Treatment Of Radiative Heat Transfer Research Articles

Development of a continuous reheating furnace state-space model based on the finite volume method

This study developed a modeling approach of a continuous steel slab reheating furnace process as a particular case of spatially distributed parameter systems involving radiative heat transfer. The aim of the resulting mathematical model, which is both detailed and computationally tractable, is to serve in prospective advanced process control (APC) and model-based optimization. The two-dimensional state-space model is introduced to accurately simulate the temperature distribution and dynamics, using the finite volume method (FVM) to incorporate essential heat transfer phenomena, including radiation, conduction, convection, advection, and simple combustion. The study presents a novel furnace measurement model that interprets temperature sensor readings (useful for state estimation), a benefit of the FVM treatment of radiative heat transfer. Strategies for linearization and model order reduction, such as balanced truncation, are proposed to facilitate real-time control. The simulation case study demonstrates the targeted capabilities of the model. The accuracy of the model is verified through comparisons with more complex computational fluid dynamics (CFD) software models. The study prioritizes theoretical modeling over empirical validation of a specific furnace unit, omitting experimental validation at this stage.

Improvement of the efficiency of the superposition method applied to the WSGG model to compute radiative transfer in gaseous mixtures

A new method for the treatment of radiative heat transfer in mixtures of participating species in the framework of the weighted-sum-of-gray-gases (WSGG) model is proposed, based on a modification of the existing superposition method. This new approach allows for a reduction in the number of times that the WSGG radiative transfer equation must be solved by decreasing the total number of gray gases that needs to be considered for modeling the mixture. Although it may be extended to mixtures of any number of species, in this paper the new method is only applied to water vapor-carbon dioxide mixtures. The reference for the comparisons is provided by line-by-line (LBL) integration of absorption spectra generated from a high-resolution spectral database. Results show that the method does not yield a loss in accuracy relative to the standard superposition method, and performs better than an existing WSGG model developed for H2O−CO2 mixtures with varying mole fraction ratio. There is also a reduction of about 50% in the computational time required for the solution compared to the original superposition method, thus making the new method more efficient and more competitive in relation to other methodologies for modeling radiative transfer in non-homogeneous mixtures.

Prediction of radiative heat transfer in 3D complex geometries using the unstructured control volume finite element method

In this paper, a 3D algorithm for the treatment of radiative heat transfer in emitting, absorbing, and scattering media is developed. The numerical approach is based on the utilization of the unstructured control volume finite element method (CVFEM) which, to the knowledge of the authors, is applied for the first time to simulate radiative heat transfer in participated media confined in 3D complex geometries. This simulation makes simultaneously the use of the merits of both the finite element method and the control volume method. Unstructured 3D triangular element grids are employed in the spatial discretization and azimuthal discretization strategy is employed in the angular discretization. The general discretization equation is presented and solved by the conditioned conjugate gradient squared method (CCGS). In order to test the efficiency of the developed method, several 3D complex geometries including a hexahedral enclosure, a 3D equilateral triangular enclosure, a 3D L-shaped enclosure and 3D elliptical enclosure are examined. The results are compared with the exact solutions or published references and the accuracy obtained in each case is shown to be highly satisfactory. Moreover, this approach required a less CPU time and iterations compared with those of even parity formulation of the discrete ordinates method.

Three-dimensional radiative transfer modeling using the control volume finite element method

In the present study, a three-dimensional algorithm for the treatment of radiative heat transfer in emitting, absorbing and scattering media is developed. The approach is based on the utilization of control volume finite element method (CVFEM) which, to the knowledge of the authors, is applied at the first time to 3D radiative heat transfer in participating media. The accuracy of the present algorithm is tested by comparing its predictions to other published works. Comparisons show that CVFEM produces good results. Moreover, this approach permits compatibility with other numerical methods used for computational fluids mechanics problems.

Numerical analyses of radiative heat transfer in any arbitrarily-shaped axisymmetric enclosures

A numerical approach for the treatment of radiative heat transfer in any irregularly-shaped axisymmetric enclosure filled with absorbing, emitting and scattering gray media is developed. Radiative transfer equation (RTE) is formulated for a general axisymmetric geometrical configurations, and the discretized equation is conducted using an unstructured meshes, generated by an appropriate computer algorithm, and the control volume finite element method which frequently adopted in CFD problems. A computer procedure has been done to solve the discretized RTE and to examine the accuracy and the computational efficiency of the proposed numerical approach. By using this computer algorithm, five test cases, a cylindrical enclosure with absorbing and emitting medium, a diffuser shaped axisymmetric enclosure, a finite axisymmetric cylindrical enclosure with a curved wall, a furnace with axially varying medium temperature and a rocket nozzle, are treated and the obtained results agree very well with other published works. Furthermore, the developed computer procedure has an accurate CPU time and it can be coupled easily with CFD codes.

Spectral Radiative Heat Transfer Analysis of the Planar SOFC

Thermo-mechanical failure of components in planar-type solid oxide fuel cells (SOFCs) depends strongly on the local temperature gradients at the interfaces of different materials. Therefore, it is of paramount importance to accurately predict the temperature fields within the stack, especially near the interfaces. Because of elevated operating temperatures (of the order of 1000K or even higher), radiation heat transfer could become a dominant mode of heat transfer in the SOFCs. In this study, we extend our recent work on radiative effects in solid oxide fuel cells [J. Power Sources, 124, No. 2, pp. 453–458] by accounting for the spectral dependence of the radiative properties of the electrolyte material. The measurements of spectral radiative properties of the polycrystalline yttria-stabilized zirconia electrolyte we performed indicate that an optically thin approximation can be used for treatment of radiative heat transfer. To this end, the Schuster–Schwartzchild two-flux approximation is used to solve the radiative transfer equation for the spectral radiative heat flux, which is then integrated over the entire spectrum using an N-band approximation to obtain the total heat flux due to thermal radiation. The divergence of the total radiative heat flux is then incorporated as a heat sink into a three-dimensional thermo-fluid model of a SOFC through the user-defined function utility in the commercial FLUENT computational fluid dynamics software. The results of sample calculations are reported and compared against the base line cases when no radiation effects are included and when the spectrally gray approximation is used for treatment of radiative heat transfer.

Control volume finite element method for radiation

In this paper a new methodology is presented by the authors for the numerical treatment of radiative heat transfer in emitting, absorbing and scattering media. This methodology is based on the utilisation of Control Volume Finite Element Method (CVFEM) and the use, for the first time, of matrix formulation of the discretized Radiative Transfer Equation (RTE). The advantages of the proposed methodology is to avoid problems that confronted when previous techniques are used to predict radiative heat transfer, essentially, in complex geometries and when there is scattering and/or non-black boundaries surfaces. Besides, the new formulation of the discretized RTE presented in this paper makes it possible to solve the algebraic system by direct or iterative numerical methods. The theoretical background of CVFEM and matrix formulation is presented in the text. The proposed technique is applied to different test problems, and the results compared favourably against other published works. Moreover this paper discusses in detail the effects of some radiative parameters, such as optical thickness and walls emissivities on the spatial evolution of the radiant heat flux. The numerical simulation of radiative heat transfer for different cases using the algorithm proposed in this work has shown that the developed computer procedure needs an accurate CPU time and is exempt of any numerical oscillations.

Variations of solid–liquid interface in the BGO low thermal gradients Cz growth for diffuse and specular crystal side surface

A global analysis of heat transfer in growing BGO (Bi 4Ge 3O 12) crystals was carried out to explain the significant variation of the solid–liquid interface shape observed in practice during crystal growth. Special attention was given to the accurate treatment of radiative heat transfer in crystal and the gap between crystal and crucible wall. Crystal side surface was assumed to be transparent and diffuse or specular (Fresnel) reflective while melt was opaque. Spectral absorptivity of crystal was approximated by a three-band model. It is shown that rotationally driven vortex dominates under the solid–liquid interface during the whole growth process and no reconstruction of flow pattern, which could lead to interface inversion, takes place. As a result, in the case of diffuse crystal surfaces, the calculated deflection of the crystallization front does not exceed several millimeters and that completely disagrees with the observations. In contrast, for the specular crystal surface the solid–liquid interface turns out to be deeply convex toward the melt at the initial stage of the growth, and then, as the crystal is pulled, its convexity strongly diminishes. Such behavior is in good agreement with the experiment and mainly determined by specular reflection at the conical part of the crystal (its shoulder) while the effect of specular reflectivity of the cylindrical part and melt-free surface is significantly less. It is also shown that radiation transfer in the wavelength band of crystal opacity in conjunction with the specular reflection of radiation in the band of crystal transparency result in the appearance of “convex–concave” isotherms in the upper part of the crystal.

A Study of Flame Structure in the Gas-Solid Two-Phase Systems Containing Inert Particle Suspensions. (3rd Report, Effectsof the Furnace Wall).

This study constitutes a part of the attempt to clarify the effects of radiative heat transfer on the flame structure and burning velocity in a gas-solid two-phase system. Although the one-dimensional model developed in the previous papers was useful to clarify the fundamental aspects of the matter based on a strict treatment of radiative heat transfer, the one-dimensionality is getting worse for a smaller system. A system of a combustible gas mixture with inert particle suspensions flowing through a circular tube is adopted and the effects of the duct wall on the energy transport in the system have been clarified in this paper. The result shows that the radiative heat transfer between walls becomes the leading mechanism of the energy recirculation from burned gas to unburned mixture when the optical thickness in the radial direction is small, and that the main role of the suspended particles shifts to the enhancement of heat transfer between the flowing gas and the duct wall. As a result, the burning velocity of the system shows its maximum at a lower loading ratio of the particles than that of the one-dimensional model.

Thermal conductivity of porous materials: II Theoretical treatment of radiative heat transfer

A theoretical background relating to radiative heat transfer in porous materials, and the effect on thermal conductivity, is presented. Simplified models are considered as well as a more rigorous analysis provided by the Hamaker two-flux model which takes into account both radiation scattering and absorption. Conventional equations derived from Hamaker assume radiation scattering only, and predict that the radiative conductivity increases with thickness to a limiting value—the 'thickness effect'. A modified expression for radiative conductivity, which includes absorption, has been derived from the Hamaker model. This might be expected to apply to insulants where absorption effects are small compared with those of scattering and which are subject to temperature conditions normally found in the built environment. The radiative conductivity still increases with increasing thickness of insulant. However as the amount of absorption is increased the radiative conductivity is reduced and the limiting value occurs at smaller thicknesses.

Study in particle percolation: Computer program

AbstractA description of a computer program giving the path of a percolating smooth spherical particle through a three‐dimensional cluster of stationary spheres, under the influence of a gravitational field is presented.The history of the moving particle starting with an arbitrary velocity and position is followed. The coefficient of restitution for the spheres is an input variable. When the gravitational force approaches zero and the coefficient of restitution is unity, the computer program can also be utilized for the treatment of radiative heat transfer and for Knudsen diffusion in packed beds.