Investigation of Temperature Distribution in a Slab Using Lattice Boltzmann Method

Abstract

In this paper, the temperature distribution in a slab was investigated. A model based on the Boltzmann transport equation without heat source was simplified using the Bhatnagar-Gross-Krook (BGK) approximation was applied. This is an example of the Lattice Boltzmann Method. The model was developed based on using a D2Q4 lattice arrangement for the medium of study. To obtain results, the model was tested on different cases: Two box-shaped slabs with different boundary conditions, and a T-shaped and an L-shaped slabs to determine the temperature distributions different times t > 0. The results obtained based on the developed model were validated with the enterprise software COMSOL Multiphysics which is based on the Finite Element Method. For the two cases of box-shaped and the T-shaped slabs, their results were in nearly perfect agreement with the finite element method. However, for the L-shaped slab, there was good agreement at most points apart from the regions where there was change of shape. In conclusion there is high agreement between the results of LBM and using COMSOL, which proves that LBM can be used to determine temperature distribution in a slab accurately.