Buoyancy-Driven Flow in Fluid-Saturated Porous Media near a Bounding Surface

An overview of prior research on buoyancy-driven convection in saturated porous media is presented. A general description is given of the general characteristics of flow and heat transfer in saturated porous materials. The form and nature of heat transfer laws for buoyant convection are presented.

The literature on buoyant flow in a saturated porous medium is reviewed for heat transfer from embedded surfaces and flow with mass transfer in packed beds. Research areas covered are experimental studies of buoyancy-driven convection from a horizontal plate, determination of stagnant and effective thermal conductivity of a saturated porous medium, natural convection heat transfer on a vertical plate embedded in a fluid-saturated porous medium, and models of dispersion in packed beds.

The chapter presents an exposition of the governing equations for heat transfer between the solid and fluid phases of a saturated porous medium. Volume-averaged equations are developed from first principles based on Wittaker’s formulation for the solid and fluid phases with application to the current case where there is convective motion and dispersion in the fluid phase. A one-equation model is developed. Determining thermal dispersion is a remaining unsolved problem.

An experimental apparatus and methodology are described for investigation of heat transfer from a vertical flat plate embedded in a saturated porous medium. The goals are to develop a Nusselt number correlation for steady heat transfer and to quantify the effects of thermal dispersion in the wall region. It has been hypothesized that the wall temperature variation as a function of time and space is an indication of the flow field developing in the porous medium and therefore a noninvasive measurement technique is used. Transient temperatures provide data for examining the behavior of a porous medium during the conduction regime and the departure from it.

The variation of wall temperature as a function of location and time for known wall heat flux is reported for the fluid-only and porous media cases. A first set of experiments examines the fluid-only case and a second is conducted using a glass-water medium. A few published studies using a glass-water porous medium provide benchmarks. The experiments also use steel and polyethylene beads. Each water-solid combination produces a specific range of Rayleigh-Darcy numbers.

Combining the analysis developed in Chap. 3 with the experimental results in Chap. 5, the effects of thermal dispersion can be estimated. Near wall stagnant conductivities are first addressed because these are implicit in most analytical and numerical studies in the literature. Separated from these effects, thermal dispersion is determined.

This chapter summarizes the key findings of this investigation. Steady state heat transfer correlations generally validate highly cited early analytically derived correlations within the limits of the precision and accuracy of the present measurements.