New upper bounds and reduced dynamical modeling for Rayleigh–Bénard convection in a fluid saturated porous layer

New rigorous upper bounds on the enhancement of heat transport in a fundamental model of porous medium convection are presented. The computational results are applied to the development of finite dimensional dynamical systems models of porous medium convection. The number of degrees of freedom in the full dynamics and the dimension of potentially faithful reduced descriptions are discussed.

► New rigorous upper bounds on the enhancement of heat transport by convection in a porous medium.
► Results are applied to the development of finite dimensional dynamical systems models.
► The number of degrees of freedom in the full dynamics and faithful reduced descriptions are estimated.