Abstract
This chapter discusses the problems of non-Darcian convective heat transfer using the Darcy-Forchheimer boundary-layer equations and a similar approach to that described by Nakayama and Pop. The unified treatment, based on this modified Peclet number, enabled them to extract all possible similarity solutions for free, forced, and mixed convection within Darcy and non-Darcy porous media There exists three limiting flow regimes––namely, (1) the forced convection, (2) the Darcy free convection, and (3) the Forchheimer free convection regimes. Appropriate dimensionless groups for identifying these regimes are the micro-scale Reynolds and Grashof numbers based on the square root of the permeability. Upon taking these dimensionless numbers as the variables, a regime map can be constructed to show the three asymptotic convection regimes, and also other three intermediate convection regimes–namely, (1) the Darcy mixed convection, (2) the Darcy-Forchheimer free convection, and (3) the Forchheimer mixed convection regimes.
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