A Lattice Boltzmann Formulation for the Analysis of Radiative Heat Transfer Problems in a Participating Medium

Overview of the entropy production of incompressible and compressible fluid dynamics

“…An example is given by some trends in the mesoscopic numerical methods. In particular, the lattice Boltzmann method [12][13][14][15][16] is a powerful numerical method applied much beyond rarefied flows, including thermal radiation [17], thermal conduction [18], combustion [19][20][21][22], porous media [23,24], multi-component flows [25,26] and turbulence [27], to mention a few. Pertinently to this paper, the entropic lattice Boltzmann method was invented by Ilya Karlin and co-workers in 1998, by applying the maximum entropy principle to lattice kinetic equations [28].…”

Coupled radiative and conjugate heat transfer in participating media using lattice Boltzmann methods

“…The LBE equations conserve the continuum mechanics equations for the macroscopic quantities such as mass, momentum and kinetic energy. A similar analogue for linear form of the general Boltzmann equation, which describes radiative transport process, has been developed with discrete angular directions for radiation field [17][18][19]. The distribution function or radiation intensity for each angular direction provides information for current and flux required in thermal energy balance calculations.…”

“…However, most of the effort was focused on coupling Discrete Ordinates Method (DOM) or other conventional deterministic methods for solving RTEs with the LBM based fluid transport or convection-diffusion solvers [13][14][15][16]. Recently, LBM based algorithms have been developed to solve RTE problems [17][18][19][20][21][22]. This paper proposes the use of those LBM algorithms for solving coupled multi physics examples.…”

Analysis of Conduction-Radiation Heat Transfer in a 2D Enclosure Using the Lattice Boltzmann Method

“…In comparison to the CFD solvers, the advantage of the LBM include simple calculation procedure, simple and efficient implementation for parallel computation, easy and robust handling of complex geometries and high computational performance ANALYSIS OF CONDUCTION-RADIATION HEAT TRANSFER 671 with regard to stability and accuracy [26,27]. It has been applied to a wide range of fluid flow and heat transfer problems [26][27][28][29][30][31][32][33][34][35][36][37][38][39]. Very recently, the usage of the LBM to formulate and solve different types of heat transfer problems involving volumetric radiation in different geometries has been extended by Mishra and co-authors [12,13,20,22,[30][31][32][33][34][35][36][37][38][39].…”

“…Recently, the usage of the LBM in solving fluid flow and heat transfer problems has taken a surge [26][27][28][29][30][31][32][33][34][35][36][37][38][39]. Unlike conventional methods such as the FDM and the FVM, which solve the discretized macroscopic Navier-Stokes equations, the LBM uses simple microscopic kinetic models to stimulate complex transport phenomena.…”