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This article investigates the effect of Rayleigh numbers, Hartmann numbers, and magnetic fields on nanofluid flow behavior and heat transfer. The flow behavior has been analyzed based on the contours and values of the flow function and heat transfer based on the temperature distribution contours and local and average Nusselt number values. Since the effects of the magnetic field are an important parameter in many technical and engineering applications such as cooling of nuclear reactors, extraction of geothermal energy, and induction casting of metals, in this study, its effect on aluminum oxide nanoparticle, Al2O3, and water, H2O, has been analyzed. The governing equations of nanofluid flow, continuity, momentum, and energy equations have been solved using the Galerkin finite element method and coded and simulated using FlexPDE software. The results obtained for both octagonal cavities containing horizontal and vertical Cassini oval barriers with specific boundary conditions show that with the Rayleigh number and nanoparticle volume fraction being constant, the value of the maximum stream function decreases with the increase of the Hartmann number, and when the Hartmann number and nanoparticle volume fraction is constant, with increasing Rayleigh number, its value increases significantly.
Roshani et al. (Sat,) studied this question.