On a Bivariate Spectral Homotopy Analysis Method for Unsteady Mixed Convection Boundary Layer Flow, Heat, and Mass Transfer due to a Stretching Surface in a Rotating Fluid

Sandile S Motsa,Zodwa G Makukula

doi:10.1155/2017/5962073

Abstract

A bivariate spectral homotopy analysis method (BSHAM) is extended to solutions of systems of nonlinear coupled partial differential equations (PDEs). The method has been used successfully to solve a nonlinear PDE and is now tested with systems. The method is based on a new idea of finding solutions that obey a rule of solution expression that is defined in terms of the bivariate Lagrange interpolation polynomials. The BSHAM is used to solve a system of coupled nonlinear partial differential equations modeling the unsteady mixed convection boundary layer flow, heat, and mass transfer due to a stretching surface in a rotating fluid, taking into consideration the effect of buoyancy forces. Convergence of the numerical solutions was monitored using the residual error of the PDEs. The effects of the flow parameters on the local skin-friction coefficient, the Nusselt number, and the Sherwood number were presented in graphs.

Highlights

Fluid flow dynamics due to a stretching surface find applications in the production of sheeting material including metal and polymer sheets
The results show convergence of the series solutions against the convergence controlling parameter, ħ, residual error curves and variation of the skin-friction coefficient, and Nusselt and Sherwood numbers with the different flow parameters
The paper extended the application of a bivariate spectral homotopy analysis method to solutions of systems of nonlinear partial differential equations

Summary

Introduction

Fluid flow dynamics due to a stretching surface find applications in the production of sheeting material including metal and polymer sheets. The two-dimensional flow in the boundary layer induced by a rotating fluid past a stretching surface was first studied by Wang [3]. Such flows have applications in geophysics and astrophysics, in solar physics involved in the sunspot development, and in self-cooled liquid metal blankets in fusion reactors when the container is being rotated [4]. Other reported studies include that of Nazar et al [6], who carried out a numerical investigation of the induced unsteady flow due to a stretching surface in a rotating fluid, where the unsteadiness is caused by the suddenly stretched surface. The resulting equations were solved using the Keller-box method

Objectives

Results

Conclusion