Radiative Heat Transfer Problems Research Articles

Transient Radiation Heat Transfer of Thermally Compact Bodies: an Explicit Solution

Abstract An explicit, analytical solution is offered to the problem of transient radiation heat transfer of thermally compact bodies. This solution is readily implemented as a calculator on a simple spreadsheet software, allowing prediction of transient radiation that can aid didactics, design, test, and operations. It is shown that transient radiation heat transfer has a few similarities, and many differences, in comparison to linear forms of transient heat transfer such as conduction and convection. Both linear and radiation forms of transient heat transfer asymptotically approach their steady state conditions. Differences of note are that transient radiation heat transfer is non-self-similar, it depends upon two nondimensional variables, transient radiative heating is generally faster than transient radiative cooling, and externally applied heat sources substantially delay transient radiation heat transfer relative to internally applied heat sources.

Influence of the greenhouse effect on heat transfer through building envelopes

The evaluation of heat input through fences is an important part of the task of predicting the summer thermal regime of a building under a transparent dome, the interest in the construction of which in the northern regions has increased recently. The calculation of the summer thermal regime of a building under a dome is complicated by taking into account the greenhouse effect, which requires solving the problem of radiative heat transfer in the system: opaque wall - semitransparent screen - environment. It is also necessary to take into account the convection in the dome space. А relatively simple model for calculating the characteristics of heat transfer through the wall of a building with a dome, which takes into account the greenhouse effect, is considered in this paper. Comparison of calculations with experimental data allows us to speak about the adequacy of the proposed model. It is shown that the presence of semitransparent screen due to the greenhouse effect leads to a significant raise in temperature under the dome and an increase in heat input into the building. The influence of ventilation in the dome space on heat access through the enclosing structure for the selected values of external parameters: external temperature and solar radiation was evaluated. The proposed model of heat transfer through the enclosing structure with a semitransparent screen can become part of a more complete model for calculating the thermal regime of a building under a dome.

Engineered Features and Artificial Neural Networks for the Identification of Temperature-Dependent Radiative Characteristics in Porous Media

The accurate and efficient prediction of radiative properties of materials plays a crucial role in numerous industrial and engineering applications. However, experimental measurement can be cumbersome, particularly for complex materials. As a result, numerical techniques such as Monte Carlo ray tracing (MCRT) have been developed to assess radiative properties. MCRT is a well-known tool for solving radiation heat transport (RHT). Despite its advantages, MCRT requires tracing a large bundle of light beams for convergency and veracity of outcomes, which necessitates further advancements in its employment. To this end, supervised learning algorithms can be used in conjunction with MCRT to provide a quick and accurate substitution for typical MCRT simulations. In this study, machine learning algorithms employing expertly designed features are used to evaluate the radiative properties of heterogeneous porous media, while considering the effects of conductive heat transfer. Directional features have been introduced into the sets of the features implemented in our previous study for the enhancement of predictions. The results show that the applied method can improve prediction accuracy compared to prior studies. Moreover, this approach is generalizable to other radiative heat transfer problems by extracting relevant characteristics in accordance with the involved physics.

Reducing skid marks on steel slabs by developing an improved design scheme of water beam

Due to the existence of cooling water pipes and thermoduric skids in the walking beam type reheating furnace, skid marks always occur on the bottom of the steel slab and the quality of the steel slab is seriously affected. In this paper, the coupled heat transfer model among steel slab, water beam, furnace gas and furnace walls is established to accurately simulate the reheating process of the steel slab. The discrete ordinates method (DOM) is adopted to solve radiative heat transfer problem in reheating furnace. To get closer to the real situation, the relative movement between steel slab and thermoduric skid is taken into account strictly. The formation process of skid mark is clarified based on the calculated results of coupled heat transfer, and an improved design scheme for water beam is proposed to make the new skid marks produced after water beam dislocation not overlap each other, which effectively reduces the skid marks. Our study can provide helpful advising for the improvement of steel slab quality and the design of water beam structure in reheating furnace.

Investigation on thermal radiation property of near- and super-critical water in the pressure range of 20–25 MPa based on line-by-line method

With the rapid development of supercritical water gasification (SCWG) technology, investigation on thermal radiation property of water up to critical state (22.1 MPa, 647 K) is becoming important for precisely analyzing thermo-chemical process in this engineering. This paper explores radiative absorption coefficients κη of water under thermodynamic states of (20−25) MPa and (773–1273) K based on line-by-line (LBL) calculations. The results are validated against experimental data and molecular dynamic (MD) simulation values. It is shown that near- and super-critical water (NSCW) has five major radiation bands within spectral range of (1−50) μm. Compared to atmospheric water vapor (0.1 MPa), NSCW holds unique spectral characteristics, including dramatically smoothed spectrum, enormous absorption coefficient, and redshift or blueshift on spectral peak positions. Based on calculation results, a gray-band model for NSCW is proposed to solve problems of radiative heat transfer in SCWG engineering.

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.

A diffusion synthetic acceleration method for steady discrete unified gas kinetic scheme in radiative heat transfer

An efficient synthetic-type iterative method is proposed to improve the convergence rate of the steady discrete unified gas kinetic scheme (SDUGKS) for steady radiative heat transfer problems. The key ingredient of the present method is the tight coupling of the mesoscopic radiative transfer equation (RTE) and the macroscopic diffusion equation. The RTE is calculated by SDUGKS, and the diffusion equation is solved to predict the incident radiation energy and angular radiation intensity used in SDUGKS to accelerate the evolution, unlike the original diffusion synthetic acceleration (DSA) method which only predicts the incident radiation energy. Furthermore, a damping factor is adopted to remedy the inconsistency of spatial discretization between the mesoscopic SDUGKS and macroscopic diffusion equation. The theoretical convergence rate of the present method is studied via the discrete Fourier analysis. Several numerical tests under a wide range of optical thicknesses are performed to show the convergence speed. The damping factor and the correction of the angular radiation intensity added in solving the macroscopic diffusion equation greatly increase the stability of the present method and also reduce its computational costs. The convergence rate of the present method becomes faster than that of previous SDUGKS when the optical thickness is larger than 10. With the increase of extinction coefficient, the speedup ratio of the present method and SDUGKS in one-dimensional problems becomes extremely large and also reaches one or two orders of magnitude in two- and three-dimensional problems.

Improved Monte Carlo method for radiative heat transfer in semitransparent media with BRDF surface

This paper proposes an improved Monte Carlo method (IMCM) for the radiative heat transfer solution in semitransparent media with BRDF surface for the first time. This method not only keeps the strong points of high precision and excellent applicability to the calculation of radiative heat transfer in complex shape scattering media with BRDF surface, but also overcomes the shortcomings of time-consuming for huge amounts of energy beams tracing in the Monte Carlo method. In the IMCM we developed, the energy beams of reflection or scattering can be worked out by proportional iteration accumulation. The scattering and reflection process only need to be sampled twice rather than lots of scattering and reflection energy beams tracing. This improvement not only retains the high accuracy of the MCM, but also greatly improves the calculation efficiency. A number of radiative heat transfer problems in semitransparent media enclosure with BRDF surface are studied. The effects of absorption coefficient, wall emissivity and scattering characteristics on radiative heat transfer are analyzed. Results indicate that the IMCM is a very efficient method with high precision for solving radiative heat transfer.

A class of linearization-based collocation methods for initial value and boundary value engineering problems

Nonlinear initial value and boundary value problems are generally classified as two different categories of problems and the methods utilized to solve them are also different. This paper proposed a uniform linearization-collocation framework through which the initial value and boundary value problems can be solved in a similar way. An optional pre-conditioning procedure is provided to guarantee the computational accuracy. Rigorous analysis about the convergence rate is given. Different from the commonly seen convergence rate analysis based on one-dimensional system and mean-value theorem, this analysis is based on multidimensional system and polynomial approximation. A perturbed orbit propagation problem, a radiation heat transfer problem and an orbit optimization problem are solved to verify the validity and efficiency of the proposed methods. The proposed methods not only outperform the highly optimized MATLAB built-in integrator ODE45 in orbit propagation, but also outperform the bvp4c and bvp5c in solving the boundary value problem. Most importantly, the proposed methods are capable of solving some problems where the bvp4c and bvp5c are invalid. The quasi-linearization-collocation method proved to be a highly accurate, efficient and stable solver for ordinary differential equations with various types of constraints.

Study on bottom thermal environment of launch vehicle during high altitude flight

Aiming at the problem of the thermal environment at the bottom of the launch vehicle in the high-altitude flight stage, taking the launch vehicle with core stage four-way machine as the model, the coupled convection / radiation heat transfer problem at the high-altitude of the launch vehicle is deeply studied through the numerical simulation method, the gas jet flow model of the launch vehicle in the high-altitude flight stage is established, and the flow field information of the rocket under different working conditions and the heat flow at the bottom of the rocket are obtained. The numerical results are compared with the experimental data to verify the effectiveness of the selected model and calculation method. The research shows that the external flow field of the rocket body will have a great impact on the thermal environment at the bottom. With the continuous increase of flight altitude, the convective heat flow at the bottom of the rocket body first rises and then decreases. In the high-altitude stage, the total heat flow at the bottom of the rocket body is dominated by radiant heat flow, the convective heat flow outside the main nozzle is dominant, and the radiant heat flow outside the traveling jet nozzle is dominant.

An improved blocked-off method for radiative heat transfer in complex enclosures with structured grids

The blocked-off based finite volume method for the radiation heat transfer problem has an obvious shortcoming that yields oscillating radiative heat flux on complex walls when using structured grids. This work aims to improve the accuracy of the blocked-off model by using a boundary radiation intensity interpolation method. The new method is validated for inclined and curved walls, and the predicted radiative heat flux has almost no fluctuations with great accuracy. This improved method works well for optically thin, moderate and thickness conditions. The deviation in radiative heat flux decreases from about 10% to less than 1% compared to previous schemes.

Heat Transfer Study in Cylindrical Cavity with Heat Absorption or Generation

Lattice Boltzmann mesoscopic (LBM) is applied to solve energy equation of a transient conduction radiation heat transfer problem in a two-dimensional cylindrical participating (absorbing, emitting and scattering) medium in the presence of heat generation/absorption coefficient. Control volume finite element method (CVFEM) formulation is used to obtain the radiative information. To study the effectiveness of the LBM-CVFEM combination on unsteady conduction-radiation problems in cylindrical media, the energy equation of the problem is also solved using the finite difference method (FDM) in which the CVFEM is used to compute radiative information. The effects of heat generation/absorption coefficient on temperature distributions in the medium are studied. Results of the present work are benchmarked against those available in the literature. The hybrid numerical model’s results are also compared with those obtained by the FDM-CVFEM combination. All the results presented in this work show that the present method is accurate and valuable for the analysis of cylindrically axisymmetric radiative heat transfer problems .

Improved Radiation Heat Transfer Model in RELAP5 for Compact Fuel Rod Bundles by the Absorption Factor Modification

Simulations of radiation heat transfer in fuel rod bundles are necessary for the thermal hydraulic design and safety analysis of open lattice gas-cooled reactors, which always operate at high temperatures. To save the computational costs, existing radiation models in system codes such as RELAP5 commonly assume each fuel rod to own the uniform radiosity over the rod surface. Previous research studies have indicated that the uniform radiosity assumption could overestimate the heat transfer flux and under-predict the maximum fuel rod temperature, and the anisotropic correction was tried by dealing with non-uniform reflected radiation. To better model the non-uniform radiosity effect, the Gehart’s method based on the non-uniform absorbed radiation is introduced in this study. By dividing the surface of each rod into six segments, the one-sixth rod view factors are derived in specific rod and near wall sections to generate the segment-to-segment absorption factors. By summarizing those segment-to-segment absorption factors, the rod-to-rod and rod-to-wall absorption factors are modified and implemented into RELAP5 to improve the radiation heat transfer model. The two-dimension radiation heat transfer problem in the nuclear fuel rod bundle is simulated in FLUENT as the benchmark and in RELAP5 for comparison. Fuel rod bundles in hexagonal arrays were investigated with various surface emissivity and pitch-to-diameter ratios (p/d). The simulations indicated that the method of rod segment division and absorption factor modification could reflect the non-uniform radiosity, and the results were related to the values of p/d and surface emissivity. The modified radiation heat transfer model in RELAP5 validated that the deviations of the maximum temperature were reduced from around 20% to 1%,3%,8% for p/d = 1.1, 1.2, and 1.3, respectively. Rod bundles with larger p/d required more radiative rods in the analyses of absorption factor modifications. The present radiation heat transfer model should be studied and tested in three-dimension cases to further prove that it is appropriate for the nuclear rod bundles.

Two Approaches to Effectively Reduce the Size of Radiative Heat Transfer Problems in Multidimensional Geometry

Two Approaches to Effectively Reduce the Size of Radiative Heat Transfer Problems in Multidimensional Geometry

Numerical results for radiative heat transfer in finite cylindrical medium with isotropic scattering

In recent years, the interest in radiative heat transfer in cylindrical media has increased primarily because of its several applications related to combustion chambers, furnaces, and high temperature heat exchangers. Although there are many papers dealing with the radiative transfer in such geometry, there is lack of high precision benchmarks. Such scarcity is related to the fact that some researches present inaccurate results and most published works are limited to presenting results only in graphics. The shortage is more evident in the case of multidimensional problems, like those in which incident radiation and radiative heat fluxes vary in the axial direction. These problems can be approached in many ways; in the integral formulation, the angular variables are completely eliminated by integration over the solid angle, which allows the elimination of the ray effect and the consequent obtainment of more accurate numerical results. A strategy that can be used simultaneously with the integral formulation is the use of the singularity-subtraction technique with the Nyström method, which provides high quality numerical results with relatively low computational times if combined with mathematical refinements. Following this methodology, in the present research, radiative heat transfer problems in finite cylindrical media with isotropic scattering are solved. High precision numerical results for incident radiation and radiative heat fluxes in the radial and axial directions are provided and validated by comparing with results available in the literature.

Analysis of radiative heat transfer in two-dimensional irregular geometries by developed immersed boundary–lattice Boltzmann method

The Immersed Boundary–lattice Boltzmann method (IB-LBM) is developed to analyze radiative heat transfer in two-dimensional (2D) irregular geometries. Lattice Boltzmann method (LBM) has been adopted to discretize the radiative heat transfer equation in an absorbing and emitting media, and the immersed boundary method (IBM) is used to model the boundaries of irregular geometries. Due to the mismatch between boundary and computational nodes in the Immersed Boundary method, a radiative density term based on the difference of radiation intensity is added to the lattice Boltzmann equation to satisfy the boundary condition. Radiative heat flux distribution is obtained for several irregular geometries which are maintained at an isothermal media or radiative equilibrium condition in the enclosure. The results are successfully validated by comparing the results obtained from other methods of irregular geometries analysis, such as the blocked-off domain, embedded boundary, and body-fitted grid method. According to the obtained results, their accuracy, and numerical cost, the combined IB-LBM benefits from the unique and worthy advantages of both IBM and LBM in solving the complicated analysis of 2D radiative heat transfer problems. Compared to the traditional methods used for the radiative analysis of irregular geometries, the immersed boundary method can solve the complexities of modeling curved boundaries effortlessly. It should be pointed that for optically thin media, the proposed model shows poor performance.

Investigation of transient coupled conduction and radiation heat transfer in the linearly anisotropic scattering cylindrical medium by spectral collocation method

In this paper, a spectral collocation method (SCM) is developed to solve transient conduction and radiation heat transfer problems in infinitely long annular cylinders with participating medium. The participating medium is an absorbing, emitting and linearly anisotropic scattering medium. To avoid the complex calculation of ray tracing, the radiative transfer equation and the transient heat conduction equation are expressed in eulerian coordinates. In the solving process, for the radiative transfer equation, both spatial and angular domains are discretized by the SCM; for the transient heat conduction equation, the spatial domain is discretized by the SCM, and the time domain is discretized by the fully implicit Euler scheme. The spatial derivative term, angular derivative term and scattering source integral term are approximated by the high order spectral collocation scheme. Compared with available data in references, the SCM can achieve very good accuracy even using few nodes. Thus, the SCM is a very effective method to achieve high order accuracy for transient coupled conduction and radiation heat transfer in an anisotropic scattering cylindrical medium. Moreover, the effects of conduction-radiation parameter, optical thickness, and wall emissivity on the transient temperature distribution and energy flow rate have also been comprehensively investigated.

A nongray-wall emissivity model for the full-spectrum correlated k-distribution method based on uniform media assumption

The walls of high-temperature combustion devices are usually assumed to be black or gray in radiative heat transfer calculations to save computing resources; however, this simplification may introduce large errors. To improve the accuracy of the Full-Spectrum Correlated K-distribution (FSCK) method in calculations of nongray-wall radiative heat transfer problems without reducing the computational efficiency, a nongray-wall emissivity model for the FSCK method is proposed based on uniform-medium assumption. The accuracy of this nongray-wall emissivity model and the commonly used Planck-function-weighted gray-wall emissivity model is evaluated in 1D isothermal and homogeneous cases, 1D non-isothermal and inhomogeneous cases, and 3D flames bounded by walls coated with fly-ash deposit or soot deposit. The results show that the nongray-wall emissivity model for FSCK demonstrates much better accuracy than the gray-wall one, especially for cases of low wall temperatures. The nongray-wall emissivity model provides good accuracy over a wide range of optical depth, while the accuracy of the gray-wall emissivity model is highly dependent on the optical depth. The nongray-wall emissivity model based on the uniform-medium assumption can be applied to non-isothermal and inhomogeneous radiative heat transfer problems involving nongray walls.

Numerical investigation of combined heat transfer (mixed convection-radiation) in 2D channel using the LBM

In this paper, the problem of combined convection (forced and natural) and radiation heat transfer between two parallel plates (channel) with isothermal walls has been numerically studied. For this purpose, the equations of momentum, energy and radiation transfer must be solved. In this study, lattice Boltzmann method is used to solve all of the equations simultaneously, that, to increase the stability for solving the energy equation by lattice Boltzmann method, a modern approach called the two relaxation time model was used. The medium inside the channel was considered as a participating medium to solve the radiation transfer equation. Finally, after the formulation of governing equations and boundary conditions for the present problem in the lattice Boltzmann method, validating the results and simultaneously solving the equations, the effects of some parameters such as optical thickness, Planck number and Richardson number with changing the angle of the channel are studied on heat transfer, flow and temperature distribution.The results showed that the radiation parameters have a significant effect on the problem and can change the velocity and temperature distribution of the channel. In between these parameters, the Planck number has the most effect on the temperature and velocity of the fluid flow. Increasing the angle of the channel relative to the horizon increases the effect of buoyancy force, fluid velocity variations and fluid temperature values.

Generalized source term multiflux method coupled with Runge-Kutta ray tracing technique for arbitrary radiative intensity of graded-index media.

The generalized source term multiflux method (GSMFM) combined with Runge-Kutta ray tracing technique is developed to calculate arbitrary directional radiative intensity of graded-index media. In this method, the finite volume method is employed to solve source terms along the curved ray path determined by the Fermat principle. Runge-Kutta ray tracing technique is adopted to obtain the ray trajectory numerical solution in graded-index media. And the GSMFM is used to solve radiative intensity to be expected. One-dimensional and two-dimensional radiative heat transfer problems are investigated to verify the performance of this method. The numerical results show that the accuracy of the GSMFM is close to that of backward Monte Carlo (BMC) method, while the efficiency of GSMFM is much higher than that of the BMC. Therefore, the GSMFM developed can be considered as a promising method to solve arbitrary radiative intensity in graded-index media.