Brownian Motion of a Fluid With Ohmic Dissipation Across a Stretched Sheet Incorporating Thermophoresis Effects With Varying Thermal Conductivity and Viscosity

ABSTRACT

This study examines the impact of the Forchheimer coefficient, chemical reaction, and Brownian parameter on the flow of Brownian motion of a viscous Newtonian fluid across a stretching sheet when there is a nonuniform heat source or sink. The model equation takes into account ohmic heating effects as well as changing fluid viscosity and thermal conductivity. The present investigation is motivated by the need to understand the coupled momentum, heat, and mass transfer behavior of an MHD fluid in a non‐Darcian porous medium under the simultaneous effects of variable viscosity, variable thermal conductivity, nonuniform heat source/sink, ohmic heating, viscous dissipation, thermal radiation, Brownian motion, and chemical reaction, which have not been considered together in the existing literature. Unlike previous studies that primarily considered selected combinations of these physical mechanisms, the present study provides a unified analysis of their combined effects on flow and heat/mass transfer characteristics over a stretching sheet. By using pertinent dimensionless variables, the flow equations are transformed. Also, the converted nonlinear equations are solved by the MATLAB–BVP4C method. Graphs and tables are used to examine the impact of the relevant parameters. The impacts of Joule heating, the viscous dissipation parameter, the radiation parameter, the Forchheimer coefficient, and the Brownian parameter on the velocity profile, temperature profile, and concentration profile are the study's key conclusions. Our key findings are that the Forchheimer parameter and variable viscosity parameter declines fluid velocity. The temperature profile increases with increasing Brownian motion and thermophoresis parameters. The concentration profile is enhanced by the Soret parameter, whereas increasing the chemical reaction and Schmidt number parameters leads to a reduction in concentration. Furthermore, the skin‐friction coefficient increases with the magnetic parameter and Forchheimer coefficient, while it decreases with increasing Prandtl number. The Nusselt number increases with the magnetic parameter and Prandtl number, but decreases with increasing Brownian motion parameter. These findings provide useful insights into the coupled momentum, heat, and mass transfer characteristics of non‐Darcian MHD flow with variable fluid properties, with potential applications in thermal management and industrial transport processes.