Thermal Modeling of Steady State Contact Resistance Between Two Dissimilar Materials

Contact resistance between two dissimilar materials of finite thickness is formulated as two cylinders in contact over a small area at their centers with their lateral surfaces insulated while the top and bottom surfaces are kept at constant temperatures. Heat diffusion equations in the cylinders are transformed to an integral equation for the heat flux through the contact area. The integral equation is solved numerically and no assumption regarding the heat flux distribution on the contact surface is made. An expression for the dimensionless contact resistance is developed using the rate of heat transfer through the contact area. The effect of the length of the cylinders on contact resistance is evaluated. The limiting case of contact resistance for long cylinders is compared with the solution reported in literature. A correlation is developed for the heat flux distribution for long cylinders as a function of dimensionless contact radius. The results are reported in dimensionless form convenient for parametric study and design analysis.