Boundary Layer Flow Over a Moving Vertical Flat Plate with Convective Thermal Boundary Condition

This paper studies the steady boundary layer flow over an impermeable moving vertical flat plate with convective boundary condition at the left side of the flat plate. The governing partial differential equations are transformed into a system of ordinary (similarity) differential equations by using corresponding similarity variables. These equations were then solved numerically using the function bvp4c from Matlab for different values of the Rayleigh number Ra, the convective heat transfer parameter γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma $$\end{document}, and the Prandtl number Pr. This paper demonstrates that a similarity solution is possible if the convective boundary condition heat transfer is associated with the hot or cooled fluid on the left side of the flat plate proportional to x-1/4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x^{-1/4}$$\end{document}. For the sake of comparison of the numerical results, the case of the static flat plate (σ=0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\sigma =0)$$\end{document} has been also studied. For the case of a moving flat plate (σ=1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\sigma =1)$$\end{document}, it is shown that the solutions have two branches in a certain range of the positive (assisting flow) and negative (opposing flow) values of the Rayleigh number Ra. In order to test the physically available solutions, a stability analysis has been also performed. The effects of the governing parameters on the skin friction, heat transfer, wall temperature, velocity and temperature profiles, as well as on the streamlines and isotherms are investigated. Comparison with results from the open literature shows a very good agreement.