Numerical analysis of natural convection in cavities with variable porosity

Abstract

This work analyzes the effects of variable porosity on the heat transfer by natural convection, in a cavity with isothermal vertical walls and adiabatic horizontal ones and a porous medium inside. The hydrodynamic field in the porous medium is modelled according to the general model obtained by Brinkman's and Forchheimer's terms. An exponential variation of the porosity near the walls was considered. The equations in terms of the real variables were numerically solved by the finite-volume method, with a staggered variables arrangement. The pressure-velocity coupling was treated with the PRIME algorithm. The simulations involved both Darcian (Da = 10 -7 ) and non-Darcian flows (Da = 10 -6 ). In each case, the modified Rayleigh range (Ra m = Ra 2 Da) was from 10 to 1,000, and from 100 to 5,000, respectively. For the numerical simulation we considered Pr = 1, Rk = 1, A = 1, and k X = 0.36. The results are shown through streamlines and isotherms and velocity and temperatures profiles. This shows that the generalized method with variable porosity means an increase in the average Nusselt number. For physical validation, some experimental sets were simulated in which glass was the porous medium, and water, alcohol, and transformer oil were used as the fluids. The simulated results indicate that the adopted model reduces the discrepancy in the experimental results obtained with water and alcohol. We proposed a correlation to evaluate the average Nusselt number as a function of six parameters: Rayleigh number, Prandtl number, the dimensionless particle diameter, thermal conductivity ratio between solid and fluid phase, porosity, and the aspect ratio of the cavity.