Effect of Grain Thermal Expansion Mismatch on Thermal Conductivity of Porous Ceramics

Many ceramics contain microcracks, which are often situated between sintered grains. These microcracks constitute thermal resistances, which may affect heat transfer through the material and its effective thermophysical properties. The thicknesses and the contact areas of the microcracks change with temperature as a result of the thermal expansion mismatch between the grains on opposite sides of the microcracks. This physical mechanism affects changes of the material's thermal conductivity, k , with temperature. The above mechanism usually plays a minor role at atmospheric pressure, where heat may flow via the gas filling the cracks. Hence, the temperature-induced changes of the crack geometry have little effect on heat transfer. However, at low gas pressures, where the heat flow between the grains occurs mainly via the contact areas, the grains' thermal expansion mismatch causes unusual temperature behavior of the material's thermal conductivity observed for several industrial refractories. In this paper, the influence of the above physical mechanism is discussed relative to other heat transfer mechanisms described in the literature. A simple physical model of the thermal expansion of grains bonded by an agent, having different thermal expansion coefficients, is developed. This model allows calculation of the contact area and the average microcrack opening between the grains as functions of the temperature, the characteristic grains sizes and their thermal expansion coefficients, and the permanent crack area. These parameters are evaluated and used to calculate the effective thermal conductivity of ceramic materials containing microcracks that appear as a result of thermal contraction of grains. The calculated thermal conductivity satisfactorily correlates with the experimental data collected for several chrome-magnesite refractories over a wide range of temperatures and gas pressures.