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

Abstract

An efficient and accurate approaehfor heat transfer evaluation on curved boundaries is proposed in the thermal lattice Boltzmann equation (TLBE) method. The boundary heat fluxes in the discrete velocity direetions of the TLBE model are obtained using the given thermal boundary condition and the temperature distribution functions at the lattiee nodes close to the boundaiy. Integration of the diserete 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 curvedboundaiy simulations. Several numerical tests are conducted to validate the applicability and accuracy of the proposed heat transfer evaluation scheme, including: (i) twodimensional (2D) steady-state thermal flow in a channel, (ii) one-dimensional (ID) transient heat conduction in an inclined semi-infinite solid, (Hi) 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 curx'ed boundaries due to the irregularly distributed lattice fractions intersected by the curved boundaiy. For test (v), the computed surface-averagedNusselt numbers agree well with published results. [DOI: 10,1115/1,4025046] Keywords: thermal lattice Boltzmann equation, heat flux, heat transfer, curved boundary while the heat transfer on the boundaries and fluid-solid interfaces, especially those with curved geometries, has not been Journal of Heat Transfer

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