Effect of anisotropic permeability on convective flow through a porous tube with viscous dissipation effect

Fully developed convective flow in a tube filled with an anisotropic porous material with viscous dissipation due to an internal heat source is considered. An analytical solution is obtained subject to constant heat flux at the wall of the tube. The effect of the anisotropy parameters (anisotropic permeability ratio 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} and inclination angle of principal axes φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi $$\end{document}) of the porous medium on the hydrodynamic and convective heat transfer inside the tube is shown. The singular behavior of the Nusselt number is discussed. Asymptotic analysis for high and low Darcy numbers is shown to support the validity of the present study. Detailed analysis showing the effect of anisotropy on the convective heat transfer is performed.