Thermal Radiation Problems Research Articles

Verification of numerical solutions of thermal radiation problems in participating and nonparticipating media

This article presents an application of the post-processing technique called Repeated Richardson Extrapolation in participating and nonparticipating media problems of radiative heat transfer. It allows us to achieve very accurate results, reducing the estimates of the discretization error of global variables with negligible additional computational time. The error estimates show to be accurate and reliable for code and solution verification. This work also presents equations that quantify the spatial discretization error inside the domain when the Discrete Ordinates Method is used to simulate participating media problems and when basic numerical integration rules are used to solve nonparticipating media problems.

Inverse Methods in Thermal Radiation Analysis and Experiment

Abstract Most thermal radiation problems are analyzed in a “forward” manner, in which the aim is to predict the response of a system based on well-defined boundary conditions. In practice, however, many thermal radiation problems are inverse problems. For example, the goal of many furnace design problems is to find a configuration that realizes a particular irradiation profile on a target, while in measurement problems, transmitted or reflected radiation measured with sensors at a boundary may be used to infer the properties of matter within the boundary. Such inverse problems are often mathematically ill-posed because they may have multiple solutions or no solution at all. Consequently, analyzing these types of problems is more complex than is required for forward problems. In this review, we examine the various types and characteristics of inverse problems, outline standard inverse solution methods for them, and review the historical and contemporary literature.

True temperature inversion for a multi-spectral pyrometer based on the inner penalty function constrained optimization algorithm

A data processing algorithm based on the inner penalty function for constrained optimization is presented for a multi-wavelength pyrometer. It can directly obtain the true temperature and spectral emissivity simultaneously without requiring for the spectral emissivity model beforehand. The simulation results show that the algorithm is suitable for continuous thermal radiation materials, and the absolute error is less than 15 K when the true temperature is 1800 K. The experimental results also verify the reliability of the algorithm. This data processing algorithm resolves the true temperature measurement by thermal radiation problem which was due to the unknown emissivity model.

Thermal radiation elimination method for high-temperature digital image correlation using polarization camera

Digital image correlation (DIC) is a material displacement and strain measurement technology based on visible light illumination. At high temperatures, the problem of thermal radiation seriously affects the quality of acquired images and restricts the development of high-temperature DIC technology which is increasingly applied in the field of high-temperature measurement due to stringent measurement temperature requirements. A thermal radiation elimination method based on the use of a polarization camera for high-temperature DIC measurements is proposed in this study. This method uses a polarization camera combined with a filter set to achieve clear image acquisition at 1200 °C and effectively eliminates the effects of thermal radiation on image acquisition. The gray average method and an image inverse filtering algorithm are adopted in this study to eliminate high-temperature thermal disturbances. Finally, a high-temperature DIC measurement system is independently designed, and a rigid-body displacement experiment is carried out on an FV566 steel specimen to obtain time–displacement curves. A set of uniaxial tensile tests is also performed on FV566 steel material to explore its strain field at 1200 °C.

Coupled radiative and convective heat transfer in enclosures: Effect of inner heater–enclosure wall emissivity contrast

The problem of thermal radiation in the presence of nonuniform emissivity arising through different types surfaces involved in thermal-control systems is addressed. In particular, its effect on natural convection driven by an inner hot plate kept inside a square enclosure is studied. The enclosure considered is either horizontally or vertically cooled, and two different primary orientations of the inner hot plate are considered. The corresponding governing partial differential equations were solved by the finite volume method on a uniform and regular grid system. While doing so, the net radiation method was used to determine the radiative surface fluxes. The effect of two opposing emissivity contrasts between the inner hot plate and enclosure walls is studied for the Rayleigh numbers Ra ≤ 107. The flow and heat transfer mechanisms at the resulting steady state are discussed via isotherms, streamlines, and average Nusselt number Nu¯. The findings arrived out of this comprehensive study shows that prominent heat transfer enhancement occurs when the emissivity of the inner hot plate is higher. Significant changes introduced by the emissivity contrast in the velocity and temperature fields can be seen for higher Rayleigh numbers. Moreover, better heat removal through the combined radiation and convection mechanism is observed invariably for the vertical hot plate in the presence of emissivity contrast. It is found that the heat transfer can be augmented up to around 35% through a good knowledge of the emissivity contrast.

Temperature Distribution in Porous Fins, Subjected to Convection and Radiation, Obtained from the Minimization of a Convex Functional

This work proposes a convex functional endowed with a minimum, which occurs for the solution of the thermal radiation and natural convection heat transfer problem in a rectangular profile porous fin with a fluid flowing through it. The minimum principle ensures the (mathematically demonstrated) uniqueness of the solution and allows the problem simulation by employing a minimization procedure. Darcy’s law with the Oberbeck–Boussinesq approximation simplifies the momentum equation. The energy equation assumes thermal equilibrium between the porous matrix and fluid, allowing comparisons with previous authors’ models, which accounts for the effects of a porosity parameter, a radiation parameter, and a temperature ratio on the temperature. Results for very long fin and finite-length fin with insulated tip were successfully compared with previous works. Closed-form exact solutions for two limiting cases (no convection and no thermal radiation) are also presented.

Thermal radiation calculation of complex surface based on Triangulation and Gauss Integral Method

To solve the problem of thermal radiation in complex geometric scenes, a finite element method based on Delaunay triangulation and three-point Gauss integral is proposed. The calculated value is compared with model existing theoretical solution of view factor, and the results show that the errors are within 3%. The method is applied to calculate the thermal radiation of combustion between adjacent liquefied petroleum gas tanks. The geometric model of conical flame and adjacent spherical tanks is also established. The result shows the maximum heat flux received by adjacent spherical tanks is 11.3 kW/m2 when the flame temperature is 1470 K without wind.

Slip Flow of Nanofluid Over A Stretching Vertical Cylinder in the Presence of Non-Linear Thermal Radiation and Non-Uniform Heat Source/Sink

An analysis is performed to study axisymmetric mixed convective boundary layer flow of a nanofluid over a vertical stretching circular cylinder in the presence of non-linear radiative heat flux. The effects of non-uniform heat source/sink and slip flow are also taken into consideration. Water as conventional base fluid containing nanoparticles of Copper (Cu) is used. By means of similarity transformations, the governing partial differential equations are reduced into highly non-linear ordinary differential equations and then solved analytically using Homotopy Analysis Method (HAM). A comparison is made with the available results in the literature and our results are in very good agreement with the known results. A parametric study of the physical parameters is made and results are presented through graphs and tables. The results indicate that, the thermal boundary layer is thicker for non-linear thermal radiation problem when compared with that of linear thermal radiation. It also found that heat transfer rate at the surface decreases with the increase in both space and time dependent heat source/sink parameters.

Transformational fluctuation electrodynamics: application to thermal radiation illusion.

Thermal radiation is a universal property for all objects with temperatures above 0K. Every object with a specific shape and emissivity has its own thermal radiation signature; such signature allows the object to be detected and recognized which can be an undesirable situation. In this paper, we apply transformation optics theory to a thermal radiation problem to develop an electromagnetic illusion by controlling the thermal radiation signature of a given object. Starting from the fluctuation dissipation theorem where thermally fluctuating sources are related to the radiative losses, we demonstrate that it is possible for objects residing in two spaces, virtual and physical, to have the same thermal radiation signature if the complex permittivities and permeabilities satisfy the standard space transformations. We emphasize the invariance of the fluctuation electrodynamics physics under transformation, and show how this result allows the mimicking in thermal radiation. We illustrate the concept using the illusion paradigm in the two-dimensional space and a numerical calculation validates all predictions. Finally, we discuss limitations and extensions of the proposed technique.

Chebyshev collocation spectral method to solve radiative transfer equation in one-dimensional cylindrical medium

A Chebyshev collocation spectral method (CCSM) is developed to solve the radiative transfer equation (RTE) in an infinitely long, cylindrically symmetric, homogeneous medium. Both the spatial and angular computational domains of the RTE are discretized by the Chebyshev collocation points. For the CCSM, taking the conservation form of RTE, which is commonly used in the discrete ordinates method (DOM), will produce poor accuracy, whereas taking the non-conservation form can yield good prediction. To test the applicability of different collocation point schemes in the radial direction, three solvers are developed. SOLVER1 and SOLVER2 use the Chebyshev-Gauss-Radau (CGR) points and the Chebyshev-Gauss-Lobatto (CGL) points on the radius, respectively. SOLVER 3 uses the CGL points on the diameter, and an even number of nodes is taken to exclude the origin. The results show that SOLVER1 and SOLVER2 suffer from the “singularity effect”. This effect can be reduced by increasing the grid number in radial direction. Whereas SOLVER3 can avoid the “singularity effect”. We also show that the mapping (the Kosloff–Tal-Ezer transformation) actually cannot improve the accuracy. Besides, the numerical accuracy is declined by using cosine of the polar angle instead of the polar angle itself as the independent variable. Our results demonstrate that the CCSM performs much better than the DOM and produces the exponential convergence in both the spatial and angular domains. The CCSM is a superior method to achieve high accuracy for thermal radiation problem of homogeneous medium with cylindrical symmetry.

Thermal conductivity prediction of magnetic composite sheet for near-field electromagnetic absorption

The magnetic composite sheets were designed by using core-shell structured magnetic fillers instead of uncoated magnetic fillers to resolve concurrently the electromagnetic interference and thermal radiation problems. To predict the thermal conductivity of composite sheet, we calculated the thermal conductivity of the uncoated magnetic fillers and core-shell structured fillers. And then, the thermal conductivity of the magnetic composites sheet filled with core-shell structured magnetic fillers was calculated and compared with that of the uncoated magnetic fillers filled in composite sheet. The magnetic core and shell material are employed the typical Fe-Al-Si flake (60 μm × 60 μm × 1 μm) and 250 nm-thick AlN with high thermal conductivity, respectively. The longitudinal thermal conductivity of the core-shell structured magnetic composite sheet (2.45 W/m·K) enhanced about 33.4% in comparison with that of uncoated magnetic fillers (1.83 W/m·K) for the 50 vol. % magnetic filler in polymer matrix.

Thermal radiation from optically driven Kerr (χ(3)) photonic cavities

We describe thermal radiation from nonlinear (χ(3)) photonic cavities coupled to external channels and subject to incident monochromatic light. Our work extends related work on nonlinear mechanical oscillators to the problem of thermal radiation, demonstrating that bistability can enhance thermal radiation by orders of magnitude and result in strong lineshape alternations, including “super-narrow spectral peaks” occurring at the onset of kinetic phase transitions. We show that when the cavities are designed to exhibit perfect linear emissivity (rate matching), such thermally activated transitions can be exploited to dramatically tune the output power and radiative properties of the cavity, leading to a kind of Kerr-mediated thermo-optic effect. Finally, we demonstrate that in certain parameter regimes, the output radiation exhibits Stokes and anti-Stokes side peaks whose relative magnitudes can be altered by tuning the internal temperature of the cavity relative to its surroundings, a consequence of strong correlations and interference between the emitted and reflected radiation.

The Thermal Discrete Dipole Approximation (T-DDA) for near-field radiative heat transfer simulations in three-dimensional arbitrary geometries

A novel numerical method called the Thermal Discrete Dipole Approximation (T-DDA) is proposed for modeling near-field radiative heat transfer in three-dimensional arbitrary geometries. The T-DDA is conceptually similar to the Discrete Dipole Approximation, except that the incident field originates from thermal oscillations of dipoles. The T-DDA is described in details in the paper, and the method is tested against exact results of radiative conductance between two spheres separated by a sub-wavelength vacuum gap. For all cases considered, the results calculated from the T-DDA are in good agreement with those from the analytical solution. When considering frequency-independent dielectric functions, it is observed that the number of sub-volumes required for convergence increases as the sphere permittivity increases. Additionally, simulations performed for two silica spheres of 0.5μm-diameter show that the resonant modes are predicted accurately via the T-DDA. For separation gaps of 0.5μm and 0.2μm, the relative differences between the T-DDA and the exact results are 0.35% and 6.4%, respectively, when 552 sub-volumes are used to discretize a sphere. Finally, simulations are performed for two cubes of silica separated by a sub-wavelength gap. The results revealed that faster convergence is obtained when considering cubical objects rather than curved geometries. This work suggests that the T-DDA is a robust numerical approach that can be employed for solving a wide variety of near-field thermal radiation problems in three-dimensional geometries.

A model of scattered thermal radiation for Venus from 3 to [formula omitted

Thermal radiation becomes a prominent feature in the continuum spectrum of Venus longwards of ∼3μm. The emission is traceable to the upper cloud and haze layers in the planet's mesosphere. Venus' thermal radiation spectrum is punctuated by CO2 bands of various strengths probing into different atmospheric depths. It is thus possible to invert measured spectra of thermal radiation to infer atmospheric temperature profiles and offer some insight into the cloud and haze structure. In practice, the retrieval becomes complicated by the fact that the outgoing radiation is multiply scattered by the ubiquitous aerosol particles before leaving the atmosphere. We numerically investigate the radiative transfer problem of thermal radiation from the Venus night side between 3 and 5μm with a purpose-built model of Venus' mesosphere. Special emphasis is laid on the significance of scattering. The simulations explore the space of model parameters, which includes the atmospheric temperature, cloud opacity, and the aerosols' size and chemical composition. We confirm that aerosol scattering must be taken into account in a prospective temperature retrieval, which means an additional complication to the already ill-posed retrieval problem. We briefly touch upon the degeneracy in the spectrum's shape associated with parameterization of the Venus clouds. Reasonable perturbations in the chemical composition and size of aerosols do not significantly impact the model simulations. Although the experiments are specific to the technical characteristics of the Visual and Infrared Thermal Imaging Spectrometer on the Venus Express spacecraft, the conclusions are generally valid.

Generalized thermal resistance and its application to thermal radiation based on entransy theory

Entransy is a novel concept developed in recent years to measure the transport ability of heat in heat transfer processes. In order to analyze and optimize thermal radiation process more conveniently and intuitively, we develop the entransy-theory-based method to the field of thermal radiation problems to define the generalized thermal resistance for multi-dimensional steady state thermal radiation systems, with a consistent dimension of those for heat conduction and convection systems proposed in previous studies. Based on it, the minimum generalized thermal resistance principle for thermal radiation is developed and its equivalence with the entransy dissipation extremum principle can be concluded by defining the concept of heat flux weighted average temperature difference for thermal radiation systems. We point out that these two principles emphasize particularly on the optimization of the mean performance for heat transfer processes. A steady state thermal radiation process in an enclosure with three opaque surfaces is taken as an example to illustrate the applicability and reliability of generalized thermal radiation resistance when it is used to optimize thermal radiation problems. Finally, a comparison between the principles of minimum generalized thermal resistance and minimum entropy generation is discussed to show that the latter might not be appropriate to optimize some thermal radiation problems.

Thermal Radiation and Unsteady Magnetohydrodynamic Flow of Nanofluid in Stretching Porous Medium

The problem of thermal radiation and unsteady magnetohydrodynamic flow of a porous medium by a nanofluid past a stretching of a sheet has been investigated numerically. The model used for the nanofluid incorporates the effect of Brownian motion and thermophoresis. By using similarity analysis, the governing differential equations are transformed into a set of nonlinear, coupled, ordinary differential equations that are solved numerically. Numerical results are presented for velocity, temperature, and nanoparticle volume fraction profiles for different parameters of the problem as unsteadiness parameter, porous medium parameter, magnetic field parameter, local Rayleigh number, buoyancy-ratio parameter, thermal radiation parameter, Brownian motion parameter, thermophoresis parameter, nanoparticle buoyancy parameter, and heat source/sink parameter, etc. Also, the effects of the pertinent parameters on skin friction, rate of heat transfer, and mass fluxes are obtained and discussed numerically and illustrated graphically.

Fixed Grid Simulation of Radiation-Conduction Dominated Solidification Process

In this paper conduction-radiation controlled solidification process of semitransparent materials was numerically analyzed. New approach in this kind of simulations, which is based on the fixed grid front tracking method combined with the immersed boundary technique, was adopted and examined. The presented method enables accurate dealing with solidification processes of semitransparent materials which have different optical and thermophysical properties of solid and liquid phases as well as with absorption, emission, and reflection of the thermal radiation at the solid-liquid interface without applying moving mesh methods. The proposed numerical approach was examined by solving several simplified thermal radiation problems with complex fixed and moving boundaries both in two-dimensional and axisymmetric spaces. For some of them the accuracy of obtained results was proved by comparing with reference works, other showed capabilities of the proposed method. For simplified solidification processes of semitransparent materials three configurations of optical properties, i.e., semitransparent solid phase and opaque liquid phase, opaque solid phase and semitransparent liquid phase, and semitransparent both phases were considered. The interface between solid and liquid phases was treated to be opaque, absorbing, emitting, and reflecting diffusely the thermal radiation. Results of the numerical simulations show that the presented numerical approach works well in this kind of problems and is promising for simulation of real solidification processes of semitransparent materials.

Lattice Boltzmann method applied to the solution of the energy equations of the transient conduction and radiation problems on non-uniform lattices

Application of the lattice Boltzmann method (LBM) to solve the energy equations of conduction–radiation problems is extended on non-uniform lattices. In the LBM on non-uniform lattices, the single relaxation time based on the minimum velocity is used. This minimum velocity corresponds to the smallest size lattice. Because information propagates with the same minimum velocity in the prescribed directions from all the lattice centers, in a given time step, they are not equidistant from the neighboring lattices. Collisions in the LBM take place at the same instant. Therefore, in the LBM on non-uniform lattices, in every time step, interpolation is required to carry the information to the neighboring lattice centers. To validate this very concept in heat transfer problems involving thermal radiation, transient conduction and radiation heat transfer problems in a 1-D planar and a 2-D rectangular geometries containing absorbing, emitting and scattering medium are considered. The finite volume method (FVM) is used to compute the radiative information. In both the geometries, results for the effects of various parameters are compared for LBM–FVM on uniform and non-uniform lattices. To establish the LBM–FVM on non-uniform lattices for the combined conduction and radiation heat transfer problems, numerical experiments were performed with different cluster values. The accurate results were found in all the cases.

Lattice Boltzmann Method Applied to Variable Thermal Conductivity Conduction and Radiation Problems

In the present article, application of the lattice Boltzmann method has been extended to solve the energy equation of a problem involving temperature dependent thermal conductivity. To validate the formulation, transient heat conduction in a planar medium with and without temperature dependent thermal conductivity was analyzed. Next, a problem involving transient conduction and radiation in a participating medium was considered. To compare with the performance of the lattice Boltzmann method, the energy equation was also solved using the finite difference method. The discrete ordinates method was used to compute the radiative information in both methods. After benchmarking the results against those available in the literature, temperature and heat flux results in the two methods were compared for different parameters. The results of the two methods were found to compare very well.

High Knudsen Number Physical Vapor Deposition: Predicting Deposition Rates and Uniformity

The problem of predicting deposition rates and film thickness variation is relevant to many high-vacuum physical vapor deposition (PVD) processes. Analytical methods for modeling the molecular flow fail when the geometry is more complicated than simple tubular or planar sources. Monte Carlo methods, which have traditionally been used for modeling PVD processes in more complicated geometries, being probabilistic in nature, entail long computation times, and thus render geometry optimization for deposition uniformity a difficult task. Free molecular flow is governed by the same line-of-sight considerations as thermal radiation. Though the existence of an analogy between the two was recognized by Knudsen (1909, Ann. Phys., 4(28), pp. 75–130) during his early experiments, it has not been exploited toward mainstream analysis of deposition processes. With the availability of commercial finite element software having advanced geometry modelers and built-in cavity radiation solvers, the analysis of diffuse thermal radiation problems has become considerably simplified. Hence, it is proposed to use the geometry modeling and radiation analysis capabilities of commercial finite element software toward analyzing and optimizing high-vacuum deposition processes by applying the radiation-molecular flow analogy. In this paper, we lay down this analogy and use the commercial finite element software ABAQUS for predicting radiation flux profiles from planar as well as tube sources. These profiles are compared to corresponding deposition profiles presented in thin-film literature. In order to test the ability of the analogy in predicting absolute values of molecular flow rates, ABAQUS was also employed for calculating the radiative flux through a long tube. The predictions are compared to Knudsen’s analytical formula for free molecular flow through long tubes. Finally, in order to see the efficacy of using the analogy in modeling the film thickness variation in a complex source-substrate configuration, an experiment was conducted where chromium films were deposited on an asymmetric arrangement of glass slides in a high-vacuum PVD chamber. The thickness of the deposited films was measured and the source-substrate configuration was simulated in ABAQUS. The variation of radiation fluxes from the simulation was compared to variation of the measured film thicknesses across the slides. The close agreement between the predictions and experimental data establishes the feasibility of using commercial finite element software for analyzing high vacuum deposition processes.