Thermal Behavior of Rectangular Flux Channels With Discretely Specified Contact Flux and Temperature

In this paper, an analytical solution for the thermal behavior of rectangular flux channels with discretely specified boundary conditions is presented. The boundary conditions along the source plane can be a combination of contact temperatures, heat fluxes, and/or adiabatic. Convective cooling is applied along the sink plane, and the edges of the channel are assumed adiabatic. The governing equation of the system is the Laplace equation which is solved using the method of separation of variables and the least squares method. The solution is presented in the form of Fourier series expansion. As a case study, a symmetrical flux channel with a combination of five discretely specified boundary conditions, including temperature, heat flux and adiabatic conditions is considered. Temperature profile along the channel is calculated and compared with the Finite Element Method (FEM) using COMSOL commercial software package [1]. A good agreement is observed between the analytical and FEM results.