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Magnetohydrodynamic and entropy generation of double-diffusive mixed convection in a curvilinear cavity filled with nano-enhanced phase change material and a rotating cylinder has been studied in this paper. Three heat sources have been considered and a range of different variables such as Reynolds number (10 ≤ Re ≤ 100), Richardson number (0.1≤ Ri ≤ 10), Hartmann number (0≤ Ha ≤50) Lewis number (0.1≤ Le ≤ 0.9), bouncy ratio (1≤ Nz ≤ 5), fusion temperature (0.1≤ θf ≤0.9) and Stephan number (0.1≤ Ste ≤0.9). These variables have been numerically solved by applying the Finite Element Method. The main results indicated that heat transfer, mass transfer and heat capacity are hugely increased with the increase of the Re, Ri and volume concentration while decreasing with the increase of the Ha number and entropy generation. Furthermore, the melting/solidification region is hugely influenced by the fusion temperature while this variable has a negligible influence on streams, heat transfer and mass transfer. Furthermore, the value of the average Nusselt number and average Sherwood number has increased by 328 % and 258 % respectively by increasing the Reynolds number from 10 to 100. Also, these two numbers have decreased by 61 % and 54 % respectively by increasing the Hartmann number from 0 to 20.

Using porous media is an efficient technique aimed at enhancing heat transfer in engineering systems. Replacing conventional fluids by ferrofluids and applying external magnetic fields through magnets is another method for heat transfer control. In this regard, understanding the behavior of ferrofluids through porous media in the presence of magnets is important. The present study aims at providing a thorough analysis of the properties of heat transfer resulting from the combination of buoyancy driven convection and thermomagnetic convection in a porous enclosure. The equations governing the two types of convection in the fluid as well as the conduction in the solid matrix are presented in the dimensionless form and solved numerically. The control volume finite element method has been used to solve the governing equations. The influence of various parameters such as the magnetic Rayleigh number, the porosity, Darcy number, and the interfacial heat transfer coefficient on the flow and temperature contours and on the Nusselt number is then investigated. For low interface coefficient, the heat transfer in the fluid is enhanced when the overall porosity in the cavity is raised, while for high coefficients, the porosity of the bottom porous layer is the main parameter affecting the heat transfer.