Combined Conductive-radiative Heat Transfer Research Articles

Experimental characterization of Al2O3 foam based on high temperature thermal response experiments

Alumina foam has potential application value in aerospace, solar energy, and other fields. This study proposes a combined radiative-conductive heat transfer model, in which the thermal conductivity and extinction coefficient are temperature-dependent, and the radiation transfer equation is solved by the Monte Carlo method. A self-designed setup is used to measure the high temperature thermal response experiments of alumina foams in 10PPI, 20PPI, and 40PPI. Combined with the genetic algorithm, the thermal conductivity, extinction coefficient, albedo and asymmetry factor of scattering are solved. According to the inversion results, the extinction coefficient of materials with a high pore density is more sensitive to temperature than those with a lower pore density. The thermal conductivity of high pore density materials is greater than that of low pore density materials. The thermal conductivity and extinction coefficient slightly remain basically unchanged as atmospheric pressure increases.

Existence results for a nonlinear coupled radiative–conductive heat transfer system

In this paper, we present existence results for a one-dimensional coupled system of nonlinear integro-differential equations on Lp-spaces with 1≤p<∞. This system describes the steady-state combined radiative–conductive heat transfer. We reformulate the full coupled system as a fixed point problem. This formulation is applied to prove existence results for the radiation intensity and the temperature fields. We treat separately the cases p=1 and p>1. The analysis for p>1 uses the Krasnosel’skii fixed point theorem, while the existence results in the case p=1 are obtained via a new variant of that theorem for the weak topology established in Latrach et al. (2006).

A Unified Lattice Boltzmann Framework for Combined Radiation-Conduction Heat Transfer

A Unified Lattice Boltzmann Framework for Combined Radiation-Conduction Heat Transfer

Inverse estimation of temperature-dependent refractive index profile in conductive-radiative media

The aim of this paper is to retrieve the temperature-dependent refractive index distribution in parallel-plane semi-transparent media with combined conduction-radiation heat transfer, by the measurement of exit intensities over the boundaries. The finite volume method in combination with the discrete ordinates method is used to solve the energy equation. The results of the direct solution for both linear-spatially and linear-temperature-dependent refractive index distributions are compared and the effects of the main parameters are examined. The results confirm a remarkable difference between the results for spatially and temperature-dependent refractive index profiles. Finally, the refractive index profile is estimated using the conjugate gradient method in an inverse manner. The coefficients of the linear profile are estimated for three cases with different levels of measurement errors; 1%, 3% and 5%. The results show that the temperature-dependent refractive index distribution can be retrieved in a good range of errors for noisy data.

Application of the immersed boundary method in solution of radiative heat transfer problems

The immersed boundary method (IBM) was developed for the first time in the present study to simulate the radiative heat transfer problems in complex geometries. The pseudo time stepping technique was applied to solve the radiative transfer equation (RTE) using the finite volume method (FVM). Also, the direct forcing-sharp interface was used in IBM. This method was validated with some benchmark problems in two states of pure radiative and combined radiative-conductive heat transfer. Then, the effects of the conduction-radiation parameter and absorption coefficient on heat flux distribution and isotherms were investigated in an enclosure with inner complex bodies. The results indicated that this method acts well in solving the radiative heat transfer problems in complex geometries. Also, due to using unique Eulerian and Lagrangian grids for solving the energy and radiative transfer equations, production of a separate grid is not required in solving combined heat transfer problems. This is one of the most significant features of the presented method.

Conductive-radiative heat transfer in a 2D semi-transparent medium with a square centered obstacle

The present paper deals with an exact semi-analytical formulation of a combined conductive-radiative heat transfer, applied to a two-dimensional semi-transparent medium carrying a square centered obstacle. The gray participating medium with black boundaries absorbs, emits but does not scatter radiation. One intends to evaluate the temperature and radiative heat flux distributions within the semi-transparent medium. The radiative transfer equation has been solved using an exact analytical expansion of Bickley-Naylor and Altaç angular integrated Bickley-Naylor functions, then solved numerically with Gauss quadrature. Energy equation has been directly discretized and approximated numerically using the centered finite differences method and consequently the dimensionless temperature has been obtained after an iterative scheme. The results of radiative quantities obtained have been verified with benchmark with an excellent agreement, both for simple and complex geometries. Simulations have been performed to obtain results for different sizes of the centered obstacle and the optical thickness. The effects of the conduction-radiation parameters, discrete directions and the size of the obstacle have also been investigated.

Transient numerical simulation of annealing process in a conjugate combined radiation conduction heat transfer

The annealing time is an important affecting factor in the performance of many furnaces. The present work deals with the transient simulation of annealing process in a cubic furnace in which a solid element is placed in its center. As the working gas can have some radiating features, a set of governing equations including the energy balance with the radiative transfer equation (RTE) for the gray radiating medium and the conduction equation inside the solid product are numerically solved with progressing in time. Numerical results which are validated against both analytical and theoretical findings in the literature demonstrate that during the starting period, a high rate of radiant energy transfers into the solid body even at small optical thickness. This behavior which hastens the rate of heat transfer at low values of the radiation conduction parameter, causes a fast annealing process in which the solid body warms up to its maximum temperature. Moreover, it is revealed that the rate of heat transfer is an increasing function of radiation-conduction parameter.

Tomography-based pore level analysis of combined conductive-radiative heat transfer in an open-cell metallic foam

Open-cell metallic foams are increasingly used in various thermal systems. The temperature distributions are significant for the comprehensive understanding of the foam-based engineering applications. This study aims to numerically analyze combined conductive-radiative transfer in a tomography-based open-cell metallic foam. The method used to carry out the simulations consists of a Monte Carlo ray-tracing method based on mesh-agglomeration approach, which avoids the error caused by block-off treatment of porous media surfaces, while greatly minimizing the computation cost for solving the Radiative Transfer Equation. A validation test case has been considered for the distribution of wall heat flux against other benchmark available in the literature. The detailed absorbed radiative flux at local strut surface is analyzed for the real nickel foam, and great difference up to 100% between the front and the back of the strut is found. In addition, the effects of average temperature (i.e. the arithmetic mean temperature of the cold and hot boundary) on the distribution of temperature, the absorbed radiative flux and radiative heat flux are investigated. The results show great fluctuation of absorbed radiative flux and radiative heat flux distribution due to the irregular porous structure. On this basis, the effective thermal conductivity and radiative conductivity of nickel foam at different temperatures are also evaluated. Results show when the temperature increases from 800 K to 1100 K, the radiative conductivity increases from 0.18 W/m•K to 0.46 W/m•K, and the effective thermal conductivity decreases from 4.81 W/m•K to 4.76 W/m•K first and then increases to 4.92 W/m•K, which indicates though the value of radiative conductivity is relatively small, it still influences the variation trend of the effective thermal conductivity with the temperature. The results also show that radiative thermal conductivity and the effective thermal conductivity are strongly dependent upon porosity.

Solar heating of ice sheets containing gas bubbles

The natural light-scattering ice contains usually numerous small gas bubbles. The absorption of solar light in ice sheets is studied on the basis of the complete problem solution including modeling the optical properties of ice, the spectral radiative transfer, and the combined radiative-conductive heat transfer in the ice sheet. The obtained analytical solutions make possible a detailed computational study of the problem. The calculated surface and volumetric absorption of solar radiation are used in numerical analysis of solar heating of ice sheets at various sizes and volume fractions of gas bubbles. The effect of the introduced scattering parameter on radiative transfer and solar heating of ice sheets is analyzed.

A hybrid strategy for solving radiation-conduction in irregular geometries filled with gray semitransparent medium using Monte Carlo method combined with blocked-off and embedded boundary treatments

Monte Carlo method (MCM) and finite volume method (FVM) are integrated to deal with combined conduction-radiation heat transfer problems in irregular geometries containing gray semitransparent media. The MCM is employed to get radiative heat source using blocked-off and embedded boundary treatments via Cartesian system. The FVM is adopted to solve the energy equation via unstructured grid system. The radiative heat source is implemented in the energy equation through geometrical mapping. The hybrid strategy is first validated regarding both pure radiation and conduction-radiation problems. Then, the features of the two boundary treatments are assessed through solving the conduction-radiation heat transfer problems in irregular geometries. The results show that both of them are highly satisfactory for calculating temperature distribution. In comparison with the embedded boundary treatment, the blocked-off treatment leads to obvious errors in predicting wall radiative heat flux for curved boundaries as well as the boundaries adjacent to the inner curved obstacle. Additionally, the hybrid strategy combined with embedded boundary treatment is promising in eliminating the ray effects.

An approximate methodology to simulate combined conduction-radiation heat transfer for multi-layer insulator

A quasi-analytical methodology was developed to model combined conduction-radiation heat transfer through the thickness of a reflective multi-layer insulator. This methodology was validated by the experimental result. It could be used for earlier steps of the design process of the high-temperature multi-layer insulators. Traditionally, radiation thermal conductivity approximation is used in the earlier stages of design. Despite the accuracy of this approach in steady-state cases, it yields to some unacceptable errors when the thermal load is transient. It was shown that old methodology can not predict maximum temperature and time of occurrences in acceptable margins. The developed model originated from the radiation thermal conductivity approximation. But unlike the primitive one, the developed model seems acceptable in transient cases. This model is based on consideration of thermal emittance through the thickness of the insulator. It can predict the maximum temperature of the structure and occurrences time with an error of less than 4%.

Numerical Simulation of a Combined Radiation-Conduction Heat Transfer in An Electric Furnace

Numerical Simulation of a Combined Radiation-Conduction Heat Transfer in An Electric Furnace

Estimation of space-dependent thermophysical properties in participating media by using a Lie-group shooting method

Estimation of space-dependent thermal conductivity and absorption coefficient in a one-dimensional participating medium was investigated in this study. For the forward problem, discrete ordinate method was used to solve the radiative transfer equation. The conduction-radiation energy equation was decoupled by the radiative source term and solved by the finite difference method. Lie-group shooting method (LGSM) was introduced to retrieve the space-dependent thermal conductivity and absorption coefficient from the coupled optical (radiative intensity profile) and thermal (temperature profile) information. LGSM was employed to solve the inverse problem of combined conduction-radiation heat transfer for the first time. This method does not require priori information about the functional form of thermal properties and initial guesses can be selected randomly. Numerical examples of the thermal conductivity and absorption coefficient under different distributions were examined to show that the new approach is highly accurate and efficient, even for identifying highly discontinuous and oscillatory parameters. The estimation was conducted in the presence of the random measurement noise. However, the estimated results still showed high accuracy, robustness and low susceptibility to the shape of property distributions.

A New Hybrid Method for Numerical Simulation of Combined Conductive-Radiative Heat Transfer in Participating Medium

This paper presents a new hybrid method for combined conductive-radiative heat transfer in two-dimensional enclosures. The participating medium is radiatively absorbing, emitting, scattering and gray. The radiative transport equation is solved by the discrete ordinate method, while the energy equation is solved by the dual reciprocity boundary element method. The various influencing factors i.e., radiation-conduction parameter, surface emissivity and single scattering albedo are investigated to demonstrate the feasibility and efficiency of the present method.

An Iterative Method for Solving of Coupled Equations for Conductive-Radiative Heat Transfer in Dielectric Layers

The mathematical model for describing combined conductive-radiative heat transfer in a dielectric layer, which emits, absorbs, and scatters IR radiation both in its volume and on the boundary, has been considered. A nonlinear stationary boundary-value problem for coupled heat and radiation transfer equations for the layer, which exchanges by energy with external medium by convection and radiation, has been formulated. In the case of optically thick layer, when its thickness is much more of photon-free path, the problem becomes a singularly perturbed one. In the inverse case of optically thin layer, the problem is regularly perturbed, and it becomes a regular (unperturbed) one, when the layer’s thickness is of order of several photon-free paths. An iterative method for solving of the unperturbed problem has been developed and its convergence has been tested numerically. With the use of the method, the temperature field and radiation fluxes have been studied. The model and method can be used for development of noncontact methods for temperature testing in dielectrics and for nondestructive determination of its radiation properties on the base of the data obtained by remote measuring of IR radiation emitted by the layer.

Calculation of combined conduction-radiation heat transfer reduction using thick concentric spheres with temperature-dependent emissivity as radiation shields

In this study, the rate of conduction-radiation heat transfer between two thick concentric spheres is analytically investigated because of the ever-increasing importance of radiation shield applications. The heat transfer rate, the percentage of reduction in heat transfer, temperature and emissivity of surfaces are calculated when one and two thick radiation shields are placed between two thick spheres. The calculations show that the use of a radiation shield with a lower emissivity is better than two radiation shields with a higher emissivity to reduce the heat transfer rate. In addition, optimal combinations of radiation shields with different materials are proposed.

Transient Combined Radiative–Conductive Heat Transfer in Two-Dimensional Complex Geometries with Variable Gas Properties

Radiation is a major component of heat transfer in the modeling of furnaces. In the present work, transient coupled radiative and conductive heat transfer problems are analyzed in two-dimensional irregular geometries with a simple Cartesian practical method named the blocked-off. By this technique, Cartesian coordinate-based ray-tracing algorithm can be applied to the geometries with inclined or curved boundaries. The S–N discrete ordinates method used to solve the radiative transfer equation and finite difference method by applying the Taylor series for solving the energy equation to obtain the transient temperature distributions inside the participating medium. The walls of the enclosures are opaque, diffuse, and gray with specified temperatures. The medium was considered to be absorbing-emitting and linear anisotropic scattering with variable thermal conductivity, variable density, and variable specific heat, as a function of temperature. In the case of constant thermophysical gas properties, results have been compared with those reported in the literature, and good agreement was found.

Modelling of conduction–radiation in a porous medium with blocked-off region approach

A new methodology to solve a heat transfer problem in a complex porous structure has been proposed in this work. The 3D numerical model considers combined conductive–radiative heat transfer with the finite volume method integrated with a blocked-off region approach. The model is capable of considering grey, diffuse behaviour of the surfaces of the solid. The work demonstrates the simplicity of this approach for solving problems with porous structure by eliminating the complexity of grid generation generally needed for any conventional methods. The representative porous structures considered for this analysis are cubic cell and honeycomb structures. The effective thermal conductivity is determined for different temperature, emissivity and thermal conductivity of the solid and absorption coefficient of the fluid. Various problems are also solved in order to validate the formulation and the subsequent implementation with the results from FLUENT 6.3 as well as literature. A good agreement of the results has been observed and reported in the paper.

Numerical Simulation of Heat Transfer in Firefighters' Protective Clothing with Multiple Air Gaps during Flash Fire Exposure

A finite volume model was developed to simulate transient heat transfer in firefighters' protective clothing during flash fire exposure. The model domain consists of three layers of fire-resistant fabrics (outer shell, moisture barrier, and thermal liner) with two air gaps between the clothing layers, the human skin, and the air gap between the clothing and the skin. The model accounts for the combined conduction-radiation heat transfer in the air gaps entrapped between the clothing layers, and between the clothing and the skin. The variation in the air gap properties and energy content during both the exposure and the cool down periods was accounted for. Predictions were obtained for the temperature and heat flux distributions in the fabric layers, skin, and air gaps as a function of time. The influence of each air gap on the clothing performance was investigated as well. This article demonstrates the importance of accurately modeling the contributions of the air gaps in order to predict the protective clothing performance.

Influence of the air gap between protective clothing and skin on clothing performance during flash fire exposure

A finite volume model was developed to simulate transient heat transfer in protective clothing during flash fire exposure. The model accounts for the combined conduction-radiation heat transfer in the air gap between the fabric and skin. The variation in the fabric and air gap properties with temperature and the thermochemical reactions in the fabric are also considered. This study investigates the influence of the air gap in protective clothing on the energy transfer through the clothing and hence on its performance. Different parameters that affect the conduction-radiation heat transfer through the air gap such as the air gap absorption coefficient and the air gap width were studied. Finally, the paper demonstrates that an innovative and potentially significant way to improve protective clothing performance is to reduce the emissivity on the backside of the fabric.