Unsteady free convective magnetohydrodynamics flow of a Casson fluid through a channel with double diffusion and ramp temperature and concentration

The generalized magnetohydrodynamics (MHD) free convection flow of a Casson fluid through a channel immersed in a porous media with mass and heat transfer is considered. With heat generation, the contribution of concentration gradient is taken into account for heat flux (Dufour effect), and chemical reaction of order first for species balance is also considered. Initially, governing equations of flow model are reduced to nondimensional equations and then solved analytically. The transformed solutions for concentration, temperature, and velocity are written in summation form to invert by Laplace transform easily. The closed form solution of field variables has been plotted graphically due to different parametric variations to analyze the behavior of concentration, temperature, and flow fields against the physical parameters. Furthermore, comparisons among fractionalized and ordinary concentration, temperature, and velocity fields are made to see the effect of parameter alpha. It is concluded that concentration, temperature, and velocity obtained with fractional derivative are smaller than that obtained by ordinary derivative. Therefore, fractional derivative is the best choice to obtain controlled concentration, temperature, and velocity.