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.

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In this evaluation, a numerical exploration is inscribed on MHD unsteady heat and mass transfer of Casson nanofluid flow where variable thermal conductivity, radiation and heat absorption are counterfeited. The model is implemented for the nanofluid which annexes the impression of thermophoresis and Brownian motion. The governing models are metamorphosed as a dimensionless silhouette by the renovation rule of mathematics and the procured dimensionless couple of partial differential equations (PDEs) are elucidated by utilizing explicit finite difference method (EFDM). The numerical aggregates are enumerated for the miscellaneous dimensionless parameters on velocity, temperature and concentration profiles along with the skin friction, Nusselt number and Sherwood number with distinct time interims. ForTran programing language is manipulated as the predominated software for executing the numerical values. Also, by wielding the initial boundary conditions U=T=C=0, X=0.83 and Y=0.50 for =0.0005, convergence criteria are exhibited with Sc 0.18 and Le0.20. At the end, the prevailed culminations are illustrated and perused after the stability convergence test (SCT) by manoeuvring graphics software tecplot-9 and streamlines and isotherms are delineated.

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