Nonlinear Convection in Porous Media: A Review

The review article deals mainly with nonlinear convection (NLC) in porous media and discusses analytical and numerical techniques to handle them. A section on experimental heat transfer in porous media relates to the state of the art on the subject. Five techniques for studying NLC are presented in a logical order of traversal. The first technique, due to Lyapunov, is useful to obtain energy bounds and in conjunction with a variation technique can be used to investigate for possible subcritical instabilities. The power integral and the spectral methods concern steady finite-amplitude convection. The former method is useful in obtaining information on physically preferred cell patterns, whereas the latter can handle cross-interaction of different modes in addition to estimating heat transfer. The Fourier decomposition for unsteady large-amplitude convection is capable of predicting chaos and quantifying heat transfer. The finite-difference method, or any numerical method, when guided by the results of the existing analytical methods and experiment, can be used effectively to handle a more general problem with realistic boundary conditions. The results of the experimental and theoretical study are meant to mutually ratify the respective findings. The present scenario on heat transfer in porous media is such that not all observed aspects can be covered in a theoretical study and also not all results predicted by the theory are experimentally realizable. It thus calls for concerted effort from various quarters. It is on this ground that the review puts together many aspects of NLC in porous media, taking essential excerpts from previous works, with an unavoidable lean on the authors' own works.