Radiative Entropy Generation Research Articles

Entropy generation analysis of a three-dimensional coal-fired furnace: A realistic study

An analysis of the entropy generation by radiative heat transfer in a three-dimensional virtual coal-fired furnace is performed. The gases, including CO2 and H2O, and particles, including soot, unburnt char and ash, are considered as a participating medium. The radiative transfer equation for a non-grey medium was solved by the discrete ordinate method, in which the radiative properties of the gases, soot, unburnt char and ash were obtained by using the statistical narrow-band correlated-k model, Rayleigh's theory, and Mie theory, respectively. The distributions of the local volumetric rate of entropy generation and the local rate of entropy generation at the wall are calculated. The contributions of various media in coal-burning furnaces to the radiative entropy generation rate (REGR) are evaluated, and the effects of several important factors, such as the oxidizer atmosphere, burnout rate, and the volume fraction of soot, unburnt char and ash on the REGR and dimensionless entropy generation were also investigated. The numerical results show that the irreversibility of the particle radiation contributes more than 80% of the volumetric radiative entropy generation. The concentration of particles also has an important effect on REGR, which decreases by 41% when the concentration of unburnt char and ash increases from 10 ppm to 50 ppm and decreases by 70% when the concentration of soot increases from 1 ppm to 6 ppm in a real-size furnace such as an optically thick furnace.

NUMERICAL ANALYSIS OF ENTROPY GENERATION IN A TWO-DIMENSIONAL POROUS HEAT RECOVERY SYSTEM

The main goal of this paper is the analysis of entropy generation in a two-dimensional porous heat recovery system. This system works based on the energy conversion between fluid enthalpy and thermal radiation. The fluid phase in this system is considered to be air assuming a non-radiative medium, whilst the solid phase is regarded as a gray radiating medium with emission, absorption, and isotropic scattering. These two phases are not in thermal equilibrium and the energy equation is separately analyzed for them. To solve the radiative equations in solid phase, the discrete ordinates method is employed. For a porous heat recovery system, the local entropy generation rate is obtained by summing the entropy generation rates due to the fluid friction and conductive and radiative heat transfer mechanisms. Besides, components of radiative entropy generation rates arise from the absorption-emission, scattering, and walls influences. However, influences of radiative parameters of optical thickness and scattering albedo on the entropy generation rates in this porous system are numerically investigated with full details. Results show that the best thermal performance of the porous heat recovery system occurs in a non-scattering medium with the highest magnitudes of optical thickness.

Thermodynamics Irreversibilities Analysis of Oxy-Fuel Diffusion Flames: The Effect of Oxygen Concentration.

In studies on the combustion process, thermodynamic analysis can be used to evaluate the irreversibility of the combustion process and improve energy utilization efficiency. In this paper, the combustion process of a laminar oxy-fuel diffusion flame was simulated, and the entropy generation due to the irreversibilities of the radiation process, the heat conduction and heat convection process, the mass diffusion process, and the chemical reaction process was calculated. The effect of the oxygen concentration in the oxidizer on the entropy generation was analyzed. The results indicated that, as the oxygen concentration in the oxidizer increases, the radiative entropy generation first increases and then decreases, and the convective and conductive entropy generation, the mass diffusion entropy generation, the chemical entropy generation, and the total entropy generation gradually increase.

Evaluation of radiative entropy generation in a high temperature system including H2O, CO2 and soot with non-gray wall

In this paper, radiative entropy generation in a high temperature parallel plate system containing H2O, CO2 and soot with non-gray wall was investigated. Based on Discrete Ordinates method and Narrow Band k-distribution model, the spectral radiative entropy generation rate and radiative entropy generation rate due to different physical processes were given. The effects of CO2, H2O, soot, spectral emissivity of wall, as well as medium temperature on radiative entropy generation were evaluated. Some conclusions were obtained as below. The irreversibility of emission and reflection process on wall has main contribution on radiative entropy generation rate of system. The radiative entropy generation rate increases with the mole fraction of gas and volume fraction of soot. CO2 has less effect on total radiative entropy generation rate, but H2O and soot particle have more effect on total radiative entropy generation rate. The radiative entropy generation rate increases with the increase of total hemispherical absorptance of wall. The radiative entropy generation rate and dimensionless radiative entropy generation increase with the increase of non-uniformity of medium temperature distribution and difference of gas temperature and soot temperature.

Heat and mass transfer of combined forced convection and thermal radiation within a channel: Entropy generation analysis

The present paper deals with a numerical modelling of thermal and mass transfer coupled by thermal radiation and forced convection in a semi-transparent medium during the evaporation of a thin water film used for wall protection within a channel. Particular attention is paid to the analysis of the entropy generation due to heat transfer and mass diffusion. The governing equations are solved numerically using the Finite Volume Method. Furthermore, the resolution of the Radiative Transfer Equation was carried out by the “Ray-Tracing” method according to a symmetric quadratic scheme of SN (S4) whereas the radiative properties of the non-grey gas were deduced by the application of the “Statistical Narrow Band Correlated-K” (SNB-CK) model. The effect of several parameters on entropy generation due to conduction, thermal radiation and mass diffusion are analysed in this paper. The results clearly demonstrate the major dominance of the wall radiative entropy generation in all the studied cases. The results also prove that for high values of drywall temperature and emissivity, the entropy generation due to mass diffusion augmented.

Analysis of spectral radiative entropy generation in a non-gray planar participating medium at radiative equilibrium with two different boundary conditions

In the present study, spectral radiative entropy generation analysis is presented for radiative heat transfer between two parallel plates containing non-gray absorbing and emitting medium at radiative equilibrium. In order to evaluate the effect of boundary condition (BC) on the entropy generation, two configurations of BC are considered. In the first configuration, two bounding walls are assumed to be at prescribed temperatures. In the second configuration, one wall is assumed to be at a prescribed temperature and the other wall is assumed to have prescribed heat flux BC. The discrete ordinates method and the finite volume method are respectively used for the angular and spatial discretization of the radiative transfer equation and radiative entropy generation equations. While the correlated-k (CK) non-gray model is used to evaluate spectral radiative properties. Five cases are considered, including two homogeneous cases and two non-homogeneous cases with a single participating gas (i.e. H2O or CO2) and one homogeneous case with a mixture of H2O, CO2 and soot particles. Spectral, volumetric and total radiative entropy generations are calculated for each BC configuration and case. Also, the effects of the concentration of participating gas, wall emissivity and total gas pressure on radiative entropy generation are attentively analyzed. The results show that irreversible radiative transfer at the wall with lower temperature is the main source of radiative entropy generation in the system. Soot particles increase radiative entropy generation due to absorption and emission process but decrease radiative entropy generation due to walls radiation. The radiative entropy generation is approximately constant when the concentration of participating gas varies for both BC's. Total radiative entropy generation for the system with the prescribed temperature at walls significantly increases with the increase of wall emissivity; conversely, for the system with mixed BC, total radiative entropy generation linearly decreases. Furthermore, for the system with the prescribed temperature at the walls, radiative entropy generation slightly decreases when medium total pressure increases; while for the problems with mixed BC, increasing medium total pressure does not significantly effect on radiative entropy generation. Finally, results demonstrate that the wall emissivity has a considerable effect on the radiative entropy generation for radiative heat transfer in the non-gray medium in radiative equilibrium.

Experimental and numerical analysis of radiative entropy generation in industrial and boiler furnaces

In this paper, based on the radiative entropy generation formula and the inverse radiation analysis, experimental and numerical analysis of the radiative entropy generation in an oil-fired industrial furnace and a coal-fired boiler furnace is presented. The radiative entropy generation in two-dimensional enclosure solved by Discrete Ordinates method was verified by the second-law thermodynamics analysis. With the reconstructed temperature distribution and radiative properties through the inverse radiation analysis, the radiative entropy generation in the furnace and total net radiative heat on the wall were given. The effects of temperature distribution and optical thickness on total net radiative heat and radiative entropy generation in the furnaces were analyzed. Numerical and experimental results proved, when the optical thickness is small, with the decrease of non-uniformity of temperature distribution of medium, the radiative entropy generation due to radiative processes of medium decreases, and total net radiative heat on the wall also decreases which causes the decrease of the radiative entropy generation due to radiative process on the wall. However, when the optical thickness is large, with the decrease of non-uniformity of temperature distribution of medium, the radiative entropy generation due to radiative processes of medium decreases, but total net radiative heat on the wall increases which causes the increase of the radiative entropy generation due to radiative process on the wall.

Spectral radiative entropy generation in a non-gray planar participating medium including H2O and CO2

Spectral radiative entropy generation through a non-gray absorbing and emitting planar medium is studied. Spectral radiative properties are calculated using the correlated-k (CK) non-gray model with updated parameters based on the HITEMP2010 high-resolution database. The angular and spatial discretization of the radiative transfer equation and radiative entropy generation equation are performed using the discrete ordinates method and the finite volume method, respectively. First, results obtained using the CK model, are compared with the results of the gray model. The calculations reveal that there is a significant difference between results obtained by the gray model and the non-gray model, and the gray assumption generates a remarkable error in the calculations of radiative entropy generation. Then, for comprehensive analysis, five cases have been considered including two homogeneous and isothermal cases, two non-homogeneous and non-isothermal cases filled with H2O or CO2 and one homogeneous and non-isothermal case with a mixture of H2O and CO2. Spectral, local and total radiative entropy generation are calculated for each case and the effect of temperature of the medium, the concentration of participating gas and wall emissivity on radiative entropy generation is attentively investigated. Results show that the radiative entropy generation in the system increases as three aforementioned parameters increase but the effect of gas temperature variations is more than others. Further, the sensitivity of radiative entropy generation due to wall radiation to wall emissivity is decreased when εw rises.

Numerical analysis of radiative entropy generation in a parallel plate system with non-uniform temperature distribution participation medium

The paper presents the numerical investigation of radiative entropy generation in a parallel plate system filling with emitting, absorbing, and scattering non-uniform temperature distribution participation medium. The DRESOR method was used to calculate the radiative entropy generation rate and dimensionless entropy generation. The accuracy of the DRESOR method solving radiative entropy generation was verified by the DO method and the second-law thermodynamics analysis. The effects of temperature difference of medium, emissivity of wall, scattering albedo of medium and optical thickness of the system on the radiative entropy generation rates and dimensionless entropy generation have been analyzed. When the temperature distribution of medium is non-uniform, the radiative entropy generation rate increases and the dimensionless entropy generation decrease as the increase of wall emissivity; and both the entropy generation rate and the dimensionless entropy generation increase as the increase of the scattering albedo. The radiative entropy generation rate increases with the increase of temperature difference of medium when optical thickness is relatively small, while the radiative entropy generation rate decreases with the increase of temperature difference of medium when optical thickness is relative large.

Radiative entropy generation in a gray absorbing, emitting, and scattering planar medium at radiative equilibrium

Radiative entropy generation through a gray absorbing, emitting, and scattering planar medium at radiative equilibrium with diffuse-gray walls is investigated. The radiative transfer equation and radiative entropy generation equations are solved using discrete ordinates method. Components of the radiative entropy generation are considered for two different boundary conditions: two walls are at a prescribed temperature and mixed boundary conditions, which one wall is at a prescribed temperature and the other is at a prescribed heat flux. The effect of wall emissivities, optical thickness, single scattering albedo, and anisotropic-scattering factor on the entropy generation is attentively investigated. The results reveal that entropy generation in the system mainly arises from irreversible radiative transfer at wall with lower temperature. Total entropy generation rate for the system with prescribed temperature at walls remarkably increases as wall emissivity increases; conversely, for system with mixed boundary conditions, total entropy generation rate slightly decreases. Furthermore, as the optical thickness increases, total entropy generation rate remarkably decreases for the system with prescribed temperature at walls; nevertheless, for the system with mixed boundary conditions, total entropy generation rate increases. The variation of single scattering albedo does not considerably affect total entropy generation rate. This parametric analysis demonstrates that the optical thickness and wall emissivities have a significant effect on the entropy generation in the system at radiative equilibrium. Considering the parameters affecting radiative entropy generation significantly, provides an opportunity to optimally design or increase overall performance and efficiency by applying entropy minimization techniques for the systems at radiative equilibrium.

Numerical analysis of entropy generation through non-grey gas radiation in a cylindrical annulus

This study is devoted to analyze the radiative heat transfer of non-grey gas confined in a cylindrical annulus with isothermal walls. The radiative heat transfer equation is resolved through the Ray Tracing method, which is associated to the statistical narrow bands correlated–k (SNBcK) model to compute the medium radiative properties. Special focus is given on the components of radiative entropy generation and its dependency on geometrical and thermodynamic parameters. The results show that entropy generation is greatly affected by gas and wall temperatures. Moreover, the dominance between wall radiative entropy generation and the volumetric one depends mainly on differences between gas and wall temperatures.

SLA (Second-law analysis) of transient radiative transfer processes

This paper concerns a SLA (second-law analysis) of transient radiative heat transfer in an absorbing, emitting and scattering medium. Based on Planck’s definition of radiative entropy, transient radiative entropy transfer equation and local radiative entropy generation in semitransparent media with uniform refractive index are derived. Transient radiative exergy transfer equation and local radiative exergy destruction are also derived based on Candau’s definition of radiative exergy. The analytical results are consistent with the Gouy–Stodola theorem of classical thermodynamics. As an application concerning transient radiative transfer, exergy destruction of diffuse pulse radiation in a semitransparent slab is studied. The transient radiative transfer equation is solved using the discontinuous finite element based discrete ordinates equation. Transient radiative exergy destruction is calculated by a post-processing procedure.

The effect of turbulence–radiation interaction on radiative entropy generation and heat transfer

The analysis under the second law of thermodynamics is the gateway for optimisation in thermal equipments and systems. Through entropy minimisation techniques it is possible to increase the efficiency and overall performance of all kinds of thermal systems. Radiation, being the dominant mechanism of heat transfer in high-temperature systems, plays a determinant role in entropy generation within such equipments. Turbulence is also known to be a major player in the phenomenon of entropy generation. Therefore, turbulence–radiation interaction is expected to have a determinant effect on entropy generation. However, this is a subject that has not been dealt with so far, at least to the extent of the authors’ knowledge. The present work attempts to fill that void, by studying the effect of turbulence–radiation interaction on entropy generation. All calculations are approached in such a way as to make them totally compatible with standard engineering methods for radiative heat transfer, namely the discrete ordinates method. It was found that turbulence–radiation interaction does not significantly change the spatial pattern of entropy generation, or heat transfer, but does change significantly their magnitude, in a way approximately proportional to the square of the intensity of turbulence.

Verification of numerical simulation method for entropy generation of radiation heat transfer in semitransparent medium

The numerical simulation method of radiative entropy generation in participating media presented by Caldas and Semiao [Entropy generation through radiative transfer in participating media: analysis and numerical computation. JQSRT 2005;96:423–37] is extended to analyze the radiative entropy generation in the enclosures filled with semitransparent media. A discrete ordinates method is used to solve radiative transfer equation and radiative entropy generation. Two different examples are employed to verify the numerical simulation method of radiative entropy generation in the enclosure. Numerical results of dimensionless radiative entropy generation of enclosure are identical to that of entire thermodynamics analysis for the enclosure system. This numerical simulation method can be used in the entropy generation analysis of high-temperature systems such as boilers and furnaces, in which radiation is the dominant mode of heat transfer.

On the Entropy Generation Formula of Radiation Heat Transfer Processes

Because thermal radiation is a long-range phenomenon, the local radiative heat flux is dependent on the temperature distribution of the entire enclosure under consideration and is not determined by the local temperature gradient. In the community of heat transfer, traditionally, the conduction-type formula of entropy generation rate is used to calculate the entropy generation rate of radiation heat transfer. In the present study, three counterexamples are considered. The discrete ordinates method is employed to solve the radiative transfer equation and then solve the radiative entropy generation rate. The results show that the traditional formulas of entropy generation rate for heat transfer generally cannot be used to calculate the local entropy generation rate of radiation heat transfer. Only in optically extremely thick situations, the traditional formula of entropy generation rate for heat transfer can be approximately used to calculate the local entropy generation rate of radiation heat transfer.