Numerical prediction of effective thermal conductivity of ceramic fiber board using lattice Boltzmann method

Abstract

Application of the lattice Boltzmann method has been extended for the analysis of combined transient conduction and radiation heat transfer through highly porous fibrous insulation media. Firstly, LBM has been employed for the analysis of combined mode of transient conduction radiation heat transfer in a 2?D rectangular enclosure containing an absorbing, emitting and scattering medium and results are compared with already published ones. The results have been found in good accord for different values of radiation-conduction parameter, scattering albedo and south (hot) wall emissivity. Furthermore, the proposed LBM for the calculation of effective thermal conductivity of ceramic fiber board has been employed. A random-generation growth method for generating micro morphology of natural ceramic fiber board has been selected. The conductive, radiative and effective thermal conductivity has been numerically estimated using the present LBM. It is found that the predicted effective thermal conductivity for different values of fibrous bulk density is in good agreement with the experimental data.     

Neural-finite difference method (NFDM) in development of improved differential approximation (IDA) and its application for coupled conduction and radiation heat transfer in a square enclosure: An experimental validation

The present numerical and experimental analysis addresses coupled conduction and radiation heat transfer (CCR) in differentially heated vertical isothermal walls and horizontal insulated walls of a square enclosure with absorbing, emitting and isotropic scattering participating gray medium. The P₁ approximation solution is utilized as the input signal to the neuron model. The computational domain is treated by the neural-finite difference method (NFDM) with ray tracing technique of ray emission model (REM) for the development of improved differential approximation (IDA). The output results are validated with the results of DOM. The practical implementation of IDA for wide range of radiative parameters are illustrated and examined. Experiments have been performed in a square enclosure with solid isothermal walls made of aluminum and insulated walls with bakelite, thus forming air filled cavity. Finally, the consistence of isotherm pattern of the numerical work with the interferogram captured by Mach–Zehnder interferometer corroborates the IDA theory and its realistic approach.     

Entropy Generation due to Combined Natural Convection and Thermal Radiation within a Rectangular Enclosure

ABSTRACT

The present work investigates entropy production due to coupled natural convection/radiation heat transfer phenomenon in an inclined rectangular enclosure, isothermally heated from the bottom side and isothermally cooled from the other sides. The discrete-ordinate method is used in modeling the radiative transport equation while the statistical narrow band correlated-k model is adopted to deduce the radiative properties of the medium. The influence of pertinent parameters such as aspect ratio, inclination angle and walls emissivities on entropy generation is studied. It is found that the volumetric entropy generation is reduced when increasing the inclination angle of the enclosure. Moreover, it is shown that the minimum entropy production due to radiation heat transfer in participating media occurs at aspect ratio equal to unity.     

Three-dimensional radiation in absorbing-emitting-scattering medium using the discrete-ordinates approximation

The discrete-ordinates method is a simple, accurate and of little computational time solution to predict the radiative heat transfer in the combustion chambers. In this paper, three-dimension radiative problems for absorbing-emitting-scattering medium are modeled using this method in the rectangular enclosure. And in addition, new discrete-ordinates are developed to study the absorbing-emitting-scattering radiation processes for complex phase function. The reasonable results can be obtained through these new ordinates, yet the deviated results are only obtained through conventional S _n ordinates.     

Numerical study on the importance of radiative heat transfer in building energy simulation

ABSTRACT

A neural network-based model for interior longwave radiative heat transfer has been developed and implemented into a new computer code, BERHT (Building Energy with Radiative Heat Transfer). The model accounts for the non-gray effect of absorbing species in a building environment and the geometric effect of a three-dimensional building structure. Numerical studies have been carried out on a rectangular single-story building. For nominal concentration of CO₂, H₂O, and small particulates, results show that the effect of radiative heat transfer is important. The surface emissivity of enclosure walls and optical properties of the absorbing/emitting medium are demonstrated to have significant effects on the distribution of heat transfer between convection and radiation, as well as the transient behavior of the indoor air temperature. Supplemental studies provide an insight that the one-zone, well-mixed model used in building energy simulation generates a “fictitious” non-local heat transfer behavior, leading to uncertainties in the understanding of the radiative heat transfer effect.     

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.     

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.     

LAMINAR AND TURBULENT NATURAL CONVECTION-RADIATION INTERACTIONS IN A SQUARE ENCLOSURE FILLED WITH A NONGRAY GAS

A numerical investigation of interactions oflaminar and turbulent natural convection and radiation in a differentially heated square enclosure was performed. Songray gas radiation was analyzed with the P^-approximation method for the radiative transfer equation and the weighted sum of gray gases model, A desirable compatibility was achieved in the resultant formulation for radiative transfer with the governing equations for natural convection flows. The Favre-averaged formulation was employed for analyzing turbulent flows together with a k-e model. In the analysis, a two-dimensional enclosure filled with carbon dioxide gas was considered. Solutions were obtained for a range of Grashof numbers and Prandtl numbers varying from 10⁴ to 10¹⁰ Characteristics of flow and temperature fields were compared with predictions in the literature and were found to be in good agreement in general.     

Application of the Haar wavelet method on a continuously moving convective‐radiative fin with variable thermal conductivity

In this paper, we numerically investigate the heat transfer in a continuously moving convective‐radiative fin with variable thermal conductivity by using Haar wavelets. Heat is dissipated to the environment simultaneously through convection and radiation. The effect of various significant parameters—in particular the thermal conductivity parameter a, convection‐sink temperature θ_a, radiation‐sink temperature θ_s, convection‐radiation parameter N_c, radiation‐conduction parameter N_r, and Peclet number Pe—on the temperature profile of the fin are discussed and interpreted physically through illustrative graphs. Computational results obtained by the present method are in good agreement with the standard numerical solutions. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21038     

Performance Evaluation of Two Heat Transfer Models of a Walking Beam Type Reheat Furnace

Two different heat transfer models for predicting the transient heat transfer characteristics of the slabs in a walking beam type reheat furnace are compared in this work. The prediction of heat flux on the slab surface and the temperature distribution inside the slab have been determined by considering thermal radiation in the furnace chamber and transient heat conduction in the slab. Both models have been compared for their accuracy and computational time. The furnace is modeled as an enclosure with a radiatively participating medium. In the first model, the three-dimensional (3D) transient heat conduction equation with a radiative heat flux boundary condition is solved using an in-house code. The radiative heat flux incident on the slab surface required in the boundary condition of the conduction code is calculated using the commercial software FLUENT. The second model uses entirely FLUENT along with a user-defined function, which has been developed to account for the movement of slabs. The results obtained from both models have a maximum temperature difference of 2.25%, whereas the computational time for the first model is 3 h and that for the second model is approximately 100 h.     

Parallel Computation for Radiative Heat Transfer Using the DOM in Combustion Applications: Direction,Frequency, Subdomain Decompositions,and Hybrid Methods

In the framework of coupled large-eddy/discrete ordinates method (LES/DOM) computations of turbulent combustion problems, various decompositions for parallel calculations of the radiative heat transfer based on the DOM are investigated. The methods analyzed are: (A) a task decomposition on the discrete directions and frequencies with two numeric strategies: Message Passing Interface (MPI) with distributed memory and OpenMP with shared memory for the direction decomposition; (B) a new algorithm for a DOM subdomain decomposition, which is proposed and tested using MPI; and (C) hybrid methods combining an OpenMP strategy for direction and MPI for tasks and subdomain decomposition. It is shown for the case of coupled simulations that the convergence and the parallel efficiency of the domain decomposition (B) are optimal. This method is limited in this work to 25 sub-domains, at which point the efficiency stagnates. Combining the directions with frequency and/or domain decompositions in a hybrid method (C) results in very good efficiency up to 1,200 processors. This hybrid strategy is also very efficient in terms of memory usage. This work shows that the best way to perform massively parallel computation for radiative heat transfer with the DOM is to combine different decomposition levels. The analysis performed in this work shows the best parallel strategy to be used in coupled simulations between radiation and LES on massively parallel architectures.     

Numerical analysis of the longitudinal size of the partition on natural convection heat transfer and fluid flow within a differentially heated porous enclosure

The article deals with the effect of longitudinal size and shape partition embedded within a differentially heated porous enclosure. The objective is to curtail the heat transfer rate across such porous enclosures by means of partitions embedded within. The partition shapes under consideration are straight vertical left-inclined, right-inclined, L-shaped, wavy, corrugated, and square-wave. It is sought to find the most effective combination of partition length and shape that could serve the required objective. Also, many times, due to the constructional constraints of the porous enclosure or cavity, using full-length partitions may not be feasible. In this regard, it is also sought to find the partition length that is to be maintained for achieving a significant reduction in heat transfer without much compromise. The results of the current study are useful for thermal design engineers particularly in the field of thermal insulation, solar heating application, and packed bed energy storage systems where the major challenge is to reduce the heat transfer across the system. The parameters under consideration are the longitudinal length L and Rayleigh number Ra. All the partitions under study are evaluated for bottom-wall and top-wall attached conditions. Some of the notable findings are that for smaller-sized partitions (B < 0.5), L-shaped partitions are most effective in controlling the convection heat transfer rate across the enclosure while for larger-sized partitions (L > 0.5), square-wave-shaped partitions should be preferred for effective reduction in the rate of convection heat transfer.     

Conjugate Wall Conduction-Fluid Natural Convection in a Three-Dimensional Inclined Enclosure

Laminar conjugate conduction-natural convection heat transfer in a 3-D inclined cubic enclosure comprised of finite thickness conductive walls and central cavity is numerically investigated. The dimensionless governing equations describing the convective flow and wall heat conduction are solved by the high accuracy multidomain pseudospectral method. Computations are performed for different Rayleigh numbers (10³ ≤ Ra* ≤ 10⁶), thermal conductivity ratios (1 ≤ k ≤ 100), dimensionless wall thickness (0 ≤ s ≤ 0.25), and enclosure inclinations (?30° ≤ α ₁ ≤ 30°, 0° ≤ α ₂ ≤ 45°). The effects of the above controlling parameters on the heat transfer performances of the enclosure system are investigated in detail, with emphases on the variations of wall conduction and fluid convection heat transfer, and the interactive heat transfer conditions between solid walls and fluid in the central cavity. Numerical results reveal that the existence of enclosure walls reduces the temperature gradient across the cavity and alters the temperature distribution within the solid walls; thus, the fluid convection is complexly determined by the combined effects of k and s, and is greatly affected by enclosure inclinations at high Rayleigh numbers. Moreover, the temperature distributions and solid-fluid interactive heat transfer conditions are provided for further interpretation and demonstration of the effects of the solid walls.     

NUMERICAL SIMULATION OF THE GAS FLOW AND MASS TRANSFER BETWEEN TWO COAXIALLY ROTATING DISKS

A problem of combined conductive and two-phase radiative heat transfer in a two-dimensional rectangular enclosure with two-phase (gas-particles) media is analyzed. A two-phase radiative transfer equation (RTE) considering radiation by both gas and particles is studied. Its nonlinear integrodifferential RTE is solved using the discrete ordinates method (DOM, or so-called S N method). To validate the program, we compare the solution in a two-dimensional rectangular black enclosure with others. The DOM is then applied to the unsteady thermal development in two-phase media contained in a rectangular enclosure. A parametric study is performed by changing the gas and particle absorption coefficients, particle number density, particle emissivity, wall emissivity, and aspect ratio of the enclosure. The results confirm a significant effect of the two-phase radiation on the thermal development in the geometry. However, it is found that the conduction is predominant near the hot wall.     

Local RBF meshless scheme for coupled radiative and conductive heat transfer

ABSTRACT

A local radial basis function meshless (LRBFM) method is developed to solve coupled radiative and conductive heat transfer problems in multidimensional participating media, in which compact support radial basis functions (RBFs) augmented on a polynomial basis are employed to construct the trial function, and the radiative transfer equation (RTE) and energy conservation equation are discretized directly at nodes by the collocation method. LRBFM belongs to a class of truly meshless methods which require no mesh or grid, and can be readily implemented in a set of uniform or irregular node distributions with no node connectivity. Performances of the LRBFM is compared to numerical results reported in the literature via a variety of coupled radiative and conductive heat transfer problems in 1D and 2D geometries. It is demonstrated that the local radial basis function meshless method provides high accuracy and great efficiency to solve coupled radiative and conductive heat transfer problems in multidimensional participating media with uniform and irregular node distribution, especially for coupled heat transfer problems in irregular geometry with Cartesian coordinates. In addition, it is extremely simple to implement.     

Convective‐radiative fins with simultaneous variation of thermal conductivity,heat transfer coefficient,and surface emissivity with temperature

This paper is a numerical study of thermal performance of a convective‐radiative fin with simultaneous variation of thermal conductivity, heat transfer coefficient, and surface emissivity with temperature. The convective heat transfer is assumed to be a power function of the local temperature between the fin and the ambient which allows simulation of different convection mechanisms such as natural convection (laminar and turbulent), boiling, etc. The thermal conductivity and the surface emissivity are treated as linear functions of the local temperature between the fin and the ambient which provide a satisfactory representation of the thermal property variations of most fin materials. The thermal performance is governed by seven parameters, namely, convection–conduction parameter Nc, radiation–conduction parameter Nr, thermal conductivity parameter A, emissivity parameter B, the exponent n associated with convective heat transfer coefficient, and the two temperature ratios, θ_a and θ_s, that characterize the temperatures of convection and radiation sinks. The effect of these parameters on the temperature distribution and fin heat transfer rate are illustrated and the results interpreted in physical terms. Compared with the constant properties model, the fin heat transfer rate can be underestimated or overestimated considerably depending on the values of the governing parameters. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20408     

Numerical investigation of coupled natural convection and radiation in a differentially heated cubic cavity filled with humid air. Effects of the cavity size

A numerical study of natural convection with surface and air/H₂O mixture radiation in a differentially heated cubic square cavity is presented. The coupled flow and heat transfers in the cavity are predicted by coupling a finite volume method with a spectral line weighted sum of gray gase model to describe gas radiative properties. The radiative transfer equation is solved by means of the discrete ordinate method. Simulations are performed at Ra?=?10⁶, considering different combinations of passive wall and/or gas radiation properties and different cavity length. It was found that in presence of a participative medium representative of building, cavity length has a strong influence on temperature and velocity fields which affect the global circulation and heat transfers in the cavity. For each steady-state solution, the convective and radiative contributions to the global heat transfer are discussed. More specifically, boundary layer thickness, thermal stratification parameter, and three-dimensional effects are compared to pure convective case results. The results suggest that radiative effects, often considered as negligible in view of the relatively low optical thickness, may not be neglected when trying to predict regime transitions.     

The radiative transfer solution of a rectangular enclosure using angular domain discrete wavelets

The wavelet expansion is used in order to evaluate the angular dependence of the radiative intensity in the solution of the radiative transfer equation. The radiative intensity is expanded in terms of orthogonal Daubechies’ wavelet basis in the angular domain. The method is applied to a two-dimensional rectangular enclosure with an absorbing, emitting and nonscattering medium in radiative equilibrium. One of the boundary surfaces is maintained at constant temperature T₁, while others are kept cold. This boundary conditions are chosen to demonstrate the effectiveness of the method in dealing with the geometries which are sensitive to ray effects. Centerline emissive power and surface heat flux distributions are compared well with the results given by the standard discrete ordinates method, the modified discrete ordinates method and also with the available exact solutions.     

Simultaneous Reconstruction of Thermal Field and Retrieval of Parameters in a Cylindrical Enclosure

This article deals with the reconstruction of temperature/heat flux profile and retrieval of parameters in a transient conduction and radiation heat transfer problem in a concentric cylindrical enclosure. Reconstruction and retrievals are achieved through the genetic algorithm (GA). In the conduction problem, the lattice Boltzmann method coupled with the GA is used for the reconstruction and retrievals; whereas in the radiation problem, the same are achieved through the discrete transfer method and the GA. The accuracies of the estimated parameters are studied for the effects of measurement errors, genetic variables such as the best fitness, the population size, and the number of generations. Reconstructed temperature and heat flux profiles and the estimated parameters are in good agreement with the exact ones.     

Effects of Wall-Located Heat Barrier on Conjugate Conduction/Natural-Convection Heat Transfer and Fluid Flow in Enclosures

The effects of a heat barrier, located in the ceiling wall of an enclosure, on conjugate conduction/natural convection are investigated numerically. The vertical walls of the enclosure are differentially heated and the horizontal walls are adiabatic. Heatline technique is used to visualize heat transport. The variations of average Nusselt number, dimensionless heat transfer rate through the ceiling wall, and dimensionless overall heat transfer rate are studied. Calculations are performed for different Rayleigh numbers (10³ ≤ Ra ≤ 10⁶), thermal conductivity ratios (1 ≤ K ≤ 100), dimensionless locations of the heat barrier (0 < X _h  < 1),and two dimensionless ceiling wall thicknesses (D = 0.05 and D = 0.20). For high thermal conductivity ratio (K = 100), the heat barrier considerably reduces the dimensionless overall heat transfer rate. The effect of the heat barrier on dimensionless heat transfer rate through the enclosure increases as the Rayleigh number decreases. For low Rayleigh number (i.e., Ra = 10³), a location exists in the ceiling wall for which the dimensionless overall heat transfer rate is minimum.