Analysis of radiative heat transfer in two-dimensional irregular geometries by developed immersed boundary–lattice Boltzmann method

Abstract

The Immersed Boundary–lattice Boltzmann method (IB-LBM) is developed to analyze radiative heat transfer in two-dimensional (2D) irregular geometries. Lattice Boltzmann method (LBM) has been adopted to discretize the radiative heat transfer equation in an absorbing and emitting media, and the immersed boundary method (IBM) is used to model the boundaries of irregular geometries. Due to the mismatch between boundary and computational nodes in the Immersed Boundary method, a radiative density term based on the difference of radiation intensity is added to the lattice Boltzmann equation to satisfy the boundary condition. Radiative heat flux distribution is obtained for several irregular geometries which are maintained at an isothermal media or radiative equilibrium condition in the enclosure. The results are successfully validated by comparing the results obtained from other methods of irregular geometries analysis, such as the blocked-off domain, embedded boundary, and body-fitted grid method. According to the obtained results, their accuracy, and numerical cost, the combined IB-LBM benefits from the unique and worthy advantages of both IBM and LBM in solving the complicated analysis of 2D radiative heat transfer problems. Compared to the traditional methods used for the radiative analysis of irregular geometries, the immersed boundary method can solve the complexities of modeling curved boundaries effortlessly. It should be pointed that for optically thin media, the proposed model shows poor performance.