Numerical Investigation of Unsteady MHD Free Convection Flow with Radiation, Chemical Reaction, Heat Source, Soret and Dufour Effects in a Porous Medium Using Crank–Nicolson Finite Difference Method

The present study investigates the unsteady magnetohydrodynamic free-convection flow of a viscous, incompressible, electrically conducting fluid through a porous medium in the presence of thermal radiation, a heat source/sink, a chemical reaction, viscous dissipation, and the Soret and Dufour effects. A uniform transverse magnetic field is applied normal to the flow direction. The governing partial differential equations describing momentum, energy, and concentration transport are transformed into dimensionless form using suitable similarity variables. The resulting coupled nonlinear dimensionless equations are solved numerically using the Crank–Nicolson implicit finite-difference method. The effects of various physical parameters, such as the thermal Grashof number, solutal Grashof number, Hartmann number, Darcy number, radiation parameter, chemical reaction parameter, Brinkman number, Dufour number, and Soret number, on the velocity, temperature, and concentration profiles are discussed graphically. Numerical values of skin friction coefficient, Nusselt number, and Sherwood number are also presented and analyzed. The study reveals that the magnetic field and chemical reaction reduce the velocity and concentration distributions, whereas thermal radiation and heat source significantly enhance the thermal field.

Magnetohydrodynamic flow; Porous medium; Thermal radiation; Chemical reaction; Soret effect

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