Heat Transfer Evaluation on Curved Boundaries in Thermal Lattice Boltzmann Equation Method

An efficient and accurate approach for heat transfer evaluation on curved boundaries is proposed in the thermal lattice Boltzmann equation (TLBE) method. The boundary heat fluxes in the discrete velocity directions of the TLBE model are obtained using the given thermal boundary condition and the temperature distribution functions at the lattice nodes close to the boundary. Integration of the discrete boundary heat fluxes with effective surface areas gives the heat flow rate across the boundary. For lattice models with square or cubic structures and uniform lattice spacing the effective surface area is constant for each discrete heat flux, thus the heat flux integration becomes a summation of all the discrete heat fluxes with constant effective surface area. The proposed heat transfer evaluation scheme does not require a determination of the normal heat flux component or a surface area approximation on the boundary; thus, it is very efficient in curved-boundary simulations. Several numerical tests are conducted to validate the applicability and accuracy of the proposed heat transfer evaluation scheme, including: (i) two-dimensional (2D) steady-state thermal flow in a channel, (ii) one-dimensional (1D) transient heat conduction in an inclined semi-infinite solid, (iii) 2D transient heat conduction inside a circle, (iv) three-dimensional (3D) steady-state thermal flow in a circular pipe, and (v) 2D steady-state natural convection in a square enclosure with a circular cylinder at the center. Comparison between numerical results and analytical solutions in tests (i)-(iv) shows that the heat transfer is second-order accurate for straight boundaries perpendicular to one of the discrete lattice velocity vectors, and first-order accurate for curved boundaries due to the irregularly distributed lattice fractions intersected by the curved boundary. For test (v), the computed surface-averaged Nusselt numbers agree well with published results.