Radiative and conductive heat transfer is fairly important in the nuclear pebble bed. A continuum model is proposed here to derive the effective thermal conductivity (ETC) of pebble bed. It is a physics-based equation determined by the temperature, number density, heat transfer coefficient, and the radial distribution function (RDF). Based on a concept of continuum, this model considers the conduction and thermal radiation in nuclear pebble bed through a uniform framework and the results are in good agreement with the existing model and correlations. It indicates that the local temperature in the radiation case without internal heat sources is determined by all possible surrounding pebbles weighted by a radiative kernel function. The discrete element method (DEM) packing results are in good agreement with the solution of the continuum model. Both the conductive and radiative continuum models converge to the heat conduction in continuum mechanics at size factor μ ≪ 1.

Spiral-coiled tube heat exchangers (SCTHE) have higher heat transfer as compared to the conventional heat transfer devices and are extensively used to extract heat from exhaust gases in the chemical processing industries and also from sunlight for domestic applications. However, no attention has been made to predict heat transfer characteristics considering combined convective and radiative heat transfer in spiral-coiled tubes. In the present study, numerical analysis has been performed to predict fluid flow and heat transfer characteristics by combined forced convection and thermal radiation in spiral-coiled tubes. The P-1 radiation and the renormalized group (RNG) k–ε turbulence models have been used to study the effect of thermal radiation and turbulent convection heat transfer in the spiral-coiled tube, respectively, over a wide range of Reynolds numbers (10,000–100,000) and curvature ratios (0.02–0.05). The emissivity and optical thickness have been varied from 0.0 to 1.0 and 0.0 to 8.0, respectively, to investigate the effect of thermal radiation on heat transfer characteristics in spiral-coiled tubes. For the considered Reynolds number range, it is found that the heat transfer is enhanced by approximately 10% when radiation is taken into account. It is found that the heat capacity increased with an increase in optical thickness and wall emissivity. Further, the effect of optical thickness on fully developed flow is observed weak and the average heat transfer coefficient is influenced by the wall emissivity over the entire flow.

The coupled phenomena of radiative–magnetohyrodynamic (MHD) natural convection in a horizontal cylindrical annulus are numerically investigated. The buoyant flow is driven by the temperature difference between the inner and outer cylinder walls, while a circumferential magnetic field induced by a constant electric current is imposed. The hybrid approach of finite volume and discrete ordinates methods (FV-DOM) is developed to solve the nonlinear integro-differential governing equations in polar coordinate system, and accordingly, the influences of Hartmann number, radiation–convection parameter, and optical properties of fluid and wall on thermal and hydrodynamic behaviors of the “downward flow,” originally occurring without consideration of radiation and magnetic field, are mainly discussed. The results indicate that both the circulating flow and heat transfer are weakened by the magnetic field, but its suppression effect on the latter is rather small. Under the influence of magnetic field, the “downward flow” pattern has not been obtained from zero initial condition even for the case of weak radiation of N R = 0.1. Besides, the variation of radiative heat transfer rate with angular positions diminishes for the fluid with strong scattering or weak absorption.

Origami tessellations have been proposed as a mechanism for control of radiative heat transfer through the use of the cavity effect. This work explores the impact of a changing projected surface area and varying apparent radiative properties on the net radiative heat transfer of an accordion fold comprised of V-grooves. The net radiative heat transfer of an accordion tessellation is obtained by a thermal energy balance at the cavity openings with radiative properties of the cavities given as a function of various cavity parameters. Results of the analytical model are experimentally confirmed. An accordion tessellation, constructed of stainless-steel shim stock, is positioned to achieve a specified fold angle and placed in a vacuum environment while heated by Joule heating. A thermal camera records the apparent temperature of the cavity openings for various fold angles. Results are compared to apparent temperatures predicted with the analytical model. Analytically and experimentally obtained temperatures agree within 5% and all measurements fall within experimental uncertainty. For diffusely irradiated surfaces, the decrease in projected surface area dominates, causing a continuous decrease in net radiative heat transfer for a collapsing accordion fold. Highly reflective specular surfaces exposed to diffuse irradiation experience large turn-down ratios (7.5× reduction in heat transfer) in the small angle ranges. Specular surfaces exposed to collimated irradiation achieve a turn down ratio of 3.35 between V-groove angles of 120 deg and 150 deg. The approach outlined here may be extended to modeling the net radiative heat transfer for other origami tessellations.

The statistical multiphase approach (MPA) proposed in the first part of this work to evaluate radiative properties of composite materials is applied to porous structures of opaque material and biological tissues. Radiative thermal conductivity is calculated for the bundle of circular rods, packed pebble beds, and metal foams. The results generally agree with the reference calculations by other methods. The small difference can be explained by different approaches to scattering and assumptions about the temperature distribution. Attenuation of light in skin tissues is calculated by the diffusion approximation. The attenuation coefficient generally agrees with the reference Monte Carlo simulation (MC). The difference observed at certain combination of parameters can be due to the assumption of regular arrangement of vessels at the MC simulation.

Heat transfer properties of two expanded polystyrene (EPS) samples of similar density, one without (white) and one with graphite opacifier particles (gray), are compared. Tomographic scans are used to obtain cell sizes of the foams. Using established models for closed-cell polymer foams, the extinction coefficient and the effective thermal conductivity are obtained. The effect of opacifiers is modeled using (1) an effective refractive index for the polystyrene walls within a cell model for the EPS and (2) a superposition of extinction due to a particle cloud upon extinction predicted by the cell model, where particles are modeled as oblate spheroids, or equivalent volume, surface, or hydraulic diameter spheres. Modeled effective conductivities are compared with measurements done on a guarded hot-plate apparatus at sample mean temperatures in the range from 0 °C to 40 °C. Typically, cells of the gray EPS are about 40% larger than those of the white EPS and the cell walls in the gray EPS are thicker. The refractive index mixing model and the model with graphite opacifier particles as oblate spheroids overpredict extinction, however, the mean error in the effective conductivity predicted by the oblate spheroids model is only 2.7%. Equivalent volume/surface sphere models underpredict extinction, but still yield a low mean error in effective conductivity of around 4%. While the oblate spheroids model has a lower mean error, the computationally less expensive equivalent volume or equivalent surface models can also be recommended to model the inclusions.

Foams, three-dimensional (3D)-printed cellular and honeycomb structures, and very oblate particles dispersed in a matrix are the examples of heterogeneous media with thin-wall morphology. Phase boundaries can also be considered by this approach. Statistical description is proposed to estimate the effective radiative properties of such media. Three orientation models are studied: (i) isotropic, (ii) surface elements parallel to a plane, and (iii) surface elements parallel to an axis. Radiative transfer equations (RTEs) are obtained and analyzed in the framework of the homogeneous phase approach (HPA) and the multiphase approach (MPA). Analytical expressions are obtained for the absorption, extinction, and scattering coefficients, the scattering phase function, and the radiative thermal conductivity for very oblate particles dispersed in an absorbing scattering matrix. The reflective properties of the platelets and their preferential orientation can be used to optimize the radiative thermal conductivity.

We investigate the near-field (NF) radiative heat transfer of the three-body system consisting of anisotropic magnetodielectric hyperbolic metamaterials (AMDHMs), which can support coupled surface phonon polaritons (SPhPs) and hyperbolic modes for both p and s polarizations. We numerically demonstrate that the NF heat transfer between two AMDHMs bodies can be further enhanced by inserting an AMDHMs slab. Due to the loss in AMDHMs, there exists an optimum thickness of the intermediate slab to maximize the NF heat flux flowing to the receiver for a fixed gap distance. Results obtained from this work will facilitate investigations of the NF heat transfer involving magnetic hyperbolic metamaterials.

Hyperbolic metamaterial (HMM) alternately stacked by graphene and silicon carbide (SiC) is proposed to theoretically study near-field radiative heat transfer. Heat transfer coefficients (HTCs) are calculated using the effective medium theory (EMT). We observe that HMMs can exhibit better heat transfer characteristic than graphene-covered SiC bulks when appropriate SiC thickness and chemical potentials of graphene are selected. Transfer matrix method (TMM) is also employed to calculate HTC between HMMs with thicker SiC, given the invalidity of EMT in this case. We deduce that with increasing SiC thickness, HTC first increases rapidly and then decreases slowly when it reaches maximum value. HTC is high for graphene with small chemical potential. Results may benefit applications of thermophotovoltaic devices.

This paper presents a methodology for the application of the weighted-sum-of-gray-gases (WSGG) model to systems where the medium is bounded by nongray surfaces. The method relies on the assumption that each gray gas absorption coefficient is randomly spread across the entire wavenumber spectrum. It follows that, in the spectral integration of the radiative transfer equation (RTE), the local emission term can be computed by the joint probability of emission from the subsections of the spectrum related to each gray gas coefficient and from each wall emissivity band. One advantage of the proposed methodology is that it allows the use without any modification of WSGG correlations that are available in the literature. The study presents a few test cases considering a one-dimensional (1D), nonuniform medium slab composed of H 2 O and CO 2 , bounded by nongray surfaces. The accuracy of the methodology is assessed by direct comparison with line-by-line (LBL) calculations.

The aim of this study is to present a reduced spectral line-based weighted sum of gray gases (SLW) model to simulate the radiation heat transfer in nongray media at high temperatures. Inverse approach is used to divide the absorption cross section band into a clear gas with one gray gas and two gray gases, which are called the S-1 and S-2 approaches, respectively. The unknown absorption cross sections are determined from the knowledge of measured total incident intensities received by wall surfaces. In order to simulate the exact solution of radiation heat transfer in nongray gaseous media, the discrete transfer method (DTM) in combination with S-20 model is used, where the nongray medium is replaced with a set of a clear gas and 20 gray gases. The inverse problem is formulated as an optimization problem to minimize a least square objective function, which is solved by the conjugate gradient method (CGM). The accuracy of the present method is verified by comparing with previous researches and the S-20 approach with a large number of gray gases. The effects of noisy data on the inverse solution are investigated by considering an extreme case with large measurement error. The results show that the unknown absorption cross sections are retrieved well, even for noisy data.

This work applies a projection-based model-reduction approach to make high-order quadrature (HOQ) computationally feasible for the discrete ordinates approximation of the radiative transfer equation (RTE) for purely absorbing applications. In contrast to traditional discrete ordinates variants, the proposed method provides easily evaluated error estimates associated with the angular discretization as well as an efficient approach for reducing this error to an arbitrary level. In particular, the proposed approach constructs a reduced basis from (high-fidelity) solutions of the radiative intensity computed at a relatively small number of ordinate directions. Then, the method computes inexpensive approximations of the radiative intensity at the (remaining) quadrature points of a high-order quadrature using a reduced-order model (ROM) constructed from this reduced basis. This strategy results in a much more accurate solution than might have been achieved using only the ordinate directions used to construct the reduced basis. One- and three-dimensional test problems highlight the efficiency of the proposed method.

In this paper, a new hybrid numerical algorithm is developed to solve coupled convection–radiation heat transfer in a two-dimensional cavity containing an absorbing, emitting, and scattering medium. The radiative information is obtained by solving the radiative transfer equation (RTE) using the control volume finite element method (CVFEM), and the density, velocity, and temperature fields are calculated using the two double population lattice Boltzmann equation (LBE). To the knowledge of the authors, this hybrid numerical method is applied at the first time to simulate combined transient convective radiative heat transfer in 2D participating media. In order to test the efficiency of the developed method, two configurations are examined: (i) free convection with radiation in a square cavity bounded by two horizontal insulating sides and two vertical isothermal walls and (ii) Rayleigh–Benard convection with and without radiative heat transfer. The obtained results are validated against available works in literature, and the proposed method is found to be efficient, accurate, and numerically stable.

Thermal analysis of fluid flow is always regarded as an important research issue within cavities in order to become familiar with the characteristics of fluid flow phenomenon in enclosures. This research paper investigates the fluid and heat transfer analysis of fluid flow inside a triangular cavity using natural element methodology (NEM). This Galerkin-based methodology has been introduced for a decade and almost demonstrated its efficiency in the numerical heat transfer analysis of problems in most engineering sciences. The fluid flow contains natural convection along with conduction and radiation heat transfer with medium's walls, which have absorbing, emitting, semitransparent, and nonscattering characteristics. The final results investigate the effects of radiative and natural convection heat transfer on the fluid flow pattern as expressed in Rayleigh number, stream function, strength of natural convection regime, etc., which are checked with other similar studies presented in the literature and shows how promising NEM can be as an efficient numerical approach to improve computational precision when dealing with fluid mechanic problems.

This paper presents correlations for the weighted-sum-of-gray-gases (WSGG) model for carbon monoxide based on HITEMP2010. The correlations are valid for pressure path lengths from 0.0001 atm·m up to 10 atm·m, total pressure in the order of 1.0 atm, and for temperatures ranging from 400 K up to 2500 K. Some test cases embodying nonhomogeneous, nonisothermal conditions are presented, and the results for the WSGG model are compared with the line-by-line (LBL) solutions for CO.

This work deals with the combined mode of non-Fourier conduction and radiation transfer in isotropically/anisotropically scattering, homogeneous, and inhomogeneous planar media with reflective boundaries subjected to the constant internal temperature of the medium and the externally isotropic diffuse incidence at one boundary. An analytical double spherical harmonics method (DP N ) is proposed to solve the radiative problem. The non-Fourier conduction is described with the Cattaneo–Vernotte model, and the governing hyperbolic energy equation is solved using the lattice Boltzmann method (LBM). For radiative problems through the layer/layered media, the radiative heat fluxes, hemispherical radiative intensities, transmissivity, and reflectivity are found, while for coupled conduction and radiation, the temperature distributions are found for various optical thicknesses, space-dependent scattering albedo, conduction–radiation parameters, and boundary reflectivities. Results of the present work are in excellent agreement with those available in the literature. Moreover, these results demonstrate that the proposed analytical double spherical method is an efficient, robust, and accurate method for radiative transfer through inhomogeneous layer/layered planar media analysis. Furthermore, it is observed that space-dependent scattering albedo and boundary reflectivities have a very significant effect in the hyperbolic sharp wave front of non-Fourier conduction.

In this work, the influence of the radiative properties of coal and ash particles on radiative heat transfer in combustion environments is investigated. Emphasis is placed on the impact on the impact of the complex index of refraction and the particle size on particle absorption and scattering efficiencies. Different data of the complex index of refraction available in the literature are compared, and their influence on predictions of the radiative wall flux and radiative source term in conditions relevant for pulverized coal combustion is investigated. The heat transfer calculations are performed with detailed spectral models. Particle radiative properties are obtained from Mie theory, and a narrow band model is applied for the gas radiation. The results show that, for the calculation of particle efficiencies, particle size is a more important parameter than the complex index of refraction. The influence of reported differences in the complex index of refraction of coal particles on radiative heat transfer is small for particle sizes and conditions of interest for pulverized coal combustion. For ash, the influence of variations in the literature data on the complex index of refraction is larger, here, differences between 10% and 40% are seen in the radiative source term and radiative heat fluxes to the walls. It is also shown that approximating a particle size distribution with a surface area weighted mean diameter, D 32 , for calculation of the particle efficiencies has a small influence on the radiative heat transfer.

The immersed boundary method (IBM) is gaining attention in the computational fluid dynamics but its applications in the field of a conjugated radiative–conductive or radiative–convective heat transfer seem limited. Therefore, the paper presents extension of this method to heat transfer problems dominated by thermal radiation in a nongray medium. The present model enables simulation of heat and fluid flows in a domain with complex stationary or moving internal and external boundaries on a fixed Cartesian grid (FCG) by applying the finite volume method. The special attention is paid to modeling thermal radiation and optical phenomena at highly curved, opaque, or transparent boundaries which confine the computational domain or separate zones of different thermophysical and optical properties, e.g., different values of a refractive index. The model is limited to a 2D planar or axisymmetric spaces. Detailed verification procedure proves accuracy and correctness of the developed model and shows its potential application field. The model may be used for simulations of a conjugated radiative–conductive or radiative–convective heat transfer in a nongray medium in a complex domain with opaque or transparent curved internal or external boundaries without unstructured or body fitted mesh generation.

Enhancing photon tunneling probability is the key to increasing the near-field radiative heat transfer between two objects. It has been shown that hexagonal boron nitride (hBN) and graphene heterostructures can enable plentiful phononic and plasmonic resonance modes. This work demonstrates that heterostructures consisting of a monolayer graphene on an hBN film can support surface plasmon–phonon polaritons that greatly enhance the photon tunneling and outperform individual structures made of either graphene or hBN. Both the thickness of the hBN films and the chemical potential of graphene can affect the tunneling probability, offering potential routes toward passive or active control of near-field heat transfer. The results presented here may facilitate the system design for near-field energy harvesting, thermal imaging, and radiative cooling applications based on two-dimensional materials.

Many researchers have studied the radiative heat transfer in a viscoelastic boundary layer flow over a stretching sheet after simplifying the complex nature of the radiative heat flux by expanding the fourth power of temperature ( T 4 ) in Taylor series about free-stream temperature ( T ∞ ) and neglecting the higher-order terms. Similarity solutions obtained by them are found to be valid only in the asymptotic region. This article suggests a modification in the linearization of T 4 by introducing wall temperature ( T w ) as well as freestream temperature ( T ∞ ) to capture the realistic nature of the temperature distribution in the boundary layer flows from locally nonsimilar solutions.