The lattice Boltzmann method and the finite volume method applied to conduction–radiation problems with heat flux boundary conditions

Abstract

SUMMARYThis article deals with the implementation of the lattice Boltzmann method (LBM) in conjunction with the finite volume method (FVM) for the solution of conduction-radiation problems with heat flux and temperature boundary conditions. Problems in 1-D planar and 2-D rectangular geometries have been considered. The radiating-conducting participating medium is absorbing, emitting and scattering. In the 1-D planar geometry, the south boundary is subjected to constant heat flux, while in the 2-D geometry the south and/or the north boundary is at constant heat flux condition. The remaining boundaries are at prescribed temperatures. The energy equation is solved using the LBM and the radiative information for the same is computed using the FVM. In the direct method, by prescribing temperatures at the boundaries, the temperature profile and heat flux are calculated. The computed heat flux values are imposed at the boundaries to establish the correctness of the numerical code in the inverse method. Effects of various parameters such as the extinction coefficient, the scattering albedo, the conduction-radiation parameter, the boundary emissivity and the total heat flux and boundary temperatures are studied on the distributions of temperature, radiative and conductive heat fluxes. The results of the LBM in conjunction with the FVM have been found to compare very well with those available in the literature.

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.…”

“…The combined mode conduction and radiation problems have been analyzed by many researchers [14], and with LBM as the solver for the energy equation and the DTM [30,32], the CDM [31], the REM [10], the DOM [12,13,33] and the FVM [20,22,34,36] as the methods for computation of radiative information, Mishra and co-workers, have solved a wide range of problems [10,12,13,20,22,[30][31][32][33][34][35][36][37]39]. A step ahead, to further extend the usage of the LBM, the present work deals with the solution of a combined mode transient conduction and radiation heat transfer problem in a 2D rectangular geometry in which both the computations of the radiative information and the solution of the energy equation are done using the LBM.…”

“…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]. However, in all such problems, although the radiative information was computed using the conventional methods like the DTM [5,6], the CDM [7,8], the DOM [11][12][13], and the REM [10] and the FVM [20,22], in terms of formulation and computational time, the solution of the energy equation by the LBM was encouraging.…”

Lattice Boltzmann method for polymer kinetic theory

“…The first one consists in coupling the heat transfer and the Navier-Stokes equations on the same lattice by introducing, in addition to the particle distribution densities, an internal-energy density distributions allowing to calculate the thermal field (see for example [32,33]). The second way considers the decoupled thermal equation and assumes for its resolution that the temperature is obtained from a single set of particle distribution functions which are independent from a real movement (see for example [23,24]). …”