An Analytical Solution of a One-Dimensional Thermal Contact Conductance Problem With One Heat Flux and One Insulated Boundary Condition

Abstract

Heat transfer across surfaces in imperfect contact occurs in many practical situations. Since the thermal contact conductance problem has appeared in the literature, substantial efforts have been made to estimate the thermal conductance across the interface. Some of the techniques recently developed of estimating thermal contact conductance are based on experimental temperature data at one or several interior positions of the contacting solids and the calculation of the temperature at these locations for known contact conductance. Consequently, an accurate and efficient method for computing temperature distributions because quite important. FDM and FEM are most widely used. However, for most contact conductance computation methods, only the temperatures at the contacting regions and several other positions near the interface need to be determined, so the general FDM and FEM are not particularly efficient in solving this problem. This paper presents an analytical temperature distribution solution to the one-dimensional symmetric system with heat flux on one outside surface and insulation on the other. This analysis provides a theoretical basis for transient measurement of thermal contact conductance. While it is common practice in steady-state measurements to use a water-cooled heat sink, it is possible to limit the transient solution to time interval prior tomore » any detectable temperature increase at the cold end. This effectively eliminates the need for water cooling and permits the use of an insulated boundary. The analytical solution to the mentioned problem obtained shows that for a symmetric system the temperature distribution solution includes two sets of distinct eigenfunctions.« less