Heat Flux Boundary Conditions for a Lattice Boltzmann Equation Model

A method simplifying the external force term for the Boltzmann equation is proposed by using the Chapman-Enskog asymptotic expansion technique, The relationship between the perturbation strength parameter and the Grashof number is presented. A heat flux boundary condition for temperature field simulation is developed according to the transforming relations between the cold and hot particles on the boundary wall. The effect of buoyant force and the heat flux boundary condition is implemented with the two-particle systems of D2Q9 and D3Q15, and the numerical results agree well with the experimental result of silicone oil.