## 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.