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Present study concerns with the numerical investigation of the MHD free convection and heat transfer fluid flow through a semi-infinite vertical porous plate with the effects of chemical reaction. A boundary layer approximation is premeditated to develop a flow model representing time dependent momentum, energy and concentration equations. The governing model equations are governed as a form of coupled nonlinear dimensionless system of partial differential equations (PDEs) by the as usual mathematical procedure of mathematical transformation and which model equations are solved by using explicit finite difference method (EFDM). Then the numerical results have been calculated by Compaq Visual FORTRAN (CVF) 6.6a and the obtained results have been capitalized for the variations of various dimensionless parameters on velocity, temperature and concentration profiles along with the skin friction coefficient, Nusselt number, Sherwood number, Isotherms and Streamlines. At the end, the obtained results are plotted and discussed after stability convergence test (SCT) by the using graphics software tecplot-9. An increases in the Grashof number is to increase the velocity distributions but by increasing the magnetic parameter which reduces the velocity profiles whereas increasing the heat generation parameter which increase the temperature profile.

In this paper, we have reported the effects of Hall current on magnetohydrodynamics (MHD) unsteady heat and mass transfer of Casson nanofluid flow through a vertical plate in the presence of radiation and chemical reaction. The model equations have been used for the Casson nanofluid and they include the effects of thermophoresis and Brownian motion. Then, the obtained model equations have been transformed into nondimensional form by the usual mathematical procedure of transformation and the resultant nondimensional couple of partial differential equations are solved by explicit finite difference technique. Then, the obtained results are plotted after stability test by using the graphical software tecplot-9 and these results indicate the fluid flow, temperature, and concentration distributions which are significantly invaded by the variation of different dimensionless parameters such as magnetic parameter, Schmidt number, thermal Grashof number, Lewis number, Prandtl number, mass Grashof number, Dufour number, thermophoresis parameter, Brownian motion parameter, chemical reaction, and radiation parameter on velocity, temperature, and concentration along with the skin friction coefficient, Nusselt number, and Sherwood number. Further, the results have been discussed also with the help of graphs. Furthermore, it is observed that with the increase of the Casson parameter, velocity puts down, whereas by increasing the heat generation parameter, the temperature profiles are decreased.

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