Effect of Inclined Magnetic Field and Injection on Magneto Hydrodynamic Boundary Layer Flow over a Porous Exponentially Stretching Sheet in Presence of Thermal Radiation

Abstract

In this study, MHD boundary layer flow of a viscous incompressible fluid over a porous exponentially stretching sheet with an inclined magnetic field in presence of thermal radiation and injection is analyzed. The general equations describing the fluid motion are discussed, after which the specific equations governing the flow are formulated. These equations include; continuity, momentum and energy equations. The externally applied inclined magnetic field is accounted for in the momentum equation via the Lorentz force and thermal radiation is taken into account in the energy equation. The porosity of the sheet is described by Darcy’s law and it is accounted for in the momentum equation. The continuity, momentum and energy equations obtained are then transformed into a system of nonlinear ordinary differential equations using similarity transformations. The resulting nonlinear ordinary differential equations are then changed to a system of first order ordinary differential equations in order to obtain the solution numerically by collocation method. The effects of magnetic field, angle of inclination, radiation, injection, permeability, prandtl number and the exponential stretching of the sheet on velocity and temperature of the fluid are discussed. From the results, it is observed that fluid velocity is suppressed by increasing the strength of magnetic field, angle of inclination and permeability property of the material, but boosted when injection and stretching on the material are increased. Fluid temperature is observed to be increasing with increase in magnetic field strength, angle of inclination, injection, permeability and radiative property of the material, but reduces due to increase in stretching parameter, stratification parameter and prandtl number of the material. It is also observed that increasing the magnetic field, angle of inclination and permeability of the material on the path of flow of the fluid lowers the skin friction, but it increases when the material is stretched exponentially and also when injection is done. Nusselt number become large when stretching, injection and prandtl number are increased, but decreases when permeability, magnetic field, angle of inclination and radiative property of the material are boosted.