Thermal Resistance of a Three-Dimensional Flux Channel with Two-Dimensional Variable Convection

Abstract

In the microelectronics industry, heat sinks are used for cooling microelectronic devices by transferring the heat generated by the device into an ambient fluid. In most applications, the heat convection along the sink plane is not uniform due to a nonuniform heat transfer coefficient that might be present according to a nonuniform distribution of the sink extended surfaces (fins or bins) or because of the nonuniform nature of a moving ambient fluid over the sink region. This can be observed when considering a jet impingement or transverse fans as cooling techniques. In this paper, analytical approximate solutions of the temperature field and the thermal resistance of a three-dimensional flux channel with eccentric heat source(s) and a variable heat transfer coefficient that varies in the two horizontal dimensions are developed. The method of the separation of variables combined with the method of least squares is used to develop these solutions. Different parametric studies are conducted to study the effect of two different variable heat transfer coefficient distributions on the dimensionless total thermal resistance of the channel and the temperature distribution along the source plane in comparison with using a uniform heat transfer coefficient. For verification reasons, the analytical results are compared with numerical solution results obtained based on the finite element method using the ANSYS commercial software package.