In this study, we numerically explore the impact of varying viscosity and thermal conductivity on a magnetohydrodynamic flow problem over a moving nonisothermal vertical plate with thermophoretic effect and viscous dissipation. The boundary conditions and flow‐regulating equations are converted into ordinary differential equations with the aid of similarity substitution. The MATLAB bvp4c solver is used to evaluate the numerical solution of the problem and it is validated by executing the numerical solution with previously published studies. The impacts of several factors, including the magnetic parameter, Eckert number, heat source parameter, thermal conductivity parameter, stratification parameter, Soret, Dufour, Prandtl number, and Schmidt number are calculated and shown graphically. Also, the skin friction coefficient, Nusselt number, and Sherwood number are calculated. Fluid velocity, temperature, and concentration significantly drop as the thermophoretic parameter and thermal stratification parameter increases. As thermal conductivity rises, it is seen that the velocity of the fluid and temperature inside the boundary layer rise as well. Also, the Soret effect drops temperature and concentration profile. The applications of this type of problem are found in the processes of nuclear reactors, corrosion of heat exchangers, lubrication theory, and so forth.

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The current study focuses on the magnetohydrodynamic flow of fluids through two vertical, insulated walls. The influences of Newtonian heating/cooling, induced magnetic field (IMF), the Soret effect, radiative heat flux, and first‐order chemical reaction are considered. By solving the set of non‐dimensional linked governing equations, we were able to determine the expressions for the velocity, temperature, concentration, and IMF. The equations for Nusselt number, induced current density, and skin friction were also obtained. The graph displays the effects of several parameters on velocity, temperature, concentration, IMF, and induced current density (ICD). Additionally, a tabular analysis is done to see how these non‐dimensional parameters affect Nusselt number and skin frictions. It is seen that the Grashof number and Soret number improve the fluid velocity and skin friction whereas the chemical reaction parameter and Schmidt number reduces skin friction.