MHD natural convection in a nanofluid filled inclined enclosure with sinusoidal wall using CVFEM

Magnetohydrodynamic flow in a nanofluid filled inclined enclosure is investigated numerically using the Control Volume based Finite Element Method. The cold wall of cavity is assumed to mimic a sinusoidal profile with different dimensionless amplitude, and the fluid in the enclosure is a water-based nanofluid containing Cu nanoparticles. The effective thermal conductivity and viscosity of nanofluid are calculated using the Maxwell–Garnetts and Brinkman models, respectively. Numerical simulations were performed for different governing parameters namely the Hartmann number, Rayleigh number, nanoparticle volume fraction and inclination angle of enclosure. The results show that in presence of magnetic field, velocity field retarded, and hence, convection and Nusselt number decreases. At Ra = 10³, maximum value of enhancement for low Hartmann number is obtained at γ = 0°, but for higher values of Hartmann number, maximum values of E occurs at γ = 90°. Also, it can be found that for all values of Hartmann number, at Ra = 10⁴ and 10⁵, maximum value of E is obtained at γ = 60° and γ = 0°, respectively.