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.     

Lattice Boltzmann Method Applied to Radiative Transport Analysis in a Planar Participating Medium

This article deals with the extension of the usage of the lattice Boltzmann method (LBM) to the analysis of radiative heat transfer with and without conduction in a one-dimensional (1-D) planar participating medium. A novel lattice needed for the calculation of the volumetric radiation spanned over the 4π spherical space has been introduced. The LBM formulation is tested for three benchmark problems, namely, radiative equilibrium, nonradiative equilibrium, and a combined mode conduction–radiation problem in a planar geometry. In the combined mode problem, with radiative information known from the proposed lattice structure, the energy equation is also formulated and solved using the LBM. The D1Q2 lattice is used in the energy equation. For validation, in problems 1 and 2, the LBM results are compared with the finite-volume method (FVM), while in problem 3, the LBM-LBM results are compared with the LBM-FVM in which FVM is used for the computation of radiative information. Comparisons are made for the effects of the governing parameters such as the extinction coefficient, the scattering albedo, and so on, on heat flux and emissive power (temperature) distributions. LBM results are found to be in excellent agreement with the benchmark results.     

Analysis of Conduction and Radiation Heat Transfer in a 2-D Cylindrical Medium Using the Modified Discrete Ordinate Method and the Lattice Boltzmann Method

This article deals with the analysis of radiative transport with and without conduction in a finite concentric cylindrical enclosure containing absorbing, emitting, and scattering medium. Isothermal medium as the radiation source confined between the cold cylinders and a nonisothermal medium with the inner cylinder as the radiation source are the two nonradiative and radiative equilibrium problems. They involve only calculation of radiative information. In the third problem, a conducting-radiating medium is thermally perturbed by raising the temperature of the inner cylinder. In all problems, radiative information is computed using the modified discrete ordinate method (MDOM), and in the third problem, the lattice Boltzmann method (LBM) is used to formulate and solve the energy equation. Depending on the problems, effects of various parameters such as the extinction coefficient, the scattering albedo, the boundary emissivity, the conduction-radiation parameter, and the radius ratio are studied on temperature and heat flux distributions. The MDOM and the LBM-MDOM results are compared with those available in the literature. To further establish the accuracy of the MDOM and the LBM-MDOM results, in all problems, comparisons are made with the results obtained from the finite volume method (FVM) and the finite difference method-FVM approach, in which FVM provides the radiative information. The selection of the FDM-FVM for the third problem is also with the objective that for this problem, not much work is reported in which the FVM is used to calculate the radiative information. MDOM and LBM-MDOM results are found to compare well with those available in the literature, and in all cases they are in excellent agreement with FVM and FDM-FVM approaches.     

A Lattice Boltzmann Formulation for 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.     

Lattice Boltzmann Method and Modified Discrete Ordinate Method Applied to Radiative Transport in a Spherical Medium with and without Conduction

This article deals with the application of the modified discrete ordinate method (MDOM) to calculate volumetric radiative information with and without conduction in a concentric spherical enclosure containing a participating medium. With radiative information known from the MDOM, the energy equation of the combined mode transient conduction and radiation heat transfer is formulated and solved using the lattice Boltzmann method (LBM). Without conduction, for pure radiation case, two benchmark problems, representing nonradiative and radiative equilibrium situations are taken up. In the case of non-radiative equilibrium, an isothermal medium is bounded by cold walls and medium is the source of radiation, while in the case of radiative equilibrium, nonisothermal medium is confined between a hot and a cold wall, and the hot (inner sphere) wall is the radiation source. Depending upon the problem, heat flux, energy flow rate, emissive power, and temperature distributions in the medium are calculated for different values of parameters such as the extinction coefficient, the scattering albedo, the conduction-radiation parameter, the boundary emissivity, and the radius ratio. To validate the MDOM and the LBM-MDOM formulations, problems are also solved using the finite volume method (FVM) and the finite-difference method (FDM)–FVM approach, in which the FVM is used to calculate the volumetric radiation and the energy equation is also solved using the FDM. Results of the MDOM, LBM–MDOM, FVM and FDM–FVM are also benchmarked against those available in the literature. MDOM and LBM–MDOM have been found to provide accurate results.     

The Radiation Element Method Coupled with the Bioheat Transfer Equation Applied to the Analysis of the Photothermal Effect of Tissues

The purpose of this study is to develop the radiation element method by ray emission method (REM²) code appropriate for coupling with the bioheat transfer equation, and to clarify the photothermal effect of various parameters inside biological tissues. First, the REM², which involves the air-tissue interface effect, is validated with the existing literature. In order to clarify the effects of optical and thermophysical properties of biological tissues, a one-dimensional tissue model of CW light transport and bioheat transfer is employed. The present study provides nondimensional results, which are obtained by varying refractive index, extinction coefficient, scattering albedo, blood perfusion parameter, and conduction-radiation parameter, show valuable guidance for understanding the coupled light and bioheat transport in tissues.     

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

Application of the lattice Boltzmann method (LBM) recently extended by Pietro et al. [P. Asinari, S. C. Mishra, and R. Borchiellini, A Lattice Boltzmann Formulation to the Analysis of Radiative Heat Transfer Problems in a Participating Medium, Numer. Heat Transfer B, 57(2), 126–146, 2010] for calculation of volumetric radiative information is extended for the analysis of a combined mode transient conduction and radiation heat transfer in a 2D rectangular enclosure containing an absorbing, emitting and scattering medium. Unlike all previous studies, with volumetric radiative information computed using the proposed LBM, the energy equation is formulated and solved using the LBM. In the combined mode conduction–radiation problem, to assess the computational advantage of computing the radiative information too using the LBM, the same problem is also solved using the LBM–finite volume method (FVM) formulation. In this LBM–FVM formulation, the FVM is used to calculate the volumetric radiative information needed for the energy equation, and the energy equation is solved using the LBM. Comparisons are made for the effects of the extinction coefficient, the scattering albedo and the conduction–radiation parameter on the temperature distributions in the medium. Although the number of iterations for the converged solution in LBM–LBM is much more than that of the LBM–FVM, computationally, the LBM–LBM is faster than the LBM–FVM.     

Simulation of Conjugate Heat Transfer Using the Lattice Boltzmann Method

The Lattice Boltzmann Method (LBM) is utilized to investigate conjugate heat transfer. Hot and cold streams enter the computational domain, and heat transfer takes place between the two streams through a finite thickness and finite thermal conductivity wall. The main objective of the work is to demonstrate that LBM can solve conjugate heat transfer by using one energy equation for solid and fluid phases. The flux continuity insures automatically. Furthermore, the effects of extended surfaces were investigated on the rate of heat transfer and pressure drop.     

Coupled Conduction,Convection, Radiation Heat Transfer with Simultaneous Mass Transfer in Ice Rinks

ABSTRACT

This article presents numerical predictions of velocity, temperature, and absolute humidity distributions in an indoor ice rink with ventilation and heating. The computational fluid dynamics (CFD) simulation includes the effects of radiation between all inside surfaces of the building envelope, turbulent mixed convection, and vapor diffusion, as well as conduction through the walls and condensation on the ice. The net radiative fluxes for each element of the envelope's inside surfaces are calculated with a modified version of Gebhart's method. This modification reduces the calculation time and the memory required to store the radiation view factors for the discretized elements of the inside surfaces of the envelope. The predicted temperatures show very good agreement with measured data. The CFD code also calculates the heat fluxes toward the ice due to convection from the air, to condensation of vapor, and to radiation from the walls and ceiling. It is shown that a low emissivity ceiling reduces the sum of these fluxes and the risk of vapor condensation on the ceiling.     

Collapsed Dimension Method Applied to Radiative Transfer Problems in Complex Enclosures with Participating Medium

Application of the collapsed dimension method is extended to solve radiative transfer problems in complex enclosures with participating medium. Formulations are provided for absorbing, emitting, and anisotropically scattering medium. Formulations are validated by solving some benchmark problems in rectangular as well as cylindrical geometries. In rectangular geometry, 2-D L-shaped, quadrilateral, and 3-D cubical enclosures are considered. In cylindrical geometry, problems in 1-D and 2-D single as well as concentric cylindrical enclosures are taken up. To check the accuracy of the results obtained from the collapsed dimension method, depending on the availability of results, comparisons are made with the exact method, discrete transfer method, P 3 approximation, Monte Carlo method, and the finite-volume method. The collapsed dimension method has been found to provide very accurate results.     

Lattice Boltzmann Method Combined with the Smoothed Profile Method for the Simulation of Particulate Flows with Heat Transfer

In this work, a hybrid method based on the lattice Boltzmann method (LBM) combined with smoothed profile method (SPM) is proposed for simulating the fluid flow and heat transfer in particulate systems. LBM is used to evaluate the flow field, while the temperature distribution is computed by a finite difference method. The no-slip and constant temperature boundary conditions on particle surfaces are treated with SPM. The following benchmarking studies are considered to validate the accuracy and robustness of the proposed method: natural convection in a square cavity with a heated circular cylinder, natural convection in a concentric annulus, and the sedimentation of single and two circular particles in a long narrow container. In all the studies, the results obtained from the present technique based on hybrid method show good agreement with the previously published results and those given by LBM combined with SPM based on the double-population model. After evaluating the central processing unit time taken by the two methods, it was found that the proposed method is about 50% more computationally efficient than the method based on double-population model in all the simulation cases considered in this work.     

Coupled Conduction and Intermittent Convective Heat Transfer from a Buried Pipe

An accurate estimate of the heat transfer from a buried pipe to the surrounding ground is essential for the design of the ground-loop portion of a ground-source heat pump. Exact analytical solutions to this problem are complicated by the fact that heat pump systems rarely operate continuously. Complete numerical simulations of system designs can be carried out, but these are unwieldy and difficult to justify for initial scoping calculations, or for preliminary performance estimates. The purpose of this article is to provide insight into the heat transfer mechanisms and to describe the development of simple algebraic correlations that can be used to approximate the intermittent overall heat transfer between a fluid flowing in an isolated buried pipe and the surrounding ground. The correlations described in this article were drawn from results of a numerical finite-difference analysis of a fluid flowing intermittently in a single round pipe and exchanging heat with the surrounding ground. It is found that the cycle average heat transfer is always lower for the intermittent case than for the continuous case, but that the average over just the active part of the cycle is always higher for any intermittent case than for the continuous case. The effect of the ground thermal diffusivity is largest when the heat transfer coefficient is large, and decreases with decreasing heat transfer coefficient. The range of heat transfer coefficients where isothermal wall conditions are approached is illustrated. Correlations for the operating average and cycle average total heat transfer are presented as functions of the thermal diffusivity, intermittence factor, and heat transfer coefficient.     

Combined Mode Conduction and Radiation Heat Transfer in a Porous Medium and Estimation of the Optical Properties of the Porous Matrix

This article deals with the analysis of combined mode conduction and radiation heat transfer in a porous medium, and simultaneous estimation of the optical properties of the porous matrix. Simultaneous solution of the gas- and solid-phase energy equations encompasses local thermal nonequilibrium, while the convective heat exchange term couples the gas- and the solid-phase energy equations. A localized uniform volumetric heat generation zone is the source of heat transfer in the porous matrix. With volumetric radiative information needed in the solid-phase energy equation computed using the discrete transfer method, the solid- and gas-phase energy equations are simultaneously solved using the finite difference method. For a given set of boundary conditions and operating parameters, the computed temperature distribution serves as the exact temperature profile necessary in the estimation of parameters. In the estimation of parameters using inverse analysis, the objective function is minimized using the genetic algorithm. Effects of measurement error, number of generations, population size, crossover probability, and mutation probability are studied in regard to the accuracy of results and the computational time required. Reasonably accurate estimations of extinction coefficient, scattering albedo, and emissivity of the porous matrix are obtained.     

Numerical Method on Natural Convection and Radiation Heat Transfer with an Isotropic Scattering Medium

The finite-volume method (FVM) for radiation heat transfer with a nonscattering medium is extended to an isotropic scattering medium, and this method is implemented in the fluid flow solver GTEA on hybrid grids. For comparison and validation, three test cases, a semicircle enclosure with a hole, a rhombic enclosure, and a square cavity, are chosen. All the results obtained by the present FVM agree very well with the numerical solutions in the references. Furthermore, the effects of the extinction coefficient and scattering albedo on the flow and temperature distribution are studied numerically in the cavity based on present approach. As the extinction coefficient increases from 0.2 to 5, the temperature gradient adjacent to the hot and cold walls gradually decreases at Ra = 10⁵, however, the temperature profiles become similar at Ra = 10⁶. For Ra = 10⁵, 10⁶, the scattering albedo affects the structures of the isotherm and streamline to some extent. As the scattering albedo increases, the convection heat transfer in the middle region of the hot wall increases, but the radiation heat transfer and the total radiation heat transfer along the hot wall decrease.     

Natural Convection Coupled with Radiation Heat Transfer in Slanted Square and Shallow Enclosures Containing an Isotropic Scattering Medium

A finite-volume method (FVM) is used to address combined heat transfer, natural convection, and volumetric radiation with an isotropic scattering medium, in a tilted shallow enclosure. Numerical simulations are performed in the in-house fluid flow software GTEA. All the results obtained by the present FVM agree very well with the numerical solutions in the references. The effects of various influencing parameters such as the Planck number (0.0001 ≤ Pl ≤ 10), the scattering albedo (0 ≤ ω ≤ 1), the inclination angle (?60° ≤ α ≤ 90°), and aspect ratio (1 ≤ AR ≤ 5) on flow and heat transfer have been numerically studied. For a constant Pl number, flow is slightly intensified at the midplane as the Ra number increases from 10⁶ to 5 × 10⁶. As the scattering albedo increases, the effect of radiation heat transfer decreases on both slanted and horizontal enclosures. In positive tilt angles, the influence of α on heat transfer is quite remarkable. The highest Nu_rad appears at α = 30° (ω = 1)and 0° (ω = 0, 0.5), whereas Nu_rad is maximum at α = ? 15° (ω = 1) and ?45° (ω = 0, 0.5). At α = ?15°, the maximum and minimum values of Nu_rad are presented for ω = 0, AR = 1 and ω = 1, AR = 5.     

Lattice Boltzmann Simulation of Convective Heat Transfer from Heated Blocks in a Horizontal Channel

This article presents the application of the multiple-relaxation-time (MRT) lattice Boltzmann equation (LBE) method with nine-velocity model to the numerical prediction of a laminar and convective-heated transfer through a two-dimensional obstructed channel flow. The obstruction is carried out by three obstacles including two located on the upper wall and the other on the lower wall of the channel. The calculations are validated against results available in literature. Various physical arrangements are regarded as the size of the obstacles and the distance between the two upper obstacles to investigate their effects on thermal and flow characteristics. Results, presented for a Prandtl number equal to 0.71 and a Reynolds number ranging from 100 to 1200, showed that the heat transfer and the air flow depend both on the Reynolds number and geometric data of the configuration.     

Mixed Convection Heat Transfer Analysis in an Enclosure with Two Hot Cylinders: A Lattice Boltzmann Approach

The aim of this work is to study laminar mixed convection heat transfer characteristics within an obstructed enclosure by using the Lattice Boltzmann method. Flow is driven by a top cold lid while other walls are stationary and adiabatic. Hot cylinders are located at different places inside the cavity to explore the best arrangement. Comparison of streamlines, isotherms, average Nusselt number are presented to evaluate the influence of Richardson number and location of cylinders on flow field and heat transfer. Results indicate that heat transfer decreases with a rise of Richardson number for all considered arrays of cylinders. Among them, horizontally‐located cylinders at the top of the cavity have the greatest heat transfer at all Richardson numbers. Horizontally located cylinders at the bottom of the cavity have the lowest heat transfer at Richardson numbers of 0.1 and 1 while the lowest heat transfer rate belongs to cross diagonal located cylinders at a Richardson number of 10.     

高低热导率相间表面强化饱和池沸腾的格子玻尔兹曼模拟

采用格子玻尔兹曼方法模拟高低热导率相间表面的饱和池沸腾过程,研究不同表面高低热导率区域热导率比值、低热导率区域宽度和深度对沸腾换热性能的影响。对比均匀热导率表面与高低热导率相间表面的沸腾曲线发现：高低热导率相间表面的沸腾过程可被分为5个阶段,并且其临界热流密度最高可达均匀表面的12倍;高低热导率相间可促使表面维持一定的温度差异,从而保持明显的气液流动;随着低热导率区域宽度增大,气液分离更加明显,低热导率区域宽度存在一个最优值,其与毛细长度的量级接近;随着低热导率区域的深度增大,表面过热度的差异更加明显。     

Nonhomogeneous Heat Conduction Problem and Its Thermal Deflection Due to Internal Heat Generation in a Thin Hollow Circular Disk

This article is concerned with the determination of temperature and thermal deflection in a thin hollow circular disk under an unsteady-state temperature field due to internal heat generation within it. Initially, the disk is kept at an arbitrary temperature F(r, z). For times t > 0 heat is generated within the thin hollow circular disk at a rate of g(r, z, t) Btu/hr ft³, while the boundary surfaces at (r = a), (r = b), (z = 0) and (z = h) are kept at temperatures f ₁(z, t) and f ₂(z, t), f ₃(r, t) and f ₄(r, t), respectively. The governing heat conduction equation has been solved by using a finite Hankel transform and the generalized finite Fourier transform. The results are obtained in series form in terms of Bessel's functions. As a special case, different metallic disks have been considered. The results for temperature change and the thermal deflection have been computed numerically and illustrated graphically.     

A High Order Control Volume Finite Element Method for Transient Heat Conduction Analysis of Multilayer Functionally Graded Materials with Mixed Grids

This paper describes a new two-dimensional(2-D) control volume finite element method(CV-FEM) for transient heat conduction in multilayer functionally graded materials(FGMs). To deal with the mixed-grid problem, 9-node quadrilateral grids and 6-node triangular grids are used. The unknown temperature and material properties are stored at the node. By using quadratic triangular grids and quadratic quadrilateral grids, the present method offers greater geometric flexibility and the potential for hig...