Hybrid Lattice Boltzmann Scheme for Conductive-convective-radiative Heat Transfer

Abstract

This paper presents the hybrid lattice Boltzmann model to study the interaction of conduction, natural convection and surface radiation. A square air-filled cavity with finite thickness walls is considered. The heat source is fixed at the top solid-fluid interface. The boundary conditions of the first, second, third and fourth kind are used to describe the problem under. The fluid flow and heat transfer under the Boussinesq approximation are analyzed by means of the lattice Boltzmann and energy equations discretized by the single relaxation time approximation and implicit finite difference schemes, respectively. Surface thermal radiation is computed in terms of the radiosity/irradiation model solved by the Gaussian elimination method. An in-house MATLAB code was carefully validated against three typical benchmark problems. For the first time, the full 2D conduction-convection-radiation coupling is numerically analyzed by the hybrid lattice Boltzmann (HLB) method. It is found that the HLB model reproduces the same conjugate heat transfer and fluid flow patterns as the vorticity-stream function (VS) formulation. For the first time, a comparative study of computational efficiency of the HLB and VS models is carried out. It is shown that the VS model outperforms the HLB scheme with a low grid resolution. However, the hybrid lattice Boltzmann model is faster than the vorticity-stream function formulation when using the mesh points more than 3612. With this regard, the HLB scheme is preferable to use in problems where the steep velocity or temperature gradients should be accurately resolved.

Keywords

• conjugate heat transfer
• surface radiation, natural convection, hybrid lattice boltzmann method, finite difference method