In the present study, a nanofluid–filled cavity with sinusoidal temperature boundary condition under the influence of an inclined magnetic field was investigated numerically. The lattice Boltzmann method (LBM) was applied to simulate the nanofluid flow with water as the carrier fluid and for three different nanoparticle types: Al2O3, Cu, and TiO2. More than 1100 individual tests were carried out in this work to show the combined effect of the nanoparticles and magnetic field situations. It goes without saying that nanoparticles are meant to improve the heat transfer rate, because unlike the magnetic field they are not present in any system on their own, but they′re added manually to enhance the Nusselt number. However, it is seen that in some magnetic situations (field intensity and direction) adding the volume fraction of nanoparticles cannot help the heat transfer increment. The flow and heat transfer behavior of these three nanofluids were observed for different Rayleigh numbers (103–106), Hartmann numbers (0–80), nanoparticle volume fraction (0– 6%), magnetic field direction θ = 0–90◦, and temperature boundary condition phase deviation γ = 0–90◦. The results indicated that the influence of nanoparticles for this geometry and boundary conditions is highly dependent on the Rayleigh and Hartmann numbers. Although the magnetic field direction plays an unimportant role in lower Rayleigh numbers, the effects will become most significant for moderate Rayleigh numbers like 105.

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