{document} and the thermal radiation parameter Rd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ R_{d} $$\end{document}. The physical aspects of the problem are discussed in detail.