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This study aims to investigate the effect of a constant magnetic field on heat transfer, flow of fluid, and entropy generation of mixed convection in a lid-driven porous medium enclosure filled with nanofluids (TiO2-water). Uniform constant heat fluxes are partially applied to the bottom wall of the enclosure, while the remaining parts of the bottom wall are considered to be adiabatic. The vertical walls are maintained at a constant cold temperature and move with a fixed velocity. A sinusoidal wall is assumed to be fixed and kept adiabatic at the top enclosure. Three scenarios are considered corresponding to different directions of the moving isothermal vertical wall (±1). The influence of pertinent parameters on the heat transfer, flow of fluid, and entropy generation in an enclosure are deliberated. The parameters are the Richardson number (R~i = 1, 10, and 100), the Hartmann number (0 ≤ H~a ≤ 75 with a 25 step), and the solid volume fraction of nanoparticles (0 ≤ Φ~ ≤ 0.15 with a 0.05 step). The Grashof and Darcy numbers are assumed to be constant at 104 and 10−3, respectively. The finite element method, utilizing the variational formulation/weak form, is applied to discretize the main governor equations. Triangular elements have been employed within the studied envelope, with the elements adapting as needed. The results showed that the streamfunction and fluid temperature decreased as the solid volume fraction increased. The local N~u number increased by more than 50% at low values of Φ~ (up to 0.1). This percentage decreases between 25% and 40% when Φ~ is in the range of 0.1 to 0.15. As H~a increases from 0 to 75, these percentages increase at low values of the value of R~i=1 and 10. These variations are primarily dependent on the value of the Richardson number.
Al-kaby et al. (Wed,) studied this question.