Dynamical flow analysis of joule heating for cross fluid model with Darcy-Forchheimer and variable thermophysical properties

This study investigates the boundary layer stagnation point flow of cross fluid over a stretching surface under the combined influences of Darcy-Forchheimer and the magnetic field. The thermal and solution investigations are carried out by incorporating the Joule heating, viscous dissipation and activation energy. To investigate the physical nature of flow, we consider the temperature-dependent viscosity and thermal conductivity while the thermal diffusion is assumed as concentration dependent. This study is significant because of its wide uses in various engineering, chemical, and industrial domains. The study formulates and solves a set of coupled partial differential equations governing the flow, thermal and diffusion processes. The similarity transformations are adopted to convert the governing partial differential equations into ordinary differential equations. The numerical solutions are achieved by using a built-in command (BVP4c) in MATLAB. This investigation aims to examine the behavior of different flow parameters graphically, offering insights into complex fluid dynamics situations with practical implications. The numerical results of physical quantities are examined due to different emerging parameters. Hartmann number and Forchheimer number cause a decrease in velocity profile likewise stretching ratio parameter and viscosity parameter cause an increase in velocity profile. The Prandtl number suppresses the temperature while Eckert number and Hartmann number elevate it. Schmidt number decreases the concentration profile, while activation energy acts to intensify it.