How does heat move through porous materials? This study investigates different heat transfer regimes in porous media convection. It uses a truncated Galerkin representation of the governing equations, leading to the Lorenz equations, and then obtains solutions both analytically and computationally. The research derives expressions for the averaged Nusselt number for steady, periodic, and weak-turbulent convection. It particularly examines the phenomenon of hysteresis in the transition between steady and weak-turbulent convection. The study reveals that, while transient solutions are sensitive to initial conditions, long-term predictability of averaged variables, like the Nusselt number, is possible, offering practical implications.
Published in the Journal of Heat Transfer, this paper aligns with the journal's focus on fundamental heat transfer phenomena. It presents a detailed analysis of heat transfer in porous media, a topic relevant to various engineering applications. The research uses mathematical modeling and computational techniques to understand complex heat transfer behaviors.