Laplace transformation technique for free convective time-dependent MHD flow over a vertical porous flat plate with heat sink and chemical reaction: An analytical approach

The free convective time-dependent magnetohydrodynamic flow through permeable vertical plate has gained considerable interest in near future for their vast applications particularly in thermal insulation, energy storage, industrial cooling, and many more. The present work is analysed on the free convective conducting time-dependent flow over a flat plate for the interaction of buoyant forces. The flow through permeable medium affecting the physical properties for the consideration of the thermal radiation, heat source and chemical reaction. Additionally, buoyant forces formulated both the occurrence of solutal and thermal convection and the plate conditions are also time-dependent. The change of governing equations into their corresponding non-dimensional form is obtained for the suitable choice of non-dimensional variable and then the solution of time-dependent problem is found analytically by applying the Laplace transform approach. The speciality of the problem is the plate condition which is time-dependent which uses Heaviside function. Depending upon the suitable conditions the results of the profiles are presented considering the values of the values of the corresponding factors involved and the physical behavior of each of the factors are elaborated briefly. Moreover, the important outcomes of the study are; the impact of buoyancy forces augments the velocity profile focusing on the cooling of the surface and the solutal concentration attenuates for the utility of heavier species but the impact is reversed for the solutal transfer rate.