ANALYSIS OF STEADY THREE-DIMENSIONAL HYDROMAGNETIC STAGNATION POINT FLOW TOWARDS A STRETCHING SHEET WITH HEAT GENERATION

Abstract

This paper is concerned with the three-dimensional hydromagnetic stagnation point flow towards a stretching sheet with heat generation.  It is assumed that a uniform magnetic field is applied normal to the plate which is maintained at a constant temperature.  The coupled partial differential equations are reduced into ordinary differential equations by using similarity transformations.  The series solutions of the coupled non-linear system is obtained using an analytical technique namely the homotopy analysis method (HAM).  We use a two-stage method, where both the convergence control parameter and the initial guess are optimally selected to minimize the residual error due to the approximation.  To do the latter, we consider a family of initial guesses parameterized by a constant which gives the decay rate of the solutions.  In several cases considered, we are able to obtain solutions with extremely small residual errors after relatively few iterations are computed.  The convergence, salient features of the flow and heat transfer characteristics are analyzed and discussed in detail through graphs.  We also discuss the effect of the strength of the uniform magnetic field, the surface stretching velocity, and the heat generation/absorption coefficient on both the flow and heat transfer.