Effective Thermal Conductivity in Multidimensional Bodies

The effective thermal conductivity in three-dimensional bodies is studied analytically. The three-dimensional model considers a spherical inclusion centrally located in a cubical body. Later, the spherical inclusion is replaced by an elliptical inclusion to study the biased effect or directionality of heat flux. Two different aspect ratios for the elliptical inclusion are considered. It is shown that the effective thermal conductivity is influenced by surface conductance in addition to geometric factors. Also, the effective thermal conductivity is measured for different samples. Spherical inclusions are placed inside cylindrical bodies for convenience of the experiments. The data show that cracks induced by applied pressure and thermal stress during the experiment reduce the thermal conductance. Using the measured effective thermal conductivity data, an analytical procedure is used to calculate the average values of the apparent contact conductance.