This study presents a mathematical investigation into the phenomena of radiative heat with an unsteady MHD electrically conducting boundary layer of chemically reactive Casson nanofluid flow due to a pored stretchable sheet immersed in a porous medium in the presence of heat generation, thermophoretic force, and Brownian motion. The surface is assumed to be not flat, and has variable thickness. The magnetic field is time-dependent, and the chemical reaction coefficient is inversely varied with the distance. The nanofluid’s velocity, heat, and concentration at the surface are nonlinearly varied. A similarity transformation is introduced, and the controlling equations are converted into nondimensional forms involving many significant physical factors. The transformed forms are analyzed numerically using a computational method based on the finite difference scheme and Newton’s linearization procedure. The impact of the involved physical parameters is performed in graphical and tabular forms. Some special cases of the current work are compared with published studies, and an excellent agreement is obtained. The main results of the present work indicate that the higher values of the Casson parameter cause an increase in both the shear stress and heat flux, but a decrease in the mass flux. Also, it is noted that the chemical reaction, the nanoparticles’ volume, and the permeability factor enhance the effect the of Casson parameter on both the shear stress and heat flux, while the variable thickness and thermal radiation field reduce it; on the other hand, the variable thickness and nanoparticles’ volume enforce the influence of the Casson parameter on mass flux, but thermal radiation, the permeability factor, and chemical reaction decrease it. The present study has important applications in mechanical engineering and natural sciences. In addition, it has significant applications in devices used for blood transfusion, dialysis and cancer therapy.

The current work analyzes the impact of thermal radiation on the nonlinear slip flow of an unsteady magnetohydrodynamic Casson hybrid nanofluid over a heated surface embedded in the Darcy−Forchheimer porous medium. The hybrid nanofluid flows in the presence of a varying magnetic field and heat generation. The viscous dissipation, Brownian motion, and thermophoretic force are taken into consideration. The surface is extendable, permeable, and variably thickened. The hybrid nanofluid includes copper, titanium dioxide nanoparticles, and water as the base fluid. The driving PDEs are turned into nondimensional ODEs using a similarity transformation. The ODEs are solved computationally by the finite difference method, incorporating Newton's linearization process. The effects of the involved factors on heat transport and solute fluxes are presented in plots and tabular forms for skin friction, heat transfer rate, and mass transfer rate. A comparison with earlier published studies is exhibited, and an excellent agreement is obtained. The computational results indicate that the slip velocity and Forchheimer factor enhance the Nusselt number and reduce the Sherwood number. The higher values of slip velocity parameters, the nanoparticle volume fractions, and thermal radiation enhance the friction force. On the other hand, the increment of the Forchheimer factor, Casson parameter, Schmidt number, and porosity parameter cause an increase in drag force. It is observed that as the TiO₂ nanoparticles volume fraction increases (0 to 5%) at fixed Cu nanoparticles volume fraction, the Nusselt number increases by 19.14%, whereas both the skin friction and Sherwood number decrease by 0.4% and 11.99%, respectively. The findings of the current study may have significant applications in engineering and biotechnology systems such as cancer therapy, dialysis, blood transfusion, and treatment.