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This paper studies the effect of thermo-diffusion, electrical field, and nonlinear thermal radiation. Thermal radiant heat transfer has several industrial applications, and the analysis of radiation heat transfer in non-Newtonian fluids under different conditions has been widely studied. To better understand the problem of thermal nonlinear radiation heat transfer flow in non-Darcy Casson fluid on stretched surfaces, this research examines such a phenomenon. The Hybrid Analytical and Numerical Method (The HAN Method) is used to precisely analyze the steady flow of incompressible Newtonian electrically conducting non-Darcy Casson fluid on a vertical permeable stretchable plate with the presence of the magnetic field. The governing equations of this problem are reduced from the system of nonlinear partial differential equations (PDEs) into a system of nonlinear ordinary differential equations (ODEs) using similarity transformations. The results showed that Casson's parameter has a small and indirect effect on temperature and mass transfer, but it affects the velocity significantly and directly. Also, the magnetic field has a direct and significant effect on temperature and velocity but an indirect and significant effect on concentration. The electric field has a direct and significant effect on temperature and velocity but an indirect and significant effect on concentration. Also, the effects of parameters such as thermal buoyancy, inertial, porous permeability, Eckert number, Prandtl number, chemical reaction, Schmidt and Soret numbers, and porosity on velocity, temperature, and concentration have been studied.
Jalili et al. (Sat,) studied this question.