Critical parameter research on natural convection of radiation-magnetohydrodynamics in a square cavity

In this work, the influence of thermal radiation on natural convection of radiation-magnetohydrodynamics (R-MHD) in a square cavity is investigated numerically under different thermal radiation levels. The range of Pl number, in which it is proved that thermal radiation can be neglected, is obtained under different Re and Ha, respectively. The finite volume method (FVM) is employed to solve the momentum equation and the energy equation along with boundary conditions, and the discrete ordinates method (DOM) is used to obtain local radiative heat flux. Distribution of velocity and temperature with different Pl is discussed. The results show that thermal radiation effects on natural convection of R-MHD decrease exponentially with Pl, and the critical number Plc also decreases exponentially with Re and increases exponentially with Ha.