Reduced model for characterization of solid wall effects for transient thermal dispersion in granular porous media

Abstract

This paper is devoted to modelling of the thermal interface condition between a solid wall and a granular porous bed through which a fluid flows. Far from the wall, the porous medium, a bed of monodisperse glass beads, is homogeneous. An average enthalpic temperature, based on spatial averaging of the local field over a representative elementary volume, is defined, and a corresponding heat equation can be derived: it uses a Darcy velocity, dispersion coefficients that depend on this velocity, and two volumetric heat capacities (fluid and solid). The presence of a solid wall modifies the local arrangement of the beads, with a porosity that varies with the distance to the wall. In a plug flow situation in the core of the bed, the local velocity becomes larger in the near-wall region, creating a channelling effect that affects the wall-to-porous medium heat transfer. This transfer is studied, for transient wall heating, using heat transfer models of increased complexity and specific analytical methods. Finally a reduced model is proposed for this channelling effect, with its advection component that modifies heat transfer between wall and core region in a way that cannot be modelled by a single heat transfer coefficient.