Heat Transfer Regimes and hysteresis in Porous Media Convection

摘要

Results of an investigation of different heat transfer regimes in porous media convection are presented by using a truncated Galerkin representation of the governing equations that yields the familiar Lorenz equations for the variation of the amplitude in the time domain. The solution to this system is obtained analytically by using a weak non-linear analysis and computationally by using Adomian's decomposition method. Expressions for the averaged Nusselt number are derived for steady, periodic, as well as weak-turbulent (temporal-chaotic) convection. The phenomenon of Hysteresis in the transition from steady to weak-turbulent convection, and backwards, is particularly investigated, identi- fying analytically its mechanism, which is confirmed by the computational results.