Local Thermal Nonequilibrium (LTNE) Modeling of a Partially Porous Channel With Spatial Variation in Biot Number

Abstract

The local thermal nonequilibrium (LTNE) model has been used widely for analyzing heat transfer during internal flow through porous media, including when a channel is only partially filled with a porous medium. In such problems, the Biot number describes the rate of convective heat transfer between solid and fluid phases. While uniform Biot number models are commonly available, recent advances in functionally graded materials necessitate the analysis of spatially varying Biot number in such geometries. This paper presents LTNE-based heat transfer analysis for fully developed flow in a channel partially filled with porous medium and with spatially varying Biot number to describe solid-fluid interactions in the porous medium. Fully uncoupled ordinary differential equations for solid and fluid temperature distributions are derived under three different boundary condition models. Solid and fluid temperature fields are presented for a variety of Biot number distributions, including quadratically and periodically varying functions. An explanation of the nature of temperature distribution predictions for such problems is provided. For special cases, the results presented here are shown to reduce to past work on constant Biot number. This work improves the theoretical understanding of porous media heat transfer and facilitates the use of such theoretical models for functionally graded materials.