Wall Emissivity Research Articles

Effective emissivity of a blackbody cavity formed by two coaxial tubes.

A blackbody cavity is developed for continuously measuring the temperature of molten steel, which consists of a cylindrical outer tube with a flat bottom, a coaxial inner tube, and an aperture diaphragm. The ray-tracing approach based on the Monte Carlo method was applied to calculate the effective emissivity for the isothermal cavity with the diffuse walls. And the dependences of the effective emissivity on the inner tube relative length were calculated for various inner tube radii, outer tube lengths, and wall emissivities. Results indicate that the effective emissivity usually has a maximum corresponding to the inner tube relative length, which can be explained by the impact of the inner tube relative length on the probability of the rays absorbed after two reflections. Thus, these results are helpful to the optimal design of the blackbody cavity.

Radiative heat transfer analysis in modern rocket combustion chambers

Radiative heat transfer is analyzed for subscale and fullscale rocket combustion chambers for H2/O2 and CH4/O2 combustion using the P1 radiation transport model in combination with various Weighted Sum of Gray Gases Models (WSGGMs). The influence of different wall emissivities, as well as the results using different WSGGMs, the size of the combustion chamber and the coupling of radiation and fluid dynamics, is investigated. Using rather simple WSGGMs for homogeneous systems yields similar results as using sophisticated models. With models for nonhomogeneous systems the radiative wall heat flux (RWHF) decreases by 25–30 % for H2/O2 combustion and by almost 50 % for CH4/O2 combustion. Enlarging the volume of the combustion chamber increases the RWHF. The influence of radiation on the flow field is found to be negligible. The local ratio of RWHF to total wall heat flux shows a maximum of 9–10 % for H2/O2 and 8 % for CH4/O2 combustion. The integrated heat load ratio is around 3 % for H2/O2 and 2.5 % for CH4/O2 combustion. With WSGGMs for nonhomogeneous systems, the local ratio decreases to 5 % (H2/O2) and 3 % (CH4/O2) while the integrated ratio is only 2 % (H2/O2) and 1.3 % (CH4/O2).

Normalization of Various Phase Functions for Radiative Heat Transfer Analysis in a Solar Absorber Tube

Normalization of various phase functions is considered for accurately predicting radiative heat transfer. A solar absorber tube filled with anisotropic scattering working medium is used as an example. Analysis of a previous normalization technique shows that while it does conserve scattered energy exactly after discrete-ordinates method (DOM) discretization, the overall asymmetry factor of the phase function is distorted, leading to substantial changes in overall scattering effect. A new normalization technique that conserves asymmetry factor and scattered energy simultaneously is investigated. The impact of lack of asymmetry factor conservation is analyzed for both the Legendre polynomial and the Henyey–Greenstein phase function approximations. Variations of medium optical thickness, scattering albedo, asymmetry factor, and side-wall emissivity are scrutinized to determine the effects of said parameters on wall heat flux and energy absorbing rate inside the absorber tube. Side-wall heat flux is found to increase with increases in asymmetry factor, optical thickness, and wall emissivity, and with decreases in scattering albedo. Energy absorbing rate profiles are found to depend greatly on optical thickness and scattering albedo.

Heating characteristics of billet in a walking hearth type reheating furnace

The heating characteristics of billet in a walking hearth type reheating furnace were studied by developing a mathematical heat transfer model. Radiation calculations were conducted by means of zone method and considering all radiation exchange paths. The weighted-sum-of-gray-gas-model was used for better accuracy of gas radiation prediction. Convective heat flux was calculated by considering suitable value of convective heat transfer coefficient at any location of the furnace. The model was substantiated through its comparison to experimental data. A comparison was drawn to evaluate the effect of constant and variable convective coefficient on convective flux distribution and billet thermal behavior. The effect of furnace wall's emissivity of each zone and whole of the furnace on the billet thermal behavior was investigated. The obtained results revealed that by increasing furnace wall's emissivity for a determined residence time, billet's temperature in primary zones rises but it has no significant effect on its final temperature. However, by increasing wall's emissivity from 0.7 to 0.95, the residence time can be declined by about 5%. Moreover, emissivity increase in non-firing and preheating zones as compared to heating and soaking zones has greater impact on the billet thermal behavior.

Interaction of Participating Medium Radiation with Thermosolutal Convection-A Critical Appraisal

The present study addresses the interaction effect of participating media radiation with the onset of double-diffusive convection in a square enclosure. Vertical walls are imposed with constant temperature and concentration, and the horizontal walls are impermeable and adiabatic. The boundaries of the enclosure are diffuse-gray, and the enclosed fluid isotropically scatters, emits, and absorbs thermal radiation. Numerical simulations have been performed for both aiding and opposing buoyancy conditions. The buoyancy ratio has been varied to simulate the effect of buoyancy driven flow and compositionally driven flow, along with transition of flow between the above. Optical properties like opacity of medium, scattering albedo, Planck number, and wall emissivity have been varied to depict their influence on flow and heat transfer. The modified MAC method is used for the solution of convective transport equations. Gradient dependent consistent hybrid upwind scheme of second order (GDCHUSSO) is used for the discretization of the convective terms. The discrete ordinate method, with S8 approximation, is used to solve the radiative transport equation. The parametric results are provided in graphical and tabular form. Flow lines, isotherms, and isoconcentration contour maps are provided to bring clarity in the understanding of the momentum, heat, and solute transport phenomenon. The stabilization effect of thermal radiation at critical buoyancy ratio for buoyancy opposed flow is observed. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21108

Inverse boundary design problem of natural convection–radiation in a square enclosure

The inverse boundary design problem of combined natural convection–radiation has been solved numerically. The aim of this study is to find the strength of heaters in a 2-D enclosure to produce desired temperature and heat flux distribution on the design surface. To obtain the optimal solution, the Levenberg–Marquardt algorithm is chosen to perform the iterative search procedure. Moreover to reduce the computation time, the sensitivity matrix is updated by Broyden combined update method. The direct problem is solved using the finite volume method for both fluid and radiative transfer equations. SIMPLE algorithm is utilized to satisfy pressure–velocity coupling. Cases of surface-to-surface radiation and radiation in a grey, emitting, absorbing and scattering media are investigated. Effects of Rayleigh number, optical thickness, scattering albedo, wall emissivity and number of heating and design elements are studied. The results show that for various cases, estimated heat fluxes on the design surface are very close to the desired values and the maximum root mean square error is less than 1%.

The Radiative Boundary Design of a Hexagonal Furnace Filled With Gray and Nongray Participating Gases

The inverse radiative boundary design problem in a hexagonal furnace is numerically investigated. The aim of this study is to find the strength of heaters in a two-dimensional (2D) enclosure to produce the desired temperature and heat flux distribution on the design surface. Conjugate gradients method is chosen to perform the iterative search procedure for obtaining the optimal solution. The medium is considered participating and both gray and nongray cases are studied. FTn finite volume method (FVM) with nonorthogonal grid is employed to solve the radiative transfer equation in the furnace. In nongray cases, the medium is filled with combustive gas products. To predict nongray behavior properly, the SLW model is used. In problems with gray medium, the effects of wall emissivity, absorption coefficient, and scattering albedo are studied. For nongray problems, the effects of gas concentration and temperature of single species and gas mixtures are analyzed. In all cases, heater power can be estimated precisely and as the results show, estimated heat flux on the design surface is very close to the desired value. For this reason, the maximum root mean square error is less than 1.6%.

Radiative heat transfer analysis in pure scattering layers to be used in vacuum insulation panels

Radiative heat transfer in the pure scattering layers in vacuum insulation panels is analyzed using Monte Carlo method for two cases; for isotropic scattering and the other for pure backward scattering. The result for isotropically-scattering medium agrees well with the diffusion solution within 1% error. This, indeed, shows that the diffusion approximation can be used as a good approximation in the tested cases. The results also suggest that the radiative heat transfer in the vacuum insulation panels can be effectively reduced by increasing the optical thickness of the core material and/or decreasing the surface emissivity by inserting more radiation shields. When the pure backward scattering is applied, significant reduction is found in the radiative heat transfer rate compared with the isotropic scattering case. It is shown that radiative thermal conductivity of the scattering layer is decreased to nearly half for the backward scattering medium when the optical thickness is large and the wall emissivity is high. Thus, the materials with highly backward scattering are recommended to be used as the core or insertion material between the radiation shields to enhance the performance of the vacuum insulation panels.

Radiation heat savings in polysilicon production: Validation of results through a CVD laboratory prototype

This work aims at a deeper understanding of the energy loss phenomenon in polysilicon production reactors by the so-called Siemens process. Contributions to the energy consumption of the polysilicon deposition step are studied in this paper, focusing on the radiation heat loss phenomenon. A theoretical model for radiation heat loss calculations is experimentally validated with the help of a laboratory CVD prototype. Following the results of the model, relevant parameters that directly affect the amount of radiation heat losses are put forward. Numerical results of the model applied to a state-of-the-art industrial reactor show the influence of these parameters on energy consumption due to radiation per kilogram of silicon produced; the radiation heat loss can be reduced by 3.8% when the reactor inner wall radius is reduced from 0.78 to 0.70m, by 25% when the wall emissivity is reduced from 0.5 to 0.3, and by 12% when the final rod diameter is increased from 12 to 15cm.

Combined gas radiation and laminar forced convection flow adjacent to a forward facing step in a duct

PurposeThe purpose of this paper is to focus on thermal characteristics behavior of forced convection flow in a duct over forward facing step (FFS), in which all of the heat transfer mechanisms, including convection, conduction and radiation, take place simultaneously in the fluid flow.Design/methodology/approachThe fluid is treated as a gray, absorbing, emitting and scattering medium. The Navier‐Stokes and energy equations are solved numerically by computational fluid dynamics (CFD) techniques to obtain the velocity and temperature fields. Discretized forms of these equations are obtained by the finite volume method and solved using the SIMPLE algorithm. Since the gas is considered as a radiating medium, all of the convection, conduction and radiation heat transfer take place simultaneously in the gas flow. For computation of the radiative term in the gas energy equation, the radiative transfer equation (RTE) is solved numerically by the discrete ordinate method (DOM) to find the radiative heat flux distribution inside the radiating medium. By this numerical approach, the velocity, pressure and temperature fields are calculated.FindingsThe effect of wall emissivity, optical thickness, albedo coefficient and the radiation‐conduction parameter on heat transfer behavior of the system are also investigated. The numerical results for two cases of convection‐conduction and conduction‐radiation problems are compared with the available data published in open literature and good agreement was obtained.Originality/valueThis is the first time in which flow over FFS in a duct, considering all heat transfer mechanisms including conduction, convection and radiation, is solved numerically.

Physical study of radiation effects on the boundary layer structure in a turbulent channel flow

A complete numerical coupling between radiation and turbulent convection in a channel gas flow has been performed for different temperature, optical thickness (pressure) and wall emissivity conditions. In this model, radiation is treated from the CK approach and a Monte Carlo transfer method; the flow by a Direct Numerical Simulation. Both the effects of turbulence on radiation fields and of radiation on turbulent fields are accounted for.Gas–gas and gas–wall radiation interactions generate antagonist effects on the temperature and flux fields. The first one tends to increase wall conductive flux while the second one to decrease it. Consequently, the structure of the temperature field and the wall conductive flux often strongly differ from results without radiation. Classical wall log-laws for temperature are then strongly modified by the global radiation effects. Many conditions encountered in applications are discussed in the paper. The observed modifications depend on all the set of conditions (temperature level, wall emissivity, pressure, Reynolds number), i.e. on the relative magnitudes of radiation gas–gas and gas–wall phenomena and of global radiation flux and conductive flux without radiation.

The effect of radiation on natural convection in slanted cavities of angle γ = 45° and 60°

A numerical investigation of combined radiation and natural convection in slanted cavities of angle 45° and 60°, respectively, has been performed for a temperature ratio of Th/Tc = 2, and Tc = 500°K. The finite volume method is used to solve the Navier Stokes, temperature and the Radiative Transfer equations, for constant thermo-physical properties and Ra = 105. The Boussinesq approximation is used to model the buoyancy. Cases of pure convection and of convection and radiation, in both a transparent and in a radiative participative medium, have been compared using the flow and isotherm patterns and the local convective, radiative and total Nusselt numbers. The radiative optical length of the medium shows a marked effect on the recirculation rate, temperature distribution and the overall heat transfer. The wall emissivity also shows a strong influence on the heat transfer whereas the scattering albedo does not do so. There is a decrease in the recirculation rate as well as the overall heat transfer with the increase of slant of the geometry. Additionally, a non-Boussinesq variable density formulation is also tested on the same geometry and conditions. The total average Nusselt number shows little significant difference between the results from the Boussinesq and the variable density formulations.

Light intensity distribution in multi-lamp photocatalytic reactors

A computational fluid dynamics approach has been used to investigate the effect of lamp separation (Xlamp) on the radiation intensity distribution in a multiple-lamp photocatalytic reactor. The optical parameters (absorption and scattering coefficients) of Aeroxide® P25 titanium dioxide (TiO2) were determined by performing experiments using a single lamp system. Since the optical properties are wavelength dependent, the range of wavelength from the UV lamp was divided into 4 bands, and optical properties in each of the bands were determined by matching the experimental observations with simulated values. Simulations were then carried on multiple-lamp (2 and 4 lamps) photoreactors as a function of lamp separation and catalyst loadings. In case of 2-lamp system, the maximum local volumetric rate of energy absorption (〈LVREA〉) occurred at Xlamp=40mm, and it was independent of the catalyst loading. With 4 lamps however, optimum Xlamp was dependent on the catalyst loading. At low loads (up to Wcat=0.06gL−1), the optimum Xlamp was 80mm but as the catalyst concentration increased, the value of the optimum lamp separation decreased considerably, with 30mm for Wcat=0.07gL−1 and decreasing further as the concentration further increased. Because of the high absorption coefficient of the catalyst, the wall emissivity had a negligible effect on the 〈LVREA〉 for both configurations, even when the lamps were close to the wall. Finally, in both cases, the optimum lamp separation was independent of the lamp emissive power.

Combined Effects of Radiation and Natural Convection in a Square Cavity Submitted to Two Combined Modes of Cross Gradients of Temperature

The present article reports numerical results of natural convection and surface radiation within a square cavity filled with air and submitted to discrete heating and cooling from all its walls. The thermally active elements are centrally located on the walls of the cavity. Two heating modes are considered: in the first mode, named VB heating mode, the cavity is heated discreetly on the left vertical and bottom horizontal walls, while in the second mode, named VT heating mode, the left vertical and top horizontal walls of the cavity are heated. The remaining portions of the walls, other than those cooled, are considered adiabatic. The parameters governing the problem are the emissivity of the walls (0 ≤ ϵ ≤ 1), the relative lengths of the active elements (), and the Rayleigh number (104 ≤ Ra ≤ 107). The effect of these parameters on heat transfer and fluid flow within the cavity is examined. Results of the study are presented and compared to those of pure natural convection (ϵ = 0) for various typical combinations of the governing parameters in terms of flow and temperature patterns, average convective, radiative and total Nusselt numbers, and heatlines visualization. The heat transfer across the cavity was found to enhance notably with the active wall emissivity, while the effect of the insulated wall emissivity was insignificant. The contribution of radiation to the total heat transfer is generally not negligible for ϵ ≥ 0.5. It was demonstrated that the VB heating mode acts such that the flow circulation is importantly intensified engendering, consequently, high values of the Nusselt number. In contrast, the VT heating mode leads to a slowdown of the fluid flow motion and, therefore, to a weaker convective heat transfer.

Influence of wall emissivity and convective heat transfer coefficient on the adiabatic surface temperature as thermal/structural parameter in fire modeling

In fire engineering analysis, one of the open problem is the transfer of thermal parameters obtained by fire CFD model to FEM models for structural analysis. In this study the new useful concept of “Adiabatic Surface Temperature” or more commonly known as AST, introduced by Wickström, is investigated. The adiabatic surface temperature offers the opportunity to transfer both thermal information of the gas and the net heat flux to the solid phase model, obtained by CFD analysis.In this study two CFD analyses are carried out in order to evaluate the effect of emissivity and of convective heat transfer coefficient to determine the AST. First one CFD analysis simulating a fire scenario, “conjugate heat transfer”, with a square steel beam exposed to hot surface is carried out to calculate AST, heat convective coefficient and temperature field in the beam. Second one, a conductive analysis is carried out on “standalone beam” imposing a third type boundary condition on its boundaries assuming the AST, evaluated in the conjugate analysis, as external temperature. Different heat convective coefficients are imposed on the beam walls. The comparison between results obtained by means of the two proposed analyses shows the use of AST as transfer thermal parameter between CFD (Computational Fluid Dynamic) and FEM (Finite Element Method) models is appropriate when the convective heat transfer coefficient is properly evaluated.

Combined double-diffusive convection and radiation in a square enclosure filled with semitransparent fluid

A 2D numerical assessment of coupled double diffusive convection and volumetric radiation in a differentially heated square enclosure filled with a gray fluid participating in absorption, emission and nonscattering is carried out. Temperatures and concentrations are imposed at the vertical walls, whereas the horizontal walls are insulated and impermeable. All cavity walls are assumed to be opaque, diffuse and gray. The governing equations are solved by a hybrid scheme with multiple relaxation time lattice Boltzmann (MRT-LBM) and finite difference method (FDM). The velocity field is computed by D2Q9 MRT model while the temperature field is determined by resolution of the energy equation using FDM. The radiative source term in the energy equation is calculated by the discrete ordinates method (DOM) with S8 quadrature. A parametric study illustrating the influence of the buoyancy number (N) and the wall emissivity (εi) on the flow field and the heat and mass transfer is performed. Results are presented in terms of isotherms, streamlines, iso-concentrations, Nusselt and Sherwood numbers. Generally the isotherms and iso-concentrations are inclined in the core cavity, the flow is more stabilized in presence of cooperating flow case but opposing flows are found to be a catalyser of the multi-cellular structures.

Chebyshev Collocation Spectral Method for Three-Dimensional Transient Coupled Radiative–Conductive Heat Transfer

Abstract A Chebyshev collocation spectral method (CSM) is presented to solve transient coupled radiative and conductive heat transfer in three-dimensional absorbing, emitting, and scattering medium in Cartesian coordinates. The walls of the enclosures are considered to be opaque, diffuse, and gray and have specified temperature boundary conditions. The CSM is adopted to solve both the radiative transfer equation (RTE) and energy conservation equation in spatial domain, and the discrete ordinates method (DOM) is used for angular discretization of RTE. The exponential convergence characteristic of the CSM for transient coupled radiative and conductive heat transfer is studied. The results using the CSM show very satisfactory calculations comparing with available results in the literature. Based on this method, the effects of various parameters, such as the scattering albedo, the conduction–radiation parameter, the wall emissivity, and the optical thickness, are analyzed.

Performance evaluation of four radiative transfer methods in solving multi-dimensional radiation and/or conduction heat transfer problems

This article reports results of the four popular and widely used numerical methods, viz., the Monte Carlo method (MCM), the discrete transfer method (DTM), the discrete ordinates method (DOM) and the finite volume method (FVM) used to calculate radiative information in any thermal problem. Different classes of problems dealing with radiation and/or conduction heat transfer problems in a 2-D rectangular absorbing, emitting and scattering participating medium have been considered. In radiative equilibrium and non-radiative equilibrium cases, the MCM results have been used as the benchmark data for comparing the performances of the DTM, the DOM and the FVM. In the combined radiation and conduction mode problem, the energy equation has been formulated using the lattice Boltzmann method (LBM). To compare the performance of the DTM, the DOM and the FVM, the required radiative field data computed using these methods have been provided to the LBM formulation. Temperature distributions obtained using the four methods and those obtained from the LBM in conjunction with the DTM, the DOM and the FVM have been compared for different parameters such as the extinction coefficient, the scattering albedo, the conduction-radiation parameter, the wall emissivity, the aspect ratio and heat generation rate. In all the cases, results of these methods have been found in good agreements. Computationally, the DTM was found the most time consuming, and the DOM was computationally the most efficient.

Average Air Temperature Inside a Room With a Semitransparent Wall With a Solar Control Film: Effect of The Emissivity

En este artículo se presenta un estudio teórico de la transferencia de calor conjugada (convección natural, conducción y radiación) en flujo turbulento de una habitación cuadrada (cavidad), considerando la variación de la emisividad en la pared opaca. La habitación consiste de una pared vertical isotérmica, dos paredes horizontales adiabáticas y una pared semitransparente con y sin película de control de radiación solar. Las ecuaciones gobernantes para flujo turbulento en 2 dimensiones se resolvieron usando una formulación de volumen finito y el modelo de turbulencia k-. Se presentan los resultados para una pared isotérmica a 21ºC y una temperatura exterior de 35ºC. Las dimensiones de la habitación son 4 m de longitud y altura y la radiación solar que cae directamente sobre la pared semitransparente es de 750W/m2 (AM2). La emisividad de las paredes opacas fue variando entre 0.1 ≤ * ≤ 1.0. Los resultados muestran que, con base en la temperatura ambiente del aire y el flujo de calor efectivo dentro de la habitación, la película de control solar bajo estudio resultó ser desventajosa para propósitos de ahorro de energía, para valores de emisividad de * ≤ 0.46. Se determinó para el sistema una correlación para la transferencia de calor en función de las emisividades.

Numerical prediction of heat transfer by natural convection and radiation in an enclosure filled with an isotropic scattering medium

This paper deals with the numerical solution for natural convection and volumetric radiation in an isotropic scattering medium within a heated square cavity using a hybrid thermal lattice Boltzmann method (HTLBM). The multiple relaxation time lattice Boltzmann method (MRT-LBM) has been coupled to the finite difference method (FDM) to solve momentum and energy equations, while the discrete ordinates method (DOM) has been adopted to solve the radiative transfer equation (RTE) using the S8 quadrature. Based on these approaches, the effects of various influencing parameters such as the Rayleigh number (Ra), the wall emissivity (ει), the Planck number (Pl), and the scattering albedo (ω), have been considered. The results presented in terms of isotherms, streamlines and averaged Nusselt number, show that in absence of radiation, the temperature and the flow fields are centro-symmetrics and the cavity core is thermally stratified. However, radiation causes an overall increase in the temperature and velocity gradients along both thermally active walls. The maximum heat transfer rate is obtained when the surfaces of the enclosure walls are regarded as blackbodies. It is also seen that the scattering medium can generate a multicellular flow.