The transient heat transfer characteristics of heterogeneous materials consisting of a microstructure of relatively small particles embedded in a matrix is investigated. A constitutive model is developed where heat is initially transferred to the matrix and is then transferred to small, separated particles embedded throughout the matrix. The heat exchange between the matrix and particles is characterized by a contact conductance. This physical model leads to a system of coupled diffusion equations for the matrix and particles, similar to the parabolic two-step model used to describe the electron-lattice interactions in microscale heat transfer. In the current investigation, a one-dimensional model with an applied surface heat flux is used.
A numerical solution to the coupled system of equations using the control volume based finite difference method is developed. This method readily allows for the inclusion of any combination of material properties, particle sizes and contact conductance. Case studies reveal that the property ratios and contact conductance can lead to a thermal lag where the temperature response to an applied heat flux is markedly different than that predicted with a homogeneous conduction model. An effective thermalization time can also be inferred from this modeling of the heterogeneous microstructure.