Coupled Conduction Radiation Heat Transfer Research Articles

Fuzzy Levenberg-Marquardt damping factor update strategy and Tikhonov regularization applied to a coupled conduction-radiation inverse heat transfer problem

The recently proposed Fuzzy Levenberg-Marquardt Damping Factor Updating Strategy (FLM) is used along with Tikhonov Regularization (TR) in order to solve a coupled conduction-radiation function estimation inverse problem. FLM consists of updating the Levenberg-Marquardt (LM) damping factor with the assist of Fuzzy Logic. To test the FLM algorithm combined with TR, a conduction-radiation problem is addressed, and it serves as test bed to the numerical experiments, where the objective is to obtain estimatives of parameters, such as the spatially variable scattering albedo, the thermal conductivity and the optical thickness, simultaneously, which is often performed separately. Two main test cases are presented, one considering only the radiation problem, used as benchmark, in order to investigate noise levels and hyperparameters. The second main test case deals with the coupled conduction-radiation heat transfer problem for different functional forms of the spatially variable scattering albedo. For all presented numerical experiments, good estimates were achieved for the sought functions and parameters. These results demonstrate that the methodology presented in this work, through the combination of the Fuzzy LM dampting factor updating strategy and the Tikhonov regularization scheme, may provide valuable tools for inverse heat transfer problems.

A Gaussian process regression accelerated multiscale model for conduction-radiation heat transfer in periodic composite materials with temperature-dependent thermal properties

Prediction of the coupled conduction-radiation heat transfer in composite materials with periodic structure is important in high-temperature applications of the materials. The temperature dependence of thermal properties complicates the problem. In this work, a multiscale model is proposed for the conduction-radiation heat transfer in periodic composite materials with temperature-dependent thermal properties. Homogenization analysis of the coupled conduction and radiative transfer equations is conducted, in which the temperature dependence of thermal properties is considered. Both the macroscopic homogenized equations and the local unit cell problems are derived. It is proved that the macroscopic average temperature can be used in the unit cell problems for the first-order corrections of the temperature and radiative intensity, and the calculations of effective thermal properties. The temperature dependence of thermal properties only influences the higher-order corrections. A multiscale numerical method is proposed based on the analysis. The Gaussian process (GP) regression is coupled into the multiscale algorithm to build a correlation between thermal properties and temperature for the macroscale iterations and prevent the repetitive solving of unit cell problems. The GP model is updated by additional solutions of unit cell problems during the iteration according to a variance threshold. Numerical simulations of conduction-radiation heat transfer in composite with isotropic and anisotropic periodic structures are used to validate the proposed multiscale model. It is found that the accuracy and efficiency of the multiscale method can be guaranteed by using a proper variance threshold for the GP model. The multiscale model can provide both the average temperature and radiative intensity fields and their detailed fluctuations due to the local structures.

Effect of ambient temperature, metabolic heat and clothing insulation on the required external active heating for the survival of humans exposed to sub-zero temperatures

Active heating in extremely cold weather clothing would be useful to save the life of an injured or sick person due to low metabolic rate. A fully dressed thermal manikin is useful in evaluating the performance of the active heating ensemble. The thermal manikin tests are time-consuming and could be done only after making the complete ensemble. An experiment that is designed to evaluate the performance of an active heating fabric fixed to a set of layers of extreme cold climate clothing using a guarded hot plate instrument would save a lot of time as it skips the processes of garmenting and subsequent evaluation on the thermal manikin. In this work, a guarded hot plate placed inside a cold chamber is used to investigate the external heating required for the prolonged comfort of the wearer at various sub-zero ambient temperatures, clothing insulation and metabolic heat. A plain woven active heating fabric sandwiched between a knitted fabric and nonwoven of different insulation/thickness is used to perform experiments. The external heat required to keep the test plate (representing the human skin) at 307 ± 1 K (34 ± 1 °C) is measured at different experimental conditions. Further, a one-dimensional numerical model based on coupled conduction–radiation heat transfer with heat generation was developed and validated with experimental results. The experimental temperature profiles match well with the numerical temperature profiles at different locations, justifying the numerical methodology adopted in this work. This suggests that the developed numerical model would also be useful to estimate the required active heating as per the wearer’s requirement and an available power source. Both the experimental and numerical results suggest that the external active heating required to maintain test plate (skin) temperatures within the human skin comfortable range is a function of ambient temperature, metabolic heat and clothing (nonwoven) insulation.

Study on dynamic thermal behavior of the steel pipes in walking beam quenching furnace

In the production process of steel pipe, the quenching is of significance to improve the quality of steel pipe. Therefore, the dynamic thermal behavior of the steel pipe in quenching furnace is studied in this work. The coupled conduction-radiation heat transfer model of steel pipe in walking beam quenching furnace is established. The thermal contact resistance, radiative heat transfer between the steel pipe and the tooth groove, the rotation process and the heating process of steel pipe are considered in this model. The effects of the rotation conditions, tooth groove temperature and size of the steel pipe on thermal behavior of steel pipe are investigated thoroughly. It can be found that keeping the rotation direction of the steel pipe unchanged can reduce the section temperature difference of steel pipe; When the loading of steel pipes is stopped for a period of time, the section temperature difference of the first steel pipe entering the furnace is very large; The large-size steel pipe usually has a large section temperature difference in the initial heating process, which means a lower temperature of tooth grooves in contact with the steel pipe during the initial heating process is required. This work can provide valuable reference for the improvement of quenching quality of steel pipe and on-line supervisory control of the production process.

Kernel-Independent Fast Multipole Boundary Element Solver for Coupled Conduction–Radiation Heat Transfer Problem

The purpose of this paper is to present a kernel-independent fast multipole accelerated boundary element method for the simulation of a system of coupled conduction–radiation heat transfer in three-dimensional participating media. Radiative transfer integral equations are considered as radiation heat transfer model in participating media. For the nonlinear energy equation, Newton–Generalized Minimal Residual (GMRES) iterative scheme is adopted. The loose coupling iterative technique is applied to this strongly coupled system. Then, the separate solutions are both obtained by the kernel-independent fast multipole boundary element method based on the collocation scheme. Numerical examples show that the present fast algorithm is effective and efficient.

A Multiscale Method for Coupled Steady-State Heat Conduction and Radiative Transfer Equations in Composite Materials

Abstract Predictions of coupled conduction-radiation heat transfer processes in periodic composite materials are important for applications of the materials in high-temperature environments. The homogenization method is widely used for the heat conduction equation, but the coupled radiative transfer equation is seldom studied. In this work, the homogenization method is extended to the coupled conduction-radiation heat transfer in composite materials with periodic microscopic structures, in which both the heat conduction equation and the radiative transfer equation are analyzed. Homogenized equations are obtained for the macroscopic heat transfer. Unit cell problems are also derived, which provide the effective coefficients for the homogenized equations and the local temperature and radiation corrections. A second-order asymptotic expansion of the temperature field and a first-order asymptotic expansion of the radiative intensity field are established. A multiscale numerical algorithm is proposed to simulate the coupled conduction-radiation heat transfer in composite materials. According to the numerical examples in this work, compared with the fully resolved simulations, the relative errors of the multiscale model are less than 13% for the temperature and less than 8% for the radiation. The computational time can be reduced from more than 300 h to less than 30 min. Therefore, the proposed multiscale method maintains the accuracy of the simulation and significantly improves the computational efficiency. It can provide both the average temperature and radiation fields for engineering applications and the local information in microstructures of composite materials.

Development of hybrid method for coupled conduction-radiation heat transfer in two-dimensional irregular enclosure considering thermo-radiative effects and varying thermal conductivity

PurposeThis study aims to perform a comprehensive investigation to model the thermal characteristics of a coupled conduction-radiation heat transfer in a two-dimensional irregular enclosure including a triangular-shaped heat source.Design/methodology/approachFor this purpose, a promising hybrid technique based on the concepts of blocked-off method, FVM and DOM is developed. The enclosure consists of several horizontal, vertical and oblique walls, and thermal conductivity within the enclosure varies directly with temperature and indirectly with position. To simplify the complex geometry, a promising mathematical model is introduced using blocked-off method. Emitting, absorbing and non-isotropic scattering gray are assumed as the main radiative characteristics of the steady medium.FindingsDOM and FVM are, respectively, applied for solving radiative transfer equation (RTE) and the energy equation, which includes conduction, radiation and heat source terms. The temperature and heat flux distributions are calculated inside the enclosure. For validation, results are compared with previous data reported in the literature under the same conditions. Results and comparisons show that this approach is highly efficient and reliable for complex geometries with coupled conduction-radiation heat transfer. Finally, the effects of thermo-radiative parameters including surface emissivity, extinction coefficient, scattering albedo, asymmetry factor and conduction-radiation parameter on temperature and heat flux distributions are studied.Originality/valueIn this paper, a hybrid numerical method is used to analyze coupled conduction-radiation heat transfer in an irregular geometry. Varying thermal conductivity is included in this analysis. By applying the method, results obtained for temperature and heat flux distributions are presented and also validated by the data provided by several previous papers.

Thermal radiation and conduction in functionally graded thermal barrier coatings. Part I: Experimental study on radiative properties

Functionally graded thermal barrier coatings (FGTBCs) are functional composites with multilayered structures whose mechanical properties are better than those of conventional ceramic thermal barrier coatings (TBCs). Although many theoretical and experimental studies concerning both the mechanical properties and heat transfer including heat conduction and thermal radiation of TBCs have been conducted, little attention was paid to heat transfer process, especially the coupled conduction-radiation heat transfer, inside FGTBCs. This two-part paper systematically studied the heat transfer inside YSZ/NiCoCrAlY FGTBCs. In Part I, we investigated their radiative properties through experimental measurements. In Part II, we presented a study on the thermal conductivity of FGTBCs and established a coupled heat transfer model. In this paper, more than thirty yttria-stabilized zirconia (YSZ)/NiCoCrAlY duplex TBC and multilayered FGTBC samples with different multilayer structures, porosities and thicknesses were fabricated via air plasma spraying. The transmittance and reflectance spectra within the 0.3–15μm wavelength range were experimentally obtained by UV–visible spectrometry and Fourier transform infrared spectroscopy. A scanning electron microscope analysis was carried out to characterize the microstructures of FGTBCs. Additionally, we studied each layer of the FGTBCs individually; the four-flux method was employed to obtain the radiative properties based on our experimental measurements. Functionally graded materials (FGM) show larger absorption coefficients and smaller scattering coefficients compared to pure YSZ. The FGTBCs show lower reflectance than YSZ TBCs. We also study the influence of the number of layers on reflectance. The results indicate that FGTBCs have worse thermal insulation ability against radiative flux tconventional ceramic TBCs of the same thickness. This paper provides practical guidance to improve the design of YSZ/NiCoCrAlY FGTBCs and other FGM coatings to reach a balance between good thermal insulation and mechanical strength.

Investigation of heat transfer in one-dimensional models of polymeric foams by using a ray-splitting and tracing technique

Purpose This paper aims to develop a numerical model to investigate coupled conduction radiation heat transfer in a multilayer semi-transparent polymeric foam. Design/methodology/approach The model uses a multi-phase approach in which the radiative transfer is determined by solving the radiative transfer equation explicitly in the whole medium incorporating an interface condition valid in the geometric optics rgime. This is executed by using a combination of ray splitting and a discrete curved ray tracing technique. Both partial photon reflection and total internal reflection at the interface are considered in the present investigation. Findings The directional distribution of intensity within the whole medium can be determined, which is used to obtain the detailed temperature profile inside the domain. The performance of the proposed methodology has been tested by simulating the modelled foam at ambient conditions. The results obtained from the simulations are in good agreement with the published results and shows that there is a global non-linearity in the temperature profile in problems where conduction to radiation parameter is small. Originality/value Specular nature of radiative transfer at the interface is accounted for in the present analysis. Instead of working with direction integrated quantities (as in the case of P1 approximation), each bundle of rays is treated separately within the whole medium. This model serves as a starting point for a detailed spatially three dimensional study of heat transfer in foams and the mathematical nature of the formulation is such that it may result in an implementation to three-dimensions.

Modeling the Effect of Infrared Opacifiers on Coupled Conduction-Radiation Heat Transfer in Expanded Polystyrene

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.

Boundary Element Solver for Coupled Conduction-Radiation Heat Transfer in Nonhomogeneous Media

In the present Paper, a boundary element solver is developed for the simulation of coupled conduction-radiation heat transfer in three-dimensional nonhomogeneous participating media. First, the boundary integral equations for radiation heat transfer in nonhomogeneous participating media are formulated. By using a simple variable transformation and with the aid of the Newton iterative scheme, the boundary integral equation for the nonlinear energy equation is obtained. For this strongly coupled system, a two-level iterative scheme is developed. Then, the boundary element method is adopted to discretize the resulting coupled system of integral equations. For the nonconvex geometries, a developed element-subdivision technique is adopted to handle with the visibility factor appearing in the radiative integral equations. Numerical examples show that the present algorithm is effective and efficient.

Simultaneous estimation of thermal conductivity and specific heat of thermal protective fabrics using experimental data of high heat flux exposure

In the present study, ant colony optimization algorithm is used for an inverse heat transfer problem of parameter estimation. Temperature dependent thermal conductivity and specific heat are estimated simultaneously. Performance of the present algorithm is first analyzed by using the temperature data obtained from the solution of direct problem. Effect of measurement error on the property estimation is then analyzed. Accuracy of estimated properties is found to be good in both the cases. Experiments are then conducted on a cotton duck fabric exposed to 40kW/m2 radiant heat flux using a bench top test according to ISO 6942. Temporal variation of sensor temperature is used to estimate the thermal conductivity and specific heat of the fabric sample. The estimated values are in agreement with the results available in the literature. Property values estimated in the study are included in a coupled conduction-radiation heat transfer model for fabrics. Performance of the fabric sample is further analyzed with the numerical model for high heat fluxes. The simulation results compare quite well with experimental data at 80kW/m2 radiant heat and 70kW/m2 flame exposures. Flame exposure experiment is conducted according to ISO 9151. Good agreement between the numerical and experimental results are found for both the exposures.

Measurement and simplified numerical prediction of effective thermal conductivity of open-cell ceramic foams at high temperature

In the present article, the effective thermal conductivity (ETC) of 10ppi open-cell ceramic foams is measured at temperatures ranging from 22°C to 750°C using the transient plane source (TPS) technique. The detailed morphology of the foam structures is reconstructed from 3D CT-scan images and their structural analysis is carried out using a volume image processing tool. The experimental results are compared with the predictions of directional ETC, obtained using a simplified 1D homogeneous model that considers coupled conduction–radiation heat transfer. The parameters, required by the model, are evaluated based only upon the information that could be extracted from 3D CT-scan images under certain simplifying assumptions. It can be concluded that the predictions of ETC for the present ceramic foam samples clearly correlate with the geometric parameters obtained from their structural analysis. It is also observed that the estimated microscopic porosity of the foam, which is not captured by 3D CT-scan images, has considerable influence on the reconstructed foam structure and hence on the predicted ETC. The predictions of ETC in the measured direction, obtained after the proposed directional averaging, compare extremely well with TPS measurements for the complete range of investigated temperatures. This suggests that the measurements of ETC, obtained employing TPS technique, are the directionally averaged representations of ETC in three perpendicular directions. The present investigation also clearly demonstrates the potential of the simplified modeling approach for characterizing even the directional ETC of open-cell ceramic foams, based primarily on their structural information.

An Iterative Technique for Coupled Conduction–Radiation Heat Transfer in Semitransparent Media

An iterative technique is developed to solve coupled conduction–radiation heat transfer in semitransparent media. Apart from a high convergence rate, the present algorithm preserves the conservation nature of the governing equation far better than other common methods and it is readily combined with other methods in solving radiative transfer. Using the technique described in this study, parametric studies are carried out for coupled heat transfer in a semitransparent slab and the results illustrate the “peak” effects of wall emissivity and scattering albedo on conductive and radiative heat fluxes, which are rarely mentioned in the existing research.

Multiphase approach to coupled conduction–radiation heat transfer in reconstructed polymeric foams

Heat insulating properties of polymeric foams at ambient temperature were investigated using the model of coupled heat transfer by conduction and radiation through computer-reconstructed domains. The proposed model considers absorbing and emitting gas and solid phases and partial photon reflection on phase interfaces. The P1-approximation is used for the description of radiation. For optically thin polymeric walls, the interface conditions are adjusted to account for specular reflection and wave interference effects. The developed model was validated using experimental data and compared with other approaches, including state-of-the-art homogeneous phase approach (HPA). Contrary to HPA, our approach doesn't treat polymeric foams as homogeneous materials with effective properties and provides temperature and radiation gradient fields, which respect foam morphology. The model predicts that the radiative heat flux can account for more than one third of the total heat flux in high porosity expanded polystyrene (EPS) or polyethylene (PE) foams and that the equivalent conductivity of polymeric foam can be significantly reduced by the careful balancing of porosity, cell size, wall thickness and strut content. The presented model doesn't use any empirical correlations and can be used for the optimization of heat transfer in any type of polymeric foam.

Heat Transfer Characteristics of an Innovative Thermal Protection System Based on Photonic Crystals

In order to protect the internal components of an aircraft from the damage caused by high temperature and heat flux, an effective thermal protection structure must be designed and developed. In this paper, heat transfer characteristics for an innovative thermal protection coating structure are investigated, based on three-dimensional photonic crystals (SiC-3D PCs). The actual system with coating material, containing photonic crystals, is simplified as a macroscopic model of one-dimensional coupled conduction–radiation heat transfer among three layers composed of semitransparent media. Moreover, according to preliminary physical parameters, heat transfer profiles and thermal protection efficiency for the whole system are estimated. In addition, the effect of the photonic crystals part is analyzed.

Detailed and simplified models for evaluation of effective thermal conductivity of open-cell porous foams at high temperatures in presence of thermal radiation

Simulations of coupled conduction–radiation heat transfer through open-cell porous foams have been performed in this article in order to evaluate the effective thermal conductivity (ETC) at high temperatures due to combined effects. For this purpose, the complex structure of foams has been generated using the knowledge obtained from 3D Computer Tomography (CT)-scan images and both detailed and simplified homogeneous modes have been employed during the present investigation. For detailed models, in addition to the energy conservation equation, the radiative transfer equation has been solved in order to obtain the distribution of radiation intensity using the blocked-off region approach, which can handle the voxel information acquired from the CT-scan data. Proposed simplified models, on the other hand, are based on homogenization approach and the performance of these simplified models has been compared with the reference model in terms of their accuracy. Simplified models mainly require information about the ETC due to pure conduction calculated from detailed 3D simulation and the extinction coefficient estimated from the CT-scan data using the image processing technique. Extensive parametric study has been conducted and the analysis of results show that ETCs estimated from the simplified models reasonably agree with those obtained from the most accurate model, depending upon the chosen value of extinction coefficient.

Second law analysis of coupled conduction–radiation heat transfer with phase change

This work considers an exergy-based analysis of two-dimensional solid-liquid phase change processes in a square cavity enclosure. The phase change material (PCM) concerns a semi-transparent absorbing, emitting and anisotropically scattering medium with constant thermodynamic properties. The enthalpy-based energy equation is solved numerically using computational fluid dynamics. Once the energy equation is solved, local exergy loss due to heat conduction and radiative heat transfer during the phase change process is calculated by post processing procedures. In this work, the radiation exergy loss in the medium and at the enclosure boundary is taken into consideration. It is found that radiation exergy loss is significant in the high-temperature phase change process. Parametric investigation is also carried out to study the effects of Stefan number, Biot number, Planck number, single scattering albedo and wall emissivity on exergy loss. The results show that the total exergy loss increases with Biot number, single scattering albedo and wall emissivity. The second law effects of the conduction–radiation coupling in the energy equation are also shown in this work.

Optimal porosity distribution of fibrous insulation

The porosity of fibrous materials is an important factor to their insulating performance. This paper considers the optimal porosity distribution of non-uniform fibrous porous medias for thermal insulation. Heat flow through the fibrous porous media is described by a coupled conduction–radiation heat transfer model which is numerically solved by using Finite Volume Method, and the optimal porosity distribution corresponding to the minimum total heat transfer is derived by applying a BFGS quasi-Newton optimization procedure. Variable analysis shows that the optimal porosity distribution is typically piecewise in conductive heat transfer dominated porous medium. For practical reasons, the change of porosity distribution across the thickness of the fibrous porous media may need to be continuous. To derive such a continuous optimal porosity distribution, a small penalty item should be introduced into the objective function. The study shows that, a continuous optimal porosity distribution generally has relatively high porosity at both boundaries and relatively low porosity in the centre region. The optimal distribution depends on many factors such as fibre radius, fibre emissivity, temperature difference, and overall mean porosity.

Coupled conduction–radiation in semi-transparent materials at high temperatures

In this paper, we solve numerically the coupled conduction–radiation heat transfer problem in semi-transparent orthotropic materials. Both the conduction and the radiation problems are solved with finite-volumes. The numerical solution obtained here is validated with results available in the literature. Results are presented for test cases involving the non-uniform heating of bodies at high-temperatures.