The effect of internal heat transfer in cavities on the overall thermal conductivity

Abstract

Based on an analytical model, degradation of the overall thermal conductivity is studied in this paper to account for the internal mechanism of heat transfer between the solid medium and the fluid inside cavities. The cavity is assumed to randomly distribute in the solid with its density measured by the volume fraction. The model is capable of characterizing the effect of internal heat transfer such as conductive and convective heat transfer across the surfaces of cavities. In the case involving the convection mode, the Biot number has been identified to be the modulus dominating the overall thermal conductivity, while in the case involving the conduction mode, the ratio of the thermal conductivity of the solid medium to that of the fluid inside cavities is the major influencing factor. The effect of interfacial conduction and convection is found to be pronounced when the volume fraction of pores in the solid exceeds 15%. The large deviation from the experimental result by considering insulated cavities is redeemed by considering heat balance of heat conduction or convection across the cavity surface.