Lie group analysis for MHD boundary layer flow and heat transfer over stretching sheet in presence of viscous dissipation and uniform heat source/sink

Abstract

An analysis for the MHD boundary layer flow and heat transfer towards stretching sheet is carried out via symmetry analysis. A steady two dimensional flow of an electrically conducting incompressible fluid flow over a stretching sheet. The flow is permeated by a uniform transverse magnetic field. The governing partial differential equations are reduced to a system of ordinary differential equations by the scaling symmetries. The symmetry groups admitted by the corresponding boundary value problem are obtained by using special Lie group transformations. The scaling of group transformations is applied to the governing equations. The system remains invariant due to some relation among the parameters of the transformations. After finding two absolute invariants a third order ordinary differential equation corresponding to momentum equation and second order differential equation corresponding to energy equation are derived. The equations along with boundary conditions solved numerically. Numerical solutions of these equations are obtained by using Runge-Kutta-Fehlberg scheme. Further more attention is paid to the effects of some physical parameters magnetic field (Mn), Prandtl number (Pr), Eckert number (Ec) and uniform heat source/sink, on velocity and thermal boundary layer. The results thus obtained are presented graphically and discussed.