Heat conduction in two and three-phase media with solid spherical particles of the same diameter

Heat conduction in two and three-phase media, composed of solid spherical particles of the same diameter, is investigated theoretically and experimentally. The theoretical model has no empirical constants and is based on the solution of the Fourier heat conduction equation, under the thermal assumption of parallel heat fluxes, in porous medium with porosity greater than 0.4764. The medium can be two-phase, fully saturated with water or air, or three-phase, partially saturated with water and air. The problem is investigated experimentally with the thermal probe, a vertical cylinder inserted into the glass beads of the diameter of 3 mm. The thermal probe, made in laboratory, has a diameter of 1.5 mm and length 150 mm, and contains an electric heater and a temperature sensor. The perfect line source theory in the transient regime is employed to measure the thermal conductivity of the water saturated glass beads. The theoretical results for the two-phase media, glass beads and water, are in good agreement with the experiments. The results of the theoretical model for the three-phase media, glass beads with water and air, are in good agreement with the experimental data of the literature, and are compared to several theoretical models of the literature.