Numerical Study of the Double Diffusion Natural Convection inside a Closed Cavity with Heat and Pollutant Sources Placed near the Bottom Wall

Abstract

A study was conducted on the double diffusion by natural convection because of the effects of heat and pollutant sources placed at one third of the closed cavity’s height. The heat and pollution sources were analyzed separately and simultaneously. The study was considered for the Rayleigh number interval 10 4 ≤ R a ≤ 10 10 . Three case studies were analyzed: (1) differentially heated closed cavity with only heat sources; (2) differentially heated closed cavity with only pollutant sources; and (3) differentially heated closed cavity with heat and pollutant sources. The governing equations of the system were solved through the finite volume technique. The turbulence solution was done with the k-ε model. The dominant influence of the buoyancy forces was found due to the pollutant diffusion on the flow pattern, and an internal temperature increase was observed with the simple diffusion. The most critical case was obtained through the double diffusive convection with an average temperature value of 32.57 °C. Finally, the Nusselt number increased as the Rayleigh number increased; however, the Sherwood number either increased or decreased when the Rayleigh number increased. The highest mean concentration recorded was 2808 ppm; this was found with the value R a = 10 6 .

Limit of the buoyancy ratio in Boussinesq approximation for double-diffusive convection in binary mixture

“…[1][2][3][4][5] The greatest portion of the more pertinent binary gas literature has focused on analytical and numerical investigations of natural convection due to horizontal temperature and concentration gradients. [6][7][8][9][10][11][12] With the exception of some works using the non-Boussinesq model, [13][14][15][16][17] it appears that the Boussinesq approximation was used in both cases of aiding and opposing buoyancy forces, which states that variations of density in the equations of motion can safely be ignored everywhere except in its association with the external force. The approximation is well justified in the case of incompressible fluids.…”