Subhash C. Mishra

Solving transient conduction and radiation heat transfer problems using the lattice Boltzmann method and the finite volume method

The lattice Boltzmann method (LBM) was used to solve the energy equation of a transient conduction-radiation heat transfer problem. The finite volume method (FVM) was used to compute the radiative information. To study the compatibility of the LBM for the energy equation and the FVM for the radiative transfer equation, transient conduction and radiation heat transfer problems in 1-D planar and 2-D rectangular geometries were considered. In order to establish the suitability of the LBM, the energy equations of the two problems were also solved using the FVM of the computational fluid dynamics. The FVM used in the radiative heat transfer was employed to compute the radiative information required for the solution of the energy equation using the LBM or the FVM (of the CFD). To study the compatibility and suitability of the LBM for the solution of energy equation and the FVM for the radiative information, results were analyzed for the effects of various parameters such as the scattering albedo, the conduction-radiation parameter and the boundary emissivity. The results of the LBM-FVM combination were found to be in excellent agreement with the FVM-FVM combination. The number of iterations and CPU times in both the combinations were found comparable.

Transient Conduction-Radiation Heat Transfer in Participating Media Using the Lattice Boltzmann Method and the Discrete Transfer Method

ABSTRACT The lattice Boltzmann method (LBM) is used to solve the energy equation of a problem involving conduction and radiation heat transfer with and without heat generation. Both steady and transient situations are considered. To demonstrate that the two different kinds of methods can be coupled, the radiative information for the governing energy equation is computed using the discrete transfer method and the LBM is used to solve the energy equation. For validation purposes, a 1-D planar conducting and radiating medium is considered. Radiatively, the medium is absorbing, emitting, and scattering. Boundaries of the medium are assumed at the specified temperatures. The heat-generation rate is considered uniform and constant throughout the medium. Transient and steady-state medium temperature and heat flux distributions are found for various values of the scattering albedo, emissivity, and conduction-radiation parameter. Results obtained by solving the energy equation using the LBM are compared against those solving the same using the finite-difference method and with those reported in the literature. Very good agreement is obtained.

Simulation of Natural Convection in the Presence of Volumetric Radiation Using the Lattice Boltzmann Method

This article deals with the application of the lattice Boltzmann method (LBM) to the analysis of natural convection in the presence of volumetric radiation in a square cavity containing an absorbing, emitting, and scattering medium. Separate particle distribution functions in the LBM are used to calculate the density and velocity fields and the thermal field. The radiative term of the energy equation is computed using the finite-volume method. Streamlines, isotherms, and Nusselt number are analyzed for the effects of different parameters such as Rayleigh number, convection-radiation parameter, extinction coefficient, and scattering albedo.

Computational efficiency improvements of the radiative transfer problems with or without conduction--a comparison of the collapsed dimension method and the discrete transfer method

Abstract This paper deals with the performance evaluation of the collapsed dimension method (CDM) and the discrete transfer method (DTM) in terms of computational time and their abilities to provide accurate results in solving radiation and/or conduction mode problems in a 2-D rectangular enclosure containing an absorbing, emitting and scattering medium. For some pure radiation cases, studies were made for two representative benchmark problems dealing with radiative equilibrium and non-radiative equilibrium. For the combined mode, the transient conduction and radiation problem was solved. The alternating direction implicit scheme was used for the solution of the finite difference part of the energy equation. For the three types of problems considered, tests were performed for a wide range of aspect ratio, extinction coefficient, scattering albedo, conduction–radiation parameter and boundary emissivity. For pure radiation problems, results from the two methods were validated against the results from the Monte Carlo method. For the combined mode, some steady-state results were compared with results available in the literature. For the transient situations, results from the two methods were validated against each other. While both the methods were found to give the same results, the CDM was found to be much more economical than the DTM.

A lattice Boltzmann formulation to the analysis of radiative heat transfer problems in a participating medium

Use of the lattice Boltzmann method (LBM) has been extended to analyze radiative transport problems in an absorbing, emitting, and scattering medium. In terms of collision and streaming, the present approach of the LBM for radiative heat transfer is similar to those being used in fluid dynamics and heat transfer for the analyses of conduction and convection problems. However, to mitigate the effect of the isotropy in the polar direction, in the present LBM approach, lattices with more number of directions than those being used for the 2-D system have been employed. The LBM formulation has been validated by solving benchmark radiative equilibrium problems in 1-D and 2-D Cartesian geometry. Temperature and heat flux distributions have been obtained for a wide range of extinction coefficients. The LBM results have been compared against the results obtained from the finite-volume method (FVM). Good comparison has been obtained. The numbers of iterations and CPU times for the LBM and the FVM have also been compared. The number of iterations in the LBM has been found to be much more than the FVM. However, computationally, the LBM has been found to be much faster than the FVM.

Discrete Transfer Method Applied To Transient Radiative Transfer Problems in Participating Medium

Application of the discrete transfer method is extended to solve transient radiative transport problems with participating medium. A one-dimensional gray planar absorbing and aniso-tropically scattering medium is considered. Both boundaries of the medium are black. The incident boundary of the medium is subjected to pulse-laser irradiation, while the other boundary is cold. For radiative parameters such as optical thickness, scattering albedo, anisotropy factor, transmittance, and reflectance at the boundaries are found. Results obtained from the present work are compared with those available in the literature. The discrete transfer method has been found to give an excellent agreement.

Analysis of solidification of a semitransparent planar layer using the lattice Boltzmann method and the discrete transfer method

ABSTRACT This article deals with the analysis of solidification of a semitransparent material. The solidification was assumed to occur at a range of temperatures and thus the presence of a mushy zone was considered. The governing energy equation in terms of an enthalpy formulation was considered. The equivalence of the enthalpy-based governing equation in the continuum approach was derived for the lattice Boltzmann method (LBM). The radiative component of the energy equation in the LBM formulation was computed using the discrete transfer method. The LBM formulation was first validated by solving solidification of a radiatively opaque planar material. Next, effects of various parameters such as the extinction coefficient, the scattering albedo, the anisotropy factor, the conduction-radiation parameter, and the latent heat on temperature distribution in three zones and the location of the mushy zone were studied. These parameters were found to have significant bearing on the results.

Heat transfer characteristics of a porous radiant burner under the influence of a 2-D radiation field

This paper deals with the heat transfer analysis of a 2-D rectangular porous radiant burner. Combustion in the porous medium is modelled as a spatially dependent heat generation zone. The gas and the solid phases are considered in non-local thermal equilibrium, and separate energy equations are used for the two phases. The solid phase is assumed to be absorbing, emitting and scattering, while the gas phase is considered transparent to radiation. The radiative part of the energy equation is solved using the collapsed dimension method. The alternating direction implicit scheme is used to solve the transient 2-D energy equations. Effects of various parameters on the performance of the burner are studied.

Lattice Boltzmann Method Applied to the Solution of Energy Equation of a Radiation and Non-Fourier Heat Conduction Problem

This article concerns the application of the lattice Boltzmann method (LBM) to solve the energy equation of a combined radiation and non-Fourier conduction heat transfer problem. The finite propagation speed of the thermal wave front is accounted by non-Fourier heat conduction equation. The governing energy equation is solved using the LBM. The finite-volume method (FVM) is used to compute the radiative information. The formulation is validated by taking test cases in 1-D planar absorbing, emitting, and scattering medium whose west boundary experiences a sudden rise in temperature, or, with adiabatic boundaries, the medium is subjected to a sudden localized energy source. Results are analyzed for the various values of parameters like the extinction coefficient, the scattering albedo, the conduction-radiation parameter, etc., on temperature distributions in the medium. Radiation has been found to help in facilitating faster distribution of energy in the medium. Unlike Fourier conduction, wave fronts have been found to reflect from the boundaries. The LBM-FVM combination has been found to provide accurate results.

Multiparameter Estimation in a Transient Conduction-Radiation Problem Using the Lattice Boltzmann Method and the Finite-Volume Method Coupled with the Genetic Algorithms

This article deals with the exploration of the lattice Boltzmann method (LBM) and the finite-volume method (FVM) in conjunction with the genetic algorithms (GA) for estimation of unknown parameters in an inverse transient conduction-radiation problem. The conducting-radiating planar participating medium is absorbing, emitting, and scattering. Its boundaries are diffuse gray. In both the direct and inverse methods, the energy equations are solved using the LBM, and the FVM is employed to compute the radiative information. In the inverse method, the optimization is achieved using the GA. For a given set of parameters, first a direct problem is solved using the LBM-FVM, and temperature fields are estimated at various time levels, which, in the inverse problem, are taken as exact. Effects of measurement errors are also considered. With temperature fields known from the direct method, in the inverse method, too, the LBM-FVM combination is used to solve the energy equation involving volumetric radiation, and the GA is used to optimize the objective function. The LBM-FVM-GA combination in the inverse method has been found to provide correct estimates of the unknown parameters in a transient conduction-radiation heat transfer problem.