Study on the Solution of a Viscous Incompressible Electically Conducting Fluid Flow over an Elastic Stretching Sheet: Similarity Approach Vs Approximate Method

Abstract

This paper presents a study of steady laminar flow of a viscous incompressible electrically conducting fluid over a stretching sheet. Exploiting the fact that some features of free-parameter method and the ''separation of variables'' method are alike, an exact solution to the problem is obtained. This solution is compared with an approximate solution to the problem, obtainable by exploiting the idea of stretching the variables of the flow problem and then using least squares method to minimize the residual of a differential equation concerned. Finally, the results obtained, in terms of a magnetic parameter, are discussed. In the applications of the free parameter method and the ‘separation of variables’ method to two-dimensional boundary layer flows, stream function \(\psi\) is introduced and subsequently a non-linear partial differential equation in \(\psi\) is also derived.