An analytical model of thermal performance for an eccentric heat source on a rectangular plate with double-sided convective cooling

Heat sources on rectangular plates with double-sided convective cooling are a common application of heat transfer in electronic packaging. However, it is considerably difficult to obtain analytical solutions for improving thermal performance because of the mixed boundary conditions on a plate’s upper surface. In this study, mixed boundary conditions were adjusted twice. Based on the method of separation of variables, a new analytical model was established and used to calculate the thermal performance of a random application case, including temperature distribution, thermal spreading resistance, and total thermal resistance. The results indicated that accurate analytical solutions can be obtained with few computing resources when more than 30 terms are used in each of single and double summations with a total mesh number of 196 in the heat source region. Subsequently, a series of thermal performances were calculated for random application cases and simulations were also conducted using the commercial software Icepak to offer a reference. The data comparisons revealed that the analytical model is able to calculate the temperature values at arbitrary point coordinates accurately over wide ranges of a plate’s thermal conductivity and heat transfer coefficient.