Entropy flow,entropy generation,exergy flux,and optimal absorbing temperature in radiative transfer between parallel plates

Taking nonequilibrium radiative heat transfer between two surfaces as an example, the nonequilibrium thermodynamics of radiation is studied and discussed. The formulas of entropy flow, entropy generation, exergy flux, and optimal temperature of absorbing surface for maximum exergy output are derived. The result is a contribution to the thermodynamic analysis and optimization of solar energy utilization and can be applied in more complex radiative heat transfer cases.     

Transient coupled heat transfer in multilayer composite with one specular boundary coated

By the ray tracing?node method, the transient coupled radiative and conductive heat transfer in absorbing, scattering multilayer composite is investigated with one surface of the composite being opaque and specular, and the others being semitransparent and specular. The effect of Fresnel’s reflective law and Snell’s refractive law on coupled heat transfer are analyzed. By using ray tracing method in combination with Hottel and Sarofim’s zonal method and spectral band model, the radiative intensity transfer model have been put forward. The difficulty for integration to solve radiative transfer coefficients (RTCs) is overcame by arranging critical angles according to their magnitudes. The RTCs are used to calculated radiative heat source term, and the transient energy equation is discretized by control volume method. The study shows that, for intensive scattering medium, if the refractive indexes are arranged decreasingly from the inner part of the composite to both side directions respectively, then, the total reflection phenomenon in the composite is advantageous for the scattered energy to be absorbed by the layer with the biggest refractive index, so at transient beginning a maximum temperature peak may appear in the layer with the biggest refractive index.     

偏振度对均匀折射率介质内矢量辐射传输过程中辐射熵产的影响

在半透明均匀折射率介质内矢量辐射传输过程中辐射熵传递方程及其数值模拟方法的基础上,研究了偏振度对矢量辐射传输过程中辐射熵产的影响。均匀折射率介质内辐射光束的起偏和改偏通过相距阵实现。计算结果表明:由介质内吸收发射过程的不可逆性产生的光谱辐射熵产数随着偏振度增加而减小,而由介质散射过程的不可逆性产生的光谱辐射熵产数随着偏振度增加而增加;偏振度对介质内的光谱辐射熵强度的影响很大,若不考虑偏振,光谱辐射熵强度的相对误差最大可达到18.04%;在整个系统中,光谱辐射熵产数满足热力学第二定律。     

Entropy flow, entropy generation, exergy flux, and optimal absorbing temperature in radiative transfer between parallel plates

Taking nonequilibrium radiative heat transfer between two surfaces as an example, the nonequilibrium thermodynamics of radiation is studied and discussed. The formulas of entropy flow, entropy generation, exergy flux, and optimal temperature of absorbing surface for maximum exergy output are derived. The result is a contribution to the thermodynamic analysis and optimization of solar energy utilization and can be applied in more complex radiative heat transfer cases.     

Second-order-accurate discrete ordinates solutions of transient radiative transfer in a scattering slab with variable refractive index

The discrete ordinates method (DOM) with a second-order upwind interpolation scheme is applied to solve transient radiative transfer in a graded index slab suddenly exposed to a diffuse strong irradiation at one of its boundaries. The planar medium is absorbing and anisotropically scattering. From the comparison of the results obtained by the first-order DOM, the second-order DOM, the modified DOM and the Monte Carlo method, it can be seen that the numerical diffusion in the transient solutions obtained by the second-order DOM is less than that in the solutions obtained by the first-order DOM, but the numerical diffusion is still noticeable, especially for optically thin and moderate cases. By contrast, for optically thick cases the numerical diffusion due to the finite difference of the advection term of the transient radiative transfer equation is minor. In general, it is still necessary to adopt a DOM with a higher order scheme to capture the wave front of transient radiative transfer accurately. Besides, the influence of numerical diffusion is a little less noticeable for the case with a larger gradient of refractive index, and the distribution of direction-integrated intensity around the irradiation boundary decreases and that around the other boundary increases with the increase of the anisotropically scattering coefficient.     

Radiative heat transfer in semitransparent solidifying slab considering space–time dependent refractive index

Radiative heat transfer in semitransparent phase-change media is of great interest in many engineering fields. Its essence is the transient coupled heat transfer of radiation and conduction along with liquid–solid phase change. The difficulty is to solve radiative heat transfer with the consideration of time–space dependent radiative properties. Especially when the refractive index is considered to vary with space and time in phase change, the problem becomes more complicated. This paper investigates the problem of the variable radiative properties with space and time during phase change in semitransparent media. The phase-change medium is assumed to have solid, mushy and liquid zones, and the solid/mushy and liquid/mushy interfaces are considered to be semitransparent and diffuse reflecting. In different zones, there are different physical property parameters. Phase interfaces are always moving in phase change, while the interfaces of control volumes are fixed. Therefore, the interfaces of control volumes and phase interfaces are not always coincided, which will bring errors into the simulation of radiative transfer in phase-change media. However, the errors can be reduced by dividing the medium into enough sub-layers. As long as the number of sub-layers is big enough, the errors can be limited in a very small range. Then using the multilayer radiative transfer model, we can solve the radiative transfer problem in the semitransparent phase-change medium. Considering time–space dependent refractive index, this paper analyzes coupled radiative and conductive heat transfer in semitransparent solidifying media. The results show that the effects of variable refractive index with time and space on transient coupled heat transfer are significant and could not be neglected inside the semitransparent phase-change medium under some conditions.     

Local entropy generation and exergy analysis of the condenser in a direct methanol fuel cell system

This paper aims to identify the irreversibilities in the condenser of a direct methanol fuel cell (DMFC) system and present possible enhancements in its design through local entropy generation analysis (L-EGA). For this purpose, the local entropy generation terms originating from heat and mass calculated from results of a pseudo two-phase computational fluid dynamic (CFD) model of the condenser. Through this analysis, the total irreversibilities due to heat and mass transfer are calculated locally (e.g., film boundary layer, vapour-gas boundary layer) under the variable operating conditions of a DMFC (undersaturated, saturated, and supersaturated conditions of the cathode exhaust gas). Moreover, the exergy destruction ratio of condenser is found to estimate the exergy performance of the condenser. The results show that in the case of supersaturated cathode exhaust gas (CEG) flow, the entropy generation rate due to mass transfer in the film region is found as 0.032 W/(m·K) which is 18 times higher than that for the undersaturated CEG flow. However, entropy generation rate due to mass transfer decreases significantly when the hot flow is just over the film region. In the film region, the entropy generation rates originating from heat transfer are found as 0.0055 W/(m·K) (for the undersaturated case), 0.0032 W/(m·K) (for the saturated case), and 0.0015 W/(m·K) (for the supersaturated case). Moreover, the maximum exergy destruction ratio is found as 0.72 when the CEG is undersaturated and the CEG velocity is 0.18 m/s, while the lowest exergy destruction ratio is calculated as 0.28 when the CEG is saturated.     

Solution of radiative heat transfer in graded index media by least square spectral element method

Least square spectral element method based on discrete-ordinates equation is extended to solve multidimensional radiative heat transfer problems in semitransparent graded index media. Chebyshev polynomial is employed as expansion set for the spectral element discretization. Five various test problems were taken as examples to verify the least square spectral element formulation for solving radiative heat transfer in semitransparent graded index media. The predicted distributions of temperature and radiative heat flux are determined by the least square spectral element method and compared with data in the references. The results show that the least square spectral element method has good accuracy for solving multidimensional radiative heat transfer problems in semitransparent graded index media.     

Heating/melting of a fused silica particle by convection and radiation

The effect of internal absorption and emission of radiation on the heating/melting process of small fused silica particles is analyzed. The particle is considered to be semitransparent to radiation, and the radiative transfer theory is used to predict the local volumetric absorption/emission rate. The transient energy equation with conduction and radiation accounted for is solved to predict the temperature distribution in the particle and the solid–liquid interface position after the melting has started. The radiative transfer calculations are carried out on the spectral basis using published spectral optical property data for fused silica. Results of parametric calculations for different diameter particles, surroundings temperatures and external flow conditions are reported and discussed.     

Meshless Method for Solving Transient Radiative and Conductive Heat Transfer in Two-Dimensional Complex Geometries

A diffuse approximation meshless method (DAM) is employed to solve the transient radiative and conductive heat transfer problem in a semitransparent medium enclosed in 2-D complex geometries. The computational spatial domain is discretized by a set of nodes scattered in the domain and boundary without information on the relationship between them. The meshless method for radiative transfer equation is based on the even-parity formulation of the discrete ordinates method without any form of upwinding. Results of dimensionless temperature distribution at different dimensionless times are obtained and validated with other benchmark approximate solutions in order to illustrate the performance of the proposed method.     

Meshless method for radiation heat transfer in graded index medium

Because ray goes along a curved path determined by the Fermat principle, curved ray tracing is very difficult and complex in graded index media. To avoid the difficult and complex computation of curved ray trajectories, a meshless local Petrov–Galerkin approach based on discrete-ordinate equations is developed to solve the radiative transfer problem in multi-dimensional absorbing–emitting–scattering semitransparent graded index media. A moving least square approximation is used to construct the shape function. Two particular test problems in radiative transfer are taken as examples to verify this meshless approach. The predicted temperature distributions and the dimensionless radiative heat fluxes are determined by the proposed method and compared with the other benchmark approximate solutions. The results show that the meshless local Petrov–Galerkin approach based on discrete-ordinate equations has a good accuracy in solving the radiative transfer problems in absorbing–emitting–scattering semitransparent graded index media.     

Radiative transfer within non Beerian porous media with semitransparent and opaque phases in non equilibrium: Application to reflooding of a nuclear reactor

A local radiative transfer model is developed for strongly anisotropic porous media with an opaque phase and a mixture of two semitransparent phases. At the optically thick limit, the homogenized phase associated with the opaque interfaces is characterized by generalized extinction and scattering coefficients at equilibrium, a phase function and an effective refraction index, by following the model of Taine et al. [1] for non Beerian media. The radiative transfer model is based on a Radiative Transfer Equation (RTE) with three source terms, which are associated with the temperature fields of the opaque interfaces and the two semitransparent phases. This RTE has been solved by a perturbation technique, which allows radiative interfacial fluxes and radiative powers per unit volume, that are exchanged between phases, to be computed at local scale. The main contributions are obtained at zeroth order perturbation. Corrective contributions at first order perturbation are also determined: Radiative fluxes and powers are then expressed from coupled Fourier’s laws, which are characterized by radiative conductivity tensors associated with each phase.Illustrative results are given for the radiative modeling of reflooding of a damaged nuclear reactor core. Pragmatic conclusions on the cooling efficiency by steam and water droplets are finally given.     

Analysis of entropy generation distribution in micro-combustors with baffles

This study presents the analysis of entropy generation distribution in H₂/air premixed flame in micro-combustors with baffles. The numerical simulation of combustion is performed with the help of Ansys Fluent code. The entropy generation rates are derived from entropy transport equation and calculated based on the numerical results. The entropy generation caused by various irreversible processes such as chemical reaction, thermal conduction and mass diffusion are studied in micro-combustors with baffles. The effects of the height of the baffles, H₂/air mass flow rate and equivalence ratio are investigated. It is found that a higher baffle will lead to more entropy generation and relatively larger destruction of available energy. The exergy efficiency decreases significantly when the H₂/air mass flow rate is increased. The lean and rich H₂/air mixture shows an obvious lower entropy generation rate and higher exergy efficiency than the stoichiometric mixture.     

Transient thermal analysis of semitransparent composite layer with an opaque boundary

Transient coupled radiative and conductive heat transfer in a two-layer, absorbing, emitting, and isotropically scattering non-gray slab is investigated by the ray tracing method in combination with Hottel's zonal method. One outer boundary is opaque, and another is semitransparent. The radiative energy transfer process in a semitransparent composite is divided into two sub-processes, one of which considers scattering, the other does not. The radiative transfer coefficients of the composite are deduced under specular and diffuse reflection and combined specular and diffuse reflection, respectively. The radiative heat source term is calculated by the radiative transfer coefficients. Temperature and heat flux are obtained by using the full implicit control-volume method in combination with the spectral band model. The method presented here needs only to disperse the space position, instead of the solid angle. A comparison with previous results shows that the results are more accurate.     

固体热辐射Yong性能分析

本文对漫灰均温物体在常物性条件下对外辐射传热的Ｙｏｎｇ值计算建立了数学模型。通过与物体内能Ｙｏｎｇ公式的数值计算比较,得出了辐射能量的Ｙｏｎｇ值不大于内能Ｙｏｎｇ值的结论。从初步的热射Ｙｏｎｇ值计算公式发现。Ｙｏｎｇ与物体表面辐射率有关。     

Inverse Radiation Problem of Boundary Incident Radiation Heat Flux in Semitransparent Planar Slab with Semitransparent Boundaries

INTRODUCTI0NInverseradiati0nproblemshavedefinedasubjectofinterestf0rthepast3Oyears0nsoandthereex-istsac0nsiderablebody0fknowledgesurroundingthesubjectthathasbeenextensivelyreviewedinaseries0fpapersbyM.C.rmick[1-4].Theyarecon-cernedwiththedeterminati0noftheradiativepr0p-ertiesandthetemperaturedistributionsofmediaus-ingvari0ustypesofradiationmeasurements.Despitetherelativelylargeinterestexpressedininverseradia-tionproblems,mostoftheworkfocusedontheinverseestimati0noftemperaturedistributions…     

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.     

TRANSIENT CONDUCTION AND RADIATION HEAT TRANSFER WITH VARIABLE THERMAL CONDUCTIVITY

The effect of variable thermal conductivity on transient conduction and radiation heat transfer in a planar medium is investigated. Thermal conductivity of the medium is assumed to vary linearly with temperature, while the other thermophysical properties and the optical properties are assumed constant. The radiative transfer equation is solved using the discrete transfer method, (DTM) and the nonlinear energy equation is solved using an implicit scheme. Transient as well as steady state results are found for an absorbing, emitting, and anisotropically scattering gray medium. Thermal conductivity has been found to have significant effects on both transient as well as steady state temperature and heat flux distributions. Some steady state results are compared with the results reported in the literature.     

Thermodynamic stability analysis of non-Fourier model-based bio-heat transfer in laser-irradiated cylindrical-shaped multilayered biological tissue

The present research focuses on examining the thermic response of living tissue in the form of a triple-layered cylindrical structure when subjected to laser light and the compatibility analysis of non-Fourier heat transfer with thermodynamics second law. The temperature field in the triple-layered cylindrical living tissue subjected to laser light is determined by numerically solving the transient radiative transfer equation in conjunction with the dual phase lag (DPL) based bioheat equation. Once the temperature field is known, the equilibrium and nonequilibrium entropy production rate (EPR) is calculated based on the hypothesis of classical irreversible thermodynamics and extended irreversible thermodynamics, respectively. The present results are verified against the data from the literature and found a good match between them. A comparative analysis of the Fourier and non-Fourier models is accomplished. The equilibrium and nonequilibrium EPR values for the Fourier model are found to be positive. While the equilibrium EPR is negative for non-Fourier heat conduction and does not satisfy the thermodynamics second law, nonequilibrium EPR is always a positive value for Fourier, DPL, and hyperbolic models and satisfies thermodynamics second law. It has been investigated how thermal relaxation times affect the temperature field and EPRs in tissue are subjected to laser light.     

Chebyshev collocation spectral method for one-dimensional radiative heat transfer in graded index media

Chebyshev spectral collocation method based on discrete ordinates equation is developed to solve radiative transfer problems in a one-dimensional absorbing, emitting and scattering semitransparent slab with spatially variable refractive index. For radiative transfer equation, the angular domain is discretized by discrete ordinates method, and the spatial domain is discretized by Chebyshev collocation spectral method. Due to the exponential convergence of spectral methods, a very high accuracy can be obtained even using few nodes for present problems. Numerical results by the Chebyshev collocation spectral-discrete ordinates method (SP-DOM) are compared with those available data in references. Effects of refractive index gradient on radiative intensity are studied for space dependent scattering media. The results show that SP-DOM has a good accuracy and efficiency for solving radiative heat transfer problems in even spatially varying absorbing, emitting, scattering, and graded index media.