Magnetohydrodynamic Free Convection Flows with Thermal Memory over a Moving Vertical Plate in ...

The unsteady hydro-magnetic free convection flow with heat transfer of a linearly viscous, incompressible, electrically conducting fluid near a moving vertical plate with constant heat is investigated. The flow domain is the porous half-space and a magnetic field of variable direction is applied. The Caputo time-fractional derivative is employed in order to introduce a thermal flux constitutive equation with a weakly memory. Exact solutions of the fractional governing differential equations for fluid temperature, Nusselt number, velocity field and skin friction are obtained by using the Laplace transform method. Numerical calculations are carried out and results are presented in graphical illustrations. The influence of the memory parameter (the fractional order of the time-derivative) on the temperature and velocity fields is analyzed and a comparison between the fluid with thermal memory and the ordinary fluid is made. It was observed that, due to evolution in time of the Caputo power-law kernel, the memory effects are stronger for the small values of the time t. Also, it is found that fluid flow is accelerated / retarded by the varying the inclination angle of the magnetic field direction.