In this paper, Casson–Williamson and Maxwell fluid flow over a stretching porous sheet is investigated numerically, taking into account the effects of thermal radiation, thermophoresis, magnetohydrodynamics (MHD), and chemical processes. The flow, heat transfer, and mass diffusion controlling partial differential equations (PDEs) are converted into ordinary differential equations (ODEs) by use of a similarity transformation. Utilizing the fourth-order Runge–Kutta (RK) method, the resulting equations are solved. The study examines key thermal and flow characteristics, including the influence of thermal radiation, the Prandtl number, Brownian motion, thermophoresis, Schmidt number, chemical reaction, magnetic field strength, Casson parameter, and Deborah number on velocity, temperature, and concentration profiles. Findings reveal that an increase in thermal radiation, Prandtl number, and Brownian motion parameter leads to a decline in temperature, whereas thermophoresis enhances fluid temperature. Higher Schmidt numbers reduce concentration due to lower mass diffusivity, while strong chemical reactions increase concentration. The application of a magnetic field results in velocity suppression due to Lorentz forces, whereas the elastic and rheological properties of Casson and Maxwell fluids further hinder fluid motion. The study presents thorough numerical results that demonstrate differences in the skin friction coefficient, Sherwood number, and Nusselt number, presented in graphical form. The research extends the theoretical framework of porous-sheet MHD flows by demonstrating how the standard boundary-layer similarity equations are modified by plastic yield (Casson), shear-rate-dependent viscosity (Williamson), and fluid elasticity (Maxwell).
Kavitha et al. (Fri,) studied this question.