Analysis of forced convection heat transfer from a circular cylinder embedded in a porous medium

Time-dependent forced convection heat transfer from a single circular cylinder embedded in a horizontal packed bed of spherical particles under local thermal non-equilibrium condition is investigated numerically using the spectral-element method. The non-Darcian effects, i.e. inclusion of the effect of solid boundaries and inertia forces, and the effect of thermal dispersion, are taken into account. The influences of the presence of the porous material and its thermal properties: solid-to-fluid thermal conductivity ratio k(r)is an element of[0.01, 1000] and Biot number Bi is an element of[0.01,100], on the rates of heat transfer and the hydrodynamic and thermal responses, are examined for the Reynolds number range Re(D)is an element of[1, 250]. These effects are quantified. Perhaps not surprisingly, the results show that the presence of the porous particles suppresses significantly the wakes behind the cylinder and enhances considerably the heat transfer. A comparison that is made between the one- and two-equation energy model predictions shows that the former model predicts a continuous increase in Nu(f) against k(r); however, the trend of Nu(f) with k(r), for k(r) > 10, is governed entirely by Bi when the latter model is used. Also, the increase in Bi decreases Nu(f) and increases Nu(s), and high values of k(r) or Bi lead to establishing a thermal equilibrium status in the porous bed. (C) 2011 Elsevier Masson SAS. All rights reserved.