Lattice Boltzmann model for conjugate heat transfer across thin walls

A lattice Boltzmann (LB) model with an efficient and accurate interface treatment for conjugate heat transfer across a thin wall between two different media is developed. The proposed interface treatment avoids fine meshing and computation within the thin layer; instead, the energy balance within the thin layer and the conjugate conditions on each interface are utilized to construct explicit updating schemes for the microscopic distribution functions of the LB model at the interior lattice nodes of the two media next to the thin layer. The proposed interface schemes reduce to the standard interface scheme for conjugate conditions in the literature in the limit of zero thickness of the thin layer, and thus it can be considered a more general interface treatment. A simplified version of the interface treatment is also proposed when the heat flux variation along the tangential direction of the thin layer is negligible. Three representative numerical tests are conducted to verify the applicability and accuracy of the proposed interface schemes. The results demonstrate that the intrinsic second-order accuracy of the LB model is preserved with the proposed interface schemes for thin layers with constant tangential fluxes, while for general situations with varying tangential fluxes, first-order accuracy is obtained. This interface treatment within the LB framework is attractive in conjugate heat transfer modeling involving thin layers for its simplicity, accuracy, and significant reduction in computational resources.