Analytical characterization and conceptual assessment of solid and fluid temperature differentials in porous media

Abstract

An analytical characterization of forced convective flow through a channel filled with a porous medium is presented in this work. Based on a two-equation model, including transverse conduction contributions, exact solutions are obtained for both fluid and solid phase temperature fields. The Nusselt number is also obtained in terms of the pertinent physical parameters, namely the Blot number for the internal heat exchange and the ratio of effective conductivities between the fluid and solid phases. It is shown that the heat transfer characteristics can be classified within three regimes, each of which is dominated by one of three distinctive heat transfer mechanisms, i.e., fluid conduction; solid conduction and internal heal exchange between solid and fluid phases. Based on these results, a complete electrical thermal network representative of transport through porous media is established. In addition, an analytical characterization and conceptual assessment of solid and fluid temperature differentials is presented. the validity of the one-equation model is investigated and a practical criterion is suggested for channels with different cross sections. (C) 1998 Elsevier Science Ltd. All rights reserved.