An analytical treatment for the exact solutions of MHD flow and heat over two–three dimensional deforming bodies. (November 2015) - Turkyilmazoglu, Mustafa
Highlights: Exponential type series solutions are shown to exist, having finite or infinite terms. Special closed-form solutions are shown to be possible when the series terminates. For infinite series, an algorithm is presented to non-iteratively evaluate the flow region. The heat domain is specifically resolved without any numerical means. Interesting algebraic solutions are found pointing to multiple solutions. Abstract: The present paper is dedicated to the mathematical analysis of MHD permeable heat and fluid flow fields induced by stretching or shrinking two–three dimensional objects. In contrast to a variety of existing numerical solutions in the open literature on the ongoing topic, obtaining exact analytical solutions is targeted either in general or in restrictive forms. Particularly, exponential type series solutions are shown to exist, having finite or infinite terms in the expansion depending on the prevailing parameters of the fields of flow and heat. Special closed-form solutions are shown to be possible when the series terminates. In the case of infinite terms are present in the series, an algorithm is presented to non-iteratively evaluate the coefficients while resolving parameter domain of the problem. The heat domain is specifically resolved without any numerical means. The occurrence of algebraic solutions corresponding to linear/nonlinear/exponential stretching/shrinking of the surface is also accounted for. Interesting algebraic solutions are found pointing to multiple solutions; even for the non-MHD stretching plate problem. These solutions are much valuable since they represent a rare class of exact solutions to boundary layer equations and they will shed light upon further studies on the physical phenomenon.