Numerical Simulation of the Two-Dimensional Heat Diffusion in the Cold Substrate and Performance Analysis of a Thermoelectric Air Cooler Using The Lattice Boltzmann Method

This article presents numerical simulations of the two-dimensional temperature distribution in the cold substrate and a performance analysis of a thermoelectric cooler with the Lattice Boltzmann Method. A detailed and concise procedure for the derivation of the source term of Lattice Boltzmann method for a thermal diffusion problem is presented. Numerical simulations are performed using the Bhatnagar-Gross-Krook collision operator with two velocity schemes, namely D2Q4 and D2Q9. The numerical validation is performed by comparisons with an approximate analytical solution and a finite difference method solution. Later, performance parameters of the thermoelectric cooler, based on thermal resistances, are computed from the obtained temperature distribution. The results show that the Lattice Boltzmann Method is capable of simulating the addressed thermal diffusion problem, with very small relative errors (maximum errors of 0.09%) for the temperature distribution. Excellent agreement is observed for the performance parameters, ensuring the robustness of the method. Furthermore, the procedure for the solution of the differential equation can be easily applied to solve other problems.