Combined influences of radiation and inclined magnetic field on natural convection in a cavity with complex geometry

Abstract

In the current study, the influence of inclined magnetic field and optical thickness on the natural convection heat transfer of participating magnetic fluid flow in a complex geometry are investigated, for the first time. The physical model is a 2D square enclosure with an internal elliptical heater. The radiative transfer equation is used instead of the Roseland approximation to calculate the divergence of the radiative heat flux. The multiple-time-relaxation lattice Boltzmann method is adopted to calculate the velocity and temperature fields. The complex boundary conditions are treated using the immersed boundary technique and the radiative transfer equation by the finite volume method. The findings are accessible in terms of streamlines, isotherms, Nusselt number, percentage reduction of the heat transfer, and correlation of Nusselt number for a wide range of optical thicknesses (0 ≤ τ ≤ 100), Hartmann numbers (0 ≤ Ha ≤ 500), and magnetic field inclinations (0° ≤ γ ≤ 90°) in fixed values of Rayleigh number (Ra = 106) and Planck number (Pl = 0.1). The results showed that at Ha = 500, in an optically thin medium (τ ≤ 1), the maximum reduction of the heat transfer because of the magnetic effect is less than 15%, while this is 61% and 66% for τ = 100 and the non-radiative state, respectively.