Using the Lattice Boltzmann Method for the numerical study of non-fourier conduction with variable thermal conductivity

Abstract

The lattice Boltzmann method (LBM) was used to analyze two-dimensional (2D) non-Fourier heat conduction with temperature-dependent thermal conductivity. To this end, the evolution of wave-like temperature distributions in a 2D plate was obtained. The temperature distributions along certain parts of the plate, which was subjected to heat generation and constant thermal conductivity conditions, were also derived and compared. The LBM results are in good agreement with those reported in other works. Additionally, the temperature contours at four different times in which steady state conditions can be achieved were analyzed. The results showed that thermal conductivity increased with rising temperature. Given the material’s considerable effectiveness in transferring heat energy under heat generation conditions, the temperature gradient of the plate decreased to a level lower than that observed under constant thermal conductivity. Keywords: Non-Fourier conduction, lattice Boltzmann method, variable thermal conductivity, constant thermal conductivity, heat generation