Thermal Resistance of a Two Dimensional Flux Channel with Eccentric Heat Source and Asymmteric Edge Cooling

In this paper, an analytical solution is presented for the temperature profile and thermal resistance of a non-symmetrical flux channel with convective cooling along the sink plane and edges. The heat transfer coefficients along the right and left edges of the channel are defined separately and both are independent from the heat transfer coefficient applied over the sink plane. The system is solved using the method of separation of variables. Due to the edge cooling and non-symmetry, the eigenvalues should be calculated using the heat transfer coefficient on both edges. For satisfying the orthogonality condition, a normalized function is defined. The temperature distribution over the channel is presented in the form of a Fourier series expansion and some expressions are presented to calculate the thermal resistance and dimensionless thermal resistance. Some case studies are considered and the results are compared with other literature and the Finite Element Method (FEM) using COMSOL commercial software package [1]. The proposed model is useful for thermal engineers who wish to model micro-electronic devices with different conductance and heat sink configurations.