Natural circulation in vertical porous annular enclosure with heat generation

Natural convection ow is considered in an annular enclosure lled with a uid-saturated porous medium. The top and bottom horizontal walls are insulated, while the outer vertical wall is cooled with a constant temperature, and a linear temperature gradient is applied to the inner vertical wall. Dimensionless equations are solved numerically using the Finite Volume Method (FVM) on a collocated non-uniform, orthogonal grid. The Darcy-Forchheimer model is used to simulate the momentum transfer in the porous medium. The eect of Rayleigh, Darcy, Prandtl, solid- uid Nusselt, heat generation parameters and eective conductivity ratio of phases on the streamlines and isotherms are presented, as well as on the rate of heat transfer from the inner and outer vertical walls of the enclosure. It is concluded that at low values of the eective conductivity ratio of phases, only the heat generation parameter has a signicant eect on the temperature eld of the solid phase and the heat transfer from inner and outer vertical walls. An analytical solution is obtained for this case and compared with the numerical solution. The results show good agreement with each other.