A local thermal non-equilibrium integral analysis for forced convective thermal boundary development in a channel filled with a fluid-saturated porous medium

Abstract

An integral solution procedure has been developed to describe the entire evolution of the thermal boundary layer in a channel filled with a fluid-saturated porous medium. The upper and lower walls are heated under a constant heat flux condition, and local thermal nonequilibrium is assumed to apply. The development of the thermal boundary layer in this channel is divided into three distinctive regions, namely, the entrance, transition and the nearly fully-developed regions, in which separate fluid and solid phase thermal boundary layers develop near heated walls with different growth rates. In this integral analysis, each region is considered in terms of the interactions between the fluid and solid thermal boundary layers; this eventually yields a set of algebraic equations for the easy and accurate estimation of the local Nusselt number. The solutions thus obtained for the three regions are combined to reveal the entire development of the local Nusselt number from the entrance to fully-developed stage. This analytic procedure, for the first time, reveals a complete region map showing the locations of the transition from one region to another, and these depend on the Biot number, the thermal conductivity ratio and the Graetz number in a complex manner.