Effect of boundary condition applying type on heat transfer modeling via double species Lattice Boltzmann method

Abstract

The principle objective of the present study is to solve the velocity and temperature fields using two different distribution functions double species thermal lattice Boltzmann method (TLBM). The study is carried out for a wide range of Rayleigh numbers, velocity and temperature distributions as well as Nusselt numbers were obtained for the Rayleigh numbers ranging from 103 to 106 with the Prandtl number around 0.718 for air. In this simulation, the Boussinesq approximation applied to the buoyancy force term. Also we evaluate the order of derivatives' effect on the accuracy of macroscopic values. So, we applied this method for all of boundary condition types same as no slip, constant temperature and adiabatic walls in two different TLBM model and macroscopic states. We showed that boundary condition applying type has not any difference and based on computer code, we can use both of them with minimum term of derivatives. Results are presented in form of streamline and isothermal plots as well as the variation of average Nusselt number at the walls and domain and compared with commercial CFD softwares and other established methods referenced through literature. A good agreement is obtained between the current solution and the previous works and it shows that we can use double species TLBM with minimum terms of derivatives on a macroscopic and TLBM parameters in boundary conditions discretization. Results are in a good independency from the grids and size of mesh. Finally it is showed that we can solve the first rows and corners (the nodes on the body) of grid with macroscopic terms then continue for other lattices with TLBM to improve accuracy and save the time.