Analysis of Thermal Conductivity in Composite Adhesives

摘要

Thermally conductive composite adhesives are desirable in many industrial applications, including computers, microelectronics, machinery and appliances. These composite adhesives are formed when a filler particle of high conductivity is added to a base adhesive. Typically, adhesives are poor thermal conductors. A thorough understanding of heat transfer through a composite adhesive would aid in the design of an efficient thermally conductive composite adhesive. In this work, we provide theoretical foundations for use in design of thermally conductive composite adhesives. For proof of concept, we consider a two dimensional model. We prove existence, uniqueness and continuous dependence theorems for the model. We formulate a probability based parameter estimation problem and present numerical results. Motivated by the results of the parameter estimation problem, we are led to derive sensitivity equations for our system. We investigate the sensitivity of composite silicones with respect to the thermal conductivity of both the base silicone polymer and the filler particles. Numerical results of this investigation are also presented.