A numerical study is conducted for the Joule heating effects on fluid flow and heat transfer of radiatively participating magnetohydrodynamics (MHD) under different levels of thermal radiation considering the Hall effects in a square cavity. In the cavity, the vertical walls are isothermal with constant but different temperatures, while the horizontal walls are adiabatic. The absorption, emission, and scattering of the fluid and the reflection, absorption, and emission of the walls are all taken into account. The governing equations for momentum and energy together with the boundary conditions are solved by the finite volume method (FVM), while the governing equation for radiative transfer is solved by the discrete ordinates method (DOM). Tabular and graphical results are presented in terms of streamlines, isotherms, Nusselt number, and the average temperature of the fluid. After detailed analysis, we found that the Joule heating has notable effects on fluid flow and heat transfer in the cavity and Joule heating cannot be neglected in certain range of parameters.

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