Numerical simulation of unsteady conjugate natural convection in a cylindrical porous domain (Darcy–Boussinesq model)

Mathematical simulation on unsteady natural convection in a closed porous cylindrical cavity having finite thickness heat-conducting solid walls in conditions of convective heat exchange with an environment has been carried out. A boundary-value problem of mathematical physics formulated in dimensionless variables such as stream function and temperature on the basis of Darcy–Boussinesq model has been solved by finite difference method. Effect of a porous medium permeability $10^{—5}\le Da < \infty$, ratio between a solid wall thickness and the inner radius of a cylinder $0.1 \le h/L \le 0.3$, a thermal conductivity ratio $1 \le \lambda_{1,2} \le 20$ and a dimensionless time on both local distributions of isolines and isotherms and integral complexes reflecting an intensity of convective flow and heat transfer has been analyzed in detail.