Dual solutions for boundary layer flow and heat transfer of biomagnetic fluid over a stretching/shrinking sheet in presence of a magnetic dipole and a prescribed heat flux

Abstract

This paper analyzes the steady boundary layer flow and heat transfer of biomagnetic fluid over a stretching/shrinking sheet with prescribed surface heat flux under the influence of a magnetic dipole. The governing equations are transformed into a set of ordinary differential equations (ODEs) by using similarity transformations. Numerical results are obtained using the boundary value problem solver bvp4c of MATLAB. The effects of various physical parameters on the velocity and temperature profiles as well as skin friction coefficient are discussed. The paper shows that dual solutions exist for certain values of stretching/shrinking sheet and suction parameters. Stability analysis is performed to determine which solution is stable and physically valid. Results of the stability analysis depict that the first solution (upper branch) is stable and physically realizable, while the second solution (lower branch) is unstable.