Semi-transient thermal analysis from MHD-Participating fluid into a square cavity with variable optical thickness

Abstract

In this study, the effect of the variable radiative absorption coeeficient in a two-dimensional closed cavity containing an electrical conductor fluid under a uniform magnetic field on the heat transfer and the fluid flow is investigated. The governing equations for the laminar flow and the boundary conditions are solved numerically using the finite volume method. The dependence of the velocity and pressure field is solved using the SIMPLER algorithm and the radiative transfer equation using the discrete ordinates method. A semi-transient algorithm is used to solve both the magnetic convection and radiation equations. The impact of the effective parameters of the maximum optical thickness in the range of 0.1–5, Hartmann number in the range of 0–800 and Rayleigh number in the range of 104-106 in two modes of the average and variable absorption coefficient with the linear temperature are investigated. The results show that by increasing the optical thickness and the Hartmann number and by changing the absorption coefficient of the medium from the average to the variable, the average Nusselt number decreases by 10.5%. Moreover, the effect of Rayleigh number on the heat transfer and fluid flow is investigated. The study of the Rayleigh number shows that the maximum percentage of heat transfer reduction which was made by switching the absorption coefficient of the medium from average to variable does not alter by changing the Rayleigh number, so it is independent of the Rayleigh number. Also, the highest percentage of the reduction in small Hartmann numbers is related to the Rayleigh number 104. Besides, the results reveal that by increasing the Hartmann number from 400 onwards for Rayleigh number 106 and 200 onwards for Rayleigh numbers 104 and 105, the average Nusselt numbers difference in the mode of average and variable absorption coefficient is almost constant.