Analytical solutions of 3D heat conduction in flux channels with nonuniform properties complex structure

Abstract

In the microelectronics industry, thermal issues due to self-heating are major problems that affect the performance, efficiency, and reliability of devices. The recent trend of producing advanced devices with smaller sizes, high power densities, and extreme performance makes thermal management an increasingly important factor in the development of microelectronic systems. In most applications, the microelectronic systems are modeled as rectangular flux channels, where heat is generated in one or more small heat-source areas and flows by conduction through the system to spread the heat into a larger convective heat-sink area, where the generated heat is then transferred by convection into an ambient fluid. In this work, analytical solutions for the temperature distribution and thermal resistance in three-dimensional (3D) flux channels with nonuniform properties and complex structures are obtained. First, general analytical solutions in 3D isotropic flux channels with nonuniform heat transfer coefficients along the sink plane are presented using the method of separation of variables combined with the method of least squares. Different parametric studies have been conducted to study the effect of different variable heat transfer coefficient functions with the same average conductance on the temperature field. Second, general analytical solutions of 3D isotropic flux channels with temperature-dependent thermal conductivities and a uniform heat transfer coefficient along the sink plane are presented by means of the Kirchhoff transform method. The solutions are used to study the effect of the temperature-dependent thermal conductivity on the temperature rise and thermal resistance for different conductivity functions. Third, general analytical solutions in 3D flux channels of multilayered structures consisting of a finite number of orthotropic layers with constant and temperature-dependent thermal conductivities are obtained. All the analytical solutions have been verified by conducting numerical simulations based on the finite element method (FEM) using the Analysis of Systems (ANSYS) software package.