In this study, we examine the effect of a uniform external magnetic field on Rayleigh-Bénard convection in a square cavity filled with a ferrofluid. Numerical simulations are based on the Lattice Boltzmann method. The effects of physical parameters, which are the Rayleigh number, the Hartmann number, and the angle of inclination of the magnetic field are studied. The results obtained are graphically illustrated and discussed for a volume fraction of four percent. These results show that the rate of heat transfer decreases by increasing the Hartmann number. For high Rayleigh number values, the maximum heat transfer rate was obtained for a specific Hartmann number when the Lorentz and buoyancy forces are perpendicular.

Heat transfer of nanofluid Fe₃O₄-H₂O generated by natural convection and thermal radiation in a diamond-shaped receiving cavity has been investigated numerically. The lower and upper corners of the rhombic receiver are kept isothermal in such a way to provide heating from the lower corner parts and maintain adiabatic the remaining nonactive portions of the walls. The lattice Bolkmann method has been used to simulate fluid flows and highlight the combined effects of the control parameters that are the Rayleigh number (Ra = 10³ to 2 × 10⁶), the radiation parameter (Rd = 0 to 3), and the nanoparticles' volume fraction (φ = 0 to 4%). The obtained flow structures are either monocellular (MF) or bicellular (BF), depending on the initial conditions and the generated heat transfer rates corresponding to the resulting structures are improved by increasing the Rayleigh number, the nanoparticles' volume fraction, and the radiation parameter. All critical Rayleigh numbers leading to different types of transitions within the considered range of this parameter undergo a change by varying the volume fraction of nanoparticles and the radiation parameter.

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