Heat transfer correlation for benard convection in a fluid saturated porous layer

Abstract

Diverse measurements of heat transfer by Benard convection in a fluid saturated porous layer are correlated by considering only the Darcy and Forschheimer asymptotes of the phenomenon. Scale analysis suggests that in the Forschheimer limit the Nusselt number must increase as ( Ra Pr p ) 1 2 , where Ra is the Darcy-Rayleigh number based on height and Pr p is an entirely new group called “the porous medium Prandtl number.” The transition from the Darcy regime to the Forschheimer regime occurs at Ra ∼ Pr p. The heat transfer correlation is Nu = {( Ra 40 ) n + [c(RaPr p) 1 2 ] n} 1 n with n = −1 65 , c = 1896.4 and Pr p = (H/bK)Pr m , where H, b, K and Pr m are the height, Forschheimer constant, permeability and Prandtl number based on the thermal conductivity of the porous medium.