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.     

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.     

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.     

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.     

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...     

Analysis of Conduction and Radiation Heat Transfer in a Differentially Heated 2‐D Square Enclosure

Radiative heat transfer with and without conduction in a differentially heated 2‐D square enclosure is analyzed. The enclosure with diffuse gray boundaries contains radiating and/or conducting gray homogeneous medium. Radiatively, the medium is absorbing, emitting and scattering. On the south boundary, four types of discrete heated regions, viz., the full boundary, the left one‐third, left two third and middle one third, are considered. In the absence of conduction, distributions of heat flux along the south boundary are studied for the effect of extinction coefficient. In the presence of conduction, distributions of radiation, conduction and total heat fluxes along the south boundary are analyzed for the effects of extinction coefficient, scattering albedo, conduction–radiation parameter, and south boundary emissivity. Effects of these parameters on centerline temperature distribution are also studied. To assess the performance of three commonly used radiative transfer methods, in all cases, the radiative transfer equation is solved using the discrete ordinate method (DOM), the conventional discrete ordinate method (CDOM) and the finite volume method (FVM). In the combined mode problem, with volumetric radiative information known from one of the three methods, viz., DOM, CDOM, and FVM, the energy equation is solved using the finite difference method (FDM). In all cases, the results from FDM‐DOM, FDM‐CDOM, and FDM‐FVM are in good agreement. Computationally, all three sets of methods are equally efficient.     

Numerical Modeling of Combined Radiation and Conduction Heat Transfer in Mineral Wool Insulations

This article addresses numerical modeling of coupled heat conduction and radiation in mineral wools under steady-state condition for prediction of its effective thermal conductivity. The radiative heat transfer is modeled using the Monte Carlo Ray-Trace Method. The radiation model is based on a random distribution of fibers in the media. The radiation distribution factor is employed in order to compute the fraction of the total radiation emitted from one fiber that is absorbed by another, due to both direct radiation and to all possible reflections within the enclosure. The radiation model is coupled with the nonlinear heat conduction equation. The results obtained by the proposed model compare well with experimental measurements of the heat flow meter apparatus. The method is easy to code, and the number of calculations during each iteration is considerably reduced.     

Sensitivity Analysis of Classical Heat Conduction Solutions Applied to Materials Characterization

This paper presents the analysis of classical heat conduction solutions applied to materials characterization. The formulas for parametric derivatives are obtained and illustrated to demonstrate the evolution of the relative sensitivity functions in time. The potential of using both front-surface and rear-surface solutions for determining material thermal properties, sample thickness, and surface heat exchange parameters is discussed. The roots of the well-known transcendent equation for a non-adiabatic plate are approximated in a polynomial form. Some practical applications of the proposed formulas are reported.     

Heat Transfer Analysis for a Concentric Tube Heat Exchanger Including the Wall Axial Conduction

The effect of wall axial conduction on the heat transfer in a concentric tube heat exchanger is examined for the inner flow laminar flow regime. The procedure used for the current analysis combines the analytical solution for the inner fluid with a numerical approximation for the wall conduction and has the capability of handling the temperature variation for the outer fluid. Both parallel and counterflow cases are evaluated for the analysis, and results are presented in terms of the axial variations of fluids and wall temperatures. Effects of the heat capacity rate ratio of the fluids on the temperature variations and on the mean heat flux are also pointed out. The effect of the exchanger length is included for the analysis. It is concluded that the total heat transfer between the fluids is greatly influenced by the wall axial conduction for the counterflow arrangement and is not ignorable when the heat capacity rate ratio of fluids are smaller than unity.     

热渗耦合的地下水源热泵抽灌井传热数值模拟

基于达西定律,分析了饱和区土壤中地下水源热泵抽灌井传热机制,构建了热渗耦合共同作用下的数学模型,研究了有无地下水渗流及渗流速度对抽灌井周围温度场变化的影响,使用COMSOL Multiphysics软件对建立的模型进行了分析模拟.实例结果表明,该模型具有较好的适用性,为系统的优化设计与参数合理匹配提供了理论支持.     

Virtual Boundary Meshless with Trefftz Method for the Steady-State Heat Conduction Crack Problem

This article presents a virtual boundary meshless with Trefftz method for calculation of the two-dimensional steady-state heat conduction crack problem, which is based on the idea of multidomain combination. The virtual source function is constructed by the radial basis functions approximation in the subdomain not containing the crack. The temperature or heat flux is calculated by crack special solution of Trefftz function in the crack subdomain. Thus, the proposed method has the advantages of both the boundary-type meshless method and the Trefftz method. No nodes or elements are distributed on the crack, because the boundary condition of the crack is automatically satisfied by employing the crack special solution of the Trefftz function. The heat stress intensity factor is simply and directly calculated.     

Lattice Boltzmann Simulation of Conjugate Heat Transfer from Multiple Heated Obstacles Mounted in a Walled Parallel Plate Channel

In the present study, lattice Boltzmann simulation of conjugate heat transfer from multiple heated obstacles mounted in a walled parallel-plate channel is carried out. The aim is to investigate the effects of the pertinent thermophysical and geometrical parameters on the local Nusselt number around the obstacle's periphery. The result showed that increasing the obstacle to fluid thermal conductivity ratio and decreasing wall-to-obstacle thermal conductivity ratio results in increasing the local Nusselt number around the obstacle's periphery. The results of the present study are compared with those available from the conventional numerical methods, and good agreement is observed.     

用于太阳热发电的铅-铋合金传热特性分析

介绍了液态铅-铋(LBE)合金的热物理及传热特性,提出了将铅-铋共晶合金用于太阳热发电高温传热工质的构想.并建立了流体传热特性计算模型,对液态铅-铋合金与传统太阳热发电传热工质-熔盐的传热特性进行了对比模拟计算.结果表明:在热力循环中,采用液态LBE合金作为传热工质与熔盐相比,不但具有更高的热效率和热经济性,而且还可大大节省投资成本,因此其作为高温传热工质在太阳能热发电领域具有广阔的应用前景.