Onset of Convection in Porous Media Induced by Transient Heat Conduction

In this study a computational fluid dynamics (CFD) package – FLUENT/UNS was adopted to simulate the occurrence of convection in an isotropic porous media. The porous layer was homogenous and bounded by two horizontal rigid surfaces. 2-D simulation for steady state and time-dependent were conducted for the bottom surface with two boundary conditions: i) Fixed Surface Temperature – FST, ii) Constant Heat Flux – CHF. The top surface was maintained at FST boundary condition and the vertical wall was adiabatic. The 2-D steady state simulations were carried out to investigate the occurrence of convection as predicted by the linear theory. The 2-D time-dependent were conducted to investigate the possibility of adopting Tan and Thorp’s transient Rayleigh number theory in deep layer of porous media saturated with water. The CFD was successful in modeling the onset of convection in saturated porous media. The range of maximum velocity at the onset of convection and the finger shape of the thermal plume were in agreement with the literatures (Horton and Roger 1949, Elder 1968). The maximum Nusselt number based on кm for the FST and CHF boundary condition were in the range between 3-4, depending on the rate of heat transfer. The steady state and time-dependent simulation results showed no significant difference in the Rayleigh number as predicted by Lapwood (1948) Rac = 39.5, Ribando and Torrance (1976) Rac = 27.1 for the FST and CHF boundary condition. The average Rayleigh numbers based on кm for the steady state simulation were respectively 32.02 and 32.71 for the FST and CHF boundary conditions. The average transient numbers for the time-dependent simulations were respective 30.90 and 30.40 for FST and CHF boundary conditions respectively. The deviation of the Rayleigh number may be due to the complexity of the heat transfer in porous media as wide difference of thermal diffusivity of the solid and liquid that are existing in the saturated porous media. Beside this, large temperature difference ATs or heat flux qº, imposed on the porous media to induce the convection was against the assumption of perturbation theory in which allows only a small disturbance or change in density of the fluid and constant fluid properties.

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