A theoretical solution of the channeling effect is presented. The details of the channeling production are investigated in detail and an approximate method for obtaining the temperature distribution is presented. These results complete a theoretical solution of the channeling effect which has a number of different applications in energy-related problems, such as fixed-bed catalytic reactors, metal processing, underground coal gasification, oil shale, chemical-reaction engineering, drying and packed-bed heat exchangers. These differential permeability problems are also encountered in several energy resource extraction applications related to underground coal conversion, vertical modified in-situ (VSIS) oil shale retortion, steam flooding and oil recovery from tar sands. The method of matched asymptotic expansions is used to obtain the theoretical solution. The effects of using the singular perturbation solution in obtaining the temperature distribution are discussed. The existence and the concept of the triple momentum boundary layer in variable porosity media is analyzed in detail. The theoretical results are found to be in good agreement with the numerical and the available experimental results.

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