Effects of viscous dissipation and free convection currents on the flow of an electrically conducting fluid past an accelerated vertical porous plate

In the present paper, the effects of free convection currents and the viscous dissipation on the unsteady flow of an electrically conducting and viscous incompressible fluid around an uniformly accelerated vertical porous plate subjected to a suction or injection velocity inversely proportional to the square root of time, in presence of a transverse magnetic field, have been investigated. Analytical solutions for the velocity and the temperature distributions, the skin-friction and the rate of heat transfer are obtained for small magnetic parameterM. During the course of discussion the effects of the Grashof number Gr, the Eckert number Ec, the suction/injection parametera have been considered for unit value of the Prandtl number Pr.Nomenclature a suction/injection parameter - C _p specific heat at constant pressure - B ₀ magnetic induction - g acceleration due to gravity - Gr Grashof number (g(T _w –T )/U ₀ ³ ) - K thermal conductivity - M magnetic field parameter (B ₀ ² /U ₀ ² ) - Pr Prandtl number (C _p/K) - T temperature of the fluid near the plate - T _w temperature of the plate - T temperature of the fluid at infinity - t time - t dimensionless time (tU ₀ ² /) - u velocity of the fluid - u non-dimensional velocity (u/U ₀) - U velocity of the plate - U dimensionless velocity of the plate (U/U ₀) - U ₀ reference velocity - v ₀ suction velocity - v ₀ non-dimensional suction velocity (v ₀/U ₀)=at ^–1/2 - Ec Eckert number ((U ₀)^2/3/C _p(T _w –T )) - T dimensionless temperature of the fluid near the plate ((T–T )/(T _w ^–T )) - x, y coordinates along and normal to the plate - x, y dimensionless coordinates (y=yU ₀/) - kinematic viscosity - coefficient of volume expansion - electric conductivity of the fluid - y/2t ^1/2 - density of the fluid - skin-friction - dimensionless skin-friction - q rate of heat transfer - q non-dimensional rate of heat transfer - coefficient of viscosity - _e magnetic permeability On leave of absence from Department of Mathematics, University of Dhaka, Bangladesh