Thermal resistance-based bounds for the effective conductivity of composite thermal interface materials

Thermally enhanced greases made of dispersions of small conductive particles suspended in fluidic polymers can offer significant advantages when used as a thermal interface material (TIM) in microelectronics cooling applications. The following study presents the application of two simple theorems for establishing bounds on the effective thermal conductivity of such inhomogeneous media. An upper bound is established when isotherms are assumed perpendicular to the direction of heat flow through the material. In a similar manner, a lower bound is established when adiabats are assumed parallel to the direction of heat flow. As an example of the application of these theorems, the TIM is assumed to be composed of a cubic array of uniform spheres in a surrounding medium. In most instances, a geometric mean of the bounding solutions determined for this case gives good agreement with experimental data available in the literature. Numerical simulations of a spherical particle in a unit cube cell confirm the validity of the model. This model is not applicable to systems in which the discontinuous phase is either well-connected throughout or has settled. The potential of extending this preliminary thermal resistance-based approach to investigate other geometries and effects associated with distribution, orientation, and boundary resistance is discussed