The current study deals with numerical simulation to analyze the effect of magnetohydrodynamic (MHD) forces on natural convection within a square enclosure including an inner corrugated circular cylinder. Also, the effect of nonlinear thermal radiation has been considered. In this model, the nanofluid composed of copper oxide (CuO) and water is diffused all throughout the porous medium of the enclosure. It is considered that the nanofluid's temperature and nanoparticle volume concentration both have an effect on determining the dynamic viscosity and thermal conductivity. The outer square-shaped enclosure is supposed to be cold when the temperature of the inner corrugated cylinder is presumed to be hot. Flow patterns and thermal patterns inside the enclosure are visualized through the distribution of streamlines and isothermal contours. Heat transfer rates are estimated on the basis of the local (NuL) and average (Nuavg) Nusselt number. Computational results are generated for several parameters, like Rayleigh number (Ra), Darcy number (Da), Hartmann number (Ha), surface temperature parameter (χ), radiation parameter (Rd), and solid volume concentration of nanoparticles (ϕ). The flow intensity of fluid is noticeably improved through intensifying Rayleigh number, radiation, surface temperature and concentration of nanoparticles but ascending Hartmann number counteracts this phenomenon. The heat transfer rate throughout the enclosure could be slowed down significantly by filling it with a porous substance.
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