Stagnation Point Flow and Heat Transfer on a Porous Stretching/Shrinking Cylinder: Analytical Procedure

Abstract

This parametric study deals with stagnation point flow and heat transfer on a stretching/shrinking cylinder under convective boundary conditions. Unlike most existing investigations that rely on numerical or semi-analytical methods, closed-form parametric solutions are obtained for both the momentum and energy equations. It is based on the similarity solution that highly non-linear Partial Differential Equations (PDEs) can be reduced to highly non-linear Ordinary Differential Equations (ODEs). Suction/injection, curvature, stretching/shrinking, heat generation/absorption, radiation parameters, as well as Biot and Prandtl numbers are several parameters encountered in this problem. The energy equation is solved analytically using a confluent hypergeometric function, enabling explicit evaluation of temperature distributions and local Nusselt numbers. Plots and tables illustrate the velocity and temperature profiles, the local skin friction coefficient, and the Nusselt number. After analyzing the data in detail, it was found that a rise in the stretching parameter accelerates the growth rate in the local skin friction coefficient of the typical flow more than that of the stagnation point flow. Furthermore, the influence of the heat sink parameter is more prominent in high Biot numbers in order to achieve maximum local Nusselt numbers.