In the present study, a nanofluid filled cavity with sinusoidal temperature boundary condition was investigated numerically. The LBM method was applied to simulate the Cu-water nanofluid flow under the influence of an inclined magnetic field. 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 by 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. More than 350 individual tests were carried out in this work to show the combined effect of the nanoparticles and magnetic field situation for different Rayleigh numbers (103–106), Hartmann numbers (0–90), nanoparticles' volume fraction (0–7%) and magnetic field direction γ = 0–90°. The results indicated that the influence of nanoparticles for this geometry and boundary condition is highly dependent to the Rayleigh and Hartmann numbers. Although the magnetic field direction plays an unimportant role in lower Rayleigh numbers but the effect may become significant formoderate or high Rayleigh numbers like 105 or 106.

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