Radiative MHD unsteady Casson fluid flow with heat source/sink through a vertical channel suspended in porous medium subject to generalized boundary conditions

Abstract

Abstract Unsteady, incompressible flow of Casson fluid between two infinitely long upward heated walls nested in a porous medium is analyzed in this work. The mass diffusion and heat transfer phenomena are also studied in the presence of thermal radiation, magnetic field, and heat source/sink. The generalized boundary conditions in terms of continuous time-dependent functions are considered for mass, energy, and momentum fields. Fick’s law, Fourier’s law, and momentum conservation principle are adopted to formulate the mathematical equations. Analytic solution for the concentration equation is established first by adding certain unit-less quantities and then by using the Laplace method of transformation. Semi-analytic solutions are calculated by means of Stehfest’s numerical Laplace inversion algorithm for energy and velocity equations. To demonstrate the verification of those solutions, a tabular comparison is drawn. Graphical illustrations along with physical descriptions are provided to discuss the essential contribution of thermo-physical parameters in heat and mass transfer and flow of the Casson fluid. The numerical computations of Sherwood number, Nusselt number, and skin friction for various inputs of related parameters are organized in tables to investigate mass transfer rate, heat transfer rate, and shear stress respectively. It is observed that porosity of the medium and buoyancy force tend to accelerate the flow. The heat and mass transfer rates are appreciated by Prandtl and Schmidt numbers respectively. Furthermore, radiation parameter and Grashof number significantly minimize the shear stress.