Magnetohydrodynamic instability of mixed convection in a differentially heated vertical channel

The present paper investigates the instability of mixed convection in a differentially heated vertical layer of an electrically conducting fluid under the influence of a uniform horizontal magnetic field. The key parameters which influence the instability characteristics of the system are the Hartman number, the Reynolds number, the Grashof number and the Prandtl number. The computational results reveal that two-dimensional disturbances are more unstable than the three-dimensional disturbances. Further, influence of the Grashof number and the Hartmann number is analyzed on the basic flow. The effect of increasing the Hartman number shows stabilizing effect on the fluid flow and dissimilar is the case with an increase in the Reynolds number and the Prandtl number. In the presence of Reynolds number, Re, stationary instability disappears altogether which is contrary to the results observed in the case of pure natural convection (Re→0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ Re\rightarrow 0$\end{document}). The numerical results obtained under the limiting cases are shown to be in excellent agreement with the existing ones.