A numerical investigation on MHD fluid flow in parabolic mode has been performed to point out its significant properties. Thermal radiation, porous medium, heat generation, chemical reaction, and thermal diffusion along with variable temperature and concentration are taken into consideration in the analysis. The novelty of the work is the inclusion of heat generation and thermal diffusion along with exponentially varying temperature and concentration. The constituent governing equations are solved by using finite difference schemes in explicit form. The fluctuations in velocity, concentration, and temperature are observed and discussed with the help of graphs as well as numerical data. Their gradients are also calculated and analyzed the flow properties by using numerical tables. The existence of heat generation, as well as viscous dissipation, creates an increment in the temperature. The gradient of heat transfer rises with the impact of Prandtl number and decay in it is examined under the existence of a source of heat and viscous dissipation.

A considerable effort has been made to draw out the flow properties of the magnetohydrodynamic fluid in parabolic movement with several parameters under cross‐diffusion. The novelty in the examination is the angle of inclination with a permeable vertical plate. The purpose of the work is to analyze the impact of some parameters on the flow in two cases, namely, obtuse angle and acute angle. The solution of the flow‐governed equations is attained by the utilization of the finite divergence technique in explicit type. The nature of the fluid velocity is observed in the cases of acute angle and obtuse angle and described accordingly with the use of graphs and tables. The validation of the method is checked with the published outcomes and pointed out a fine agreement with it. One of the major findings is that for increasing values of porosity the velocity enhances in the case of an acute angle and falls in the case of an obtuse angle.

In the presence of Soret and Dufour effects, a numerical analysis is performed for an unstable magnetohydrodynamics convective flow of parabolic motion with variable temperature and concentration.The finite-difference method is used to solve the set of nondimensional governing equations with boundary conditions numerically. Graphs are used to investigate the effect of various physical characteristics on flow quantities. Variations in skin friction, Nusselt number, and Sherwood number are also examined using tables for physical curiosity. This study is unique in that it takes into account changeable temperature as well as concentration with Soret and Dufour effects. The magnetic parameter, Prandtl number, heat source, radiation parameter, Schmidt number, and chemical reaction parameter show a significant increase in skin friction, whereas the Grashof number, modified Grashof number, permeability parameter, radiation absorption parameter, Dufour number, and Soret number show the opposite trend. As the Soret number rises, the concentration rises as well, whereas the opposite is true for the Schmidt number and the chemical reaction parameter. The current study is highly supported by previously published data that have been verified.