The first Stokes problem of radiative-convective MHD flow in a porous medium

Analytic study on the transient mixed radiative convection flow of viscous, incompressible fluids past an impulsively-started infinite vertical plate is performed. The plate is located in the transverse magnetic field embedded in a porous medium. It is assumed that the transversely applied magnetic field and the magnetic Reynolds number are very small and hence the induced magnetic field is negligible. The fluid considered here is a gray, absorbing-emitting radiation but a non-scattering medium. The Rosseland approximation is used to describe radiative heat transfer in the limit of optically thick fluids. It is also assumed here that the porous medium as an assemblage of small identical spherical particles fixed in space. The relevant transformed dimensionless governing equations are solved by using the Laplace transform technique. The obtaining results concerning velocity and temperature across the boundary layer are illustrated graphically for different values of the parameters entering into the problem under consideration. Results show that for an increase in magnetic field parameter, there is a fall in the velocity, whereas there is a rise in the velocity of the fluid for an increase in porous parameter.