A heat transfer model for the analysis of transient heating of the slab in a direct-fired walking beam type reheating furnace

A mathematical heat transfer model for the prediction of heat flux on the slab surface and temperature distribution in the slab has been developed by considering the thermal radiation in the furnace chamber and transient heat conduction governing equations in the slab, respectively. The furnace is modeled as radiating medium with spatially varying temperature and constant absorption coefficient. The steel slabs are moved on the next fixed beam by the walking beam after being heated up through the non-firing, charging, preheating, heating, and soaking zones in the furnace. Radiative heat flux calculated from the radiative heat exchange within the furnace modeled using the FVM by considering the effect of furnace wall, slab, and combustion gases is introduced as the boundary condition of the transient conduction equation of the slab. Heat transfer characteristics and temperature behavior of the slab is investigated by changing such parameters as absorption coefficient and emissivity of the slab. Comparison with the experimental work show that the present heat transfer model works well for the prediction of thermal behavior of the slab in the reheating furnace.     

Transient radiative heating characteristics of slabs in a walking beam type reheating furnace

Transient radiative heating characteristics of slabs in a walking beam type reheating furnace is predicted by the finite-volume method (FVM) for radiation. The FVM can calculate the radiative intensity absorbed and emitted by hot gas as well as emitted by the wall with curvilinear geometry. The non-gray weighted sum of gray gas model (WSGGM) which is more realistic than the gray gas model is used for better accurate prediction of gas radiation. The block-off procedure is applied to the treatment of the slabs inside which intensity has no meaning. Entire domain is divided into eight sub-zones to specify temperature distribution, and each sub-zone has different temperatures and the same species composition. Temperature field of a slab is acquired by solving the transient 3D heat conduction equation. Incident radiation flux into a slab is used for the boundary condition of the heat conduction equation governing the slab temperature. The movement of the slabs is taken into account and calculation is performed during the residence time of a slab in the furnace. The slab heating characteristics is also investigated for the various slab residence times. Main interest of this study is the transient variation of the average temperature and temperature non-uniformity of the slabs.     

Efficiency analysis of radiative slab heating in a walking-beam-type reheating furnace

The thermal efficiency of a reheating furnace was predicted by considering radiative heat transfer to the slabs and the furnace wall. The entire furnace was divided into fourteen sub-zones, and each sub-zone was assumed to be homogeneous in temperature distribution with one medium temperature and wall temperature, which were computed on the basis of the overall heat balance for all of the sub-zones. The thermal energy inflow, thermal energy outflow, heat generation by fuel combustion, heat loss by the skid system, and heat loss by radiation through the boundary of each sub-zone were considered to give the two temperatures of each sub-zone. The radiative heat transfer was solved by the FVM radiation method, and a blocked-off procedure was applied to the treatment of the slabs. The temperature field of a slab was calculated by solving the transient heat conduction equation with the boundary condition of impinging radiation heat flux from the hot combustion gas and furnace wall. Additionally, the slab heating characteristics and thermal behavior of the furnace were analyzed for various fuel feed conditions.     

Performance Evaluation of Two Heat Transfer Models of a Walking Beam Type Reheat Furnace

Two different heat transfer models for predicting the transient heat transfer characteristics of the slabs in a walking beam type reheat furnace are compared in this work. The prediction of heat flux on the slab surface and the temperature distribution inside the slab have been determined by considering thermal radiation in the furnace chamber and transient heat conduction in the slab. Both models have been compared for their accuracy and computational time. The furnace is modeled as an enclosure with a radiatively participating medium. In the first model, the three-dimensional (3D) transient heat conduction equation with a radiative heat flux boundary condition is solved using an in-house code. The radiative heat flux incident on the slab surface required in the boundary condition of the conduction code is calculated using the commercial software FLUENT. The second model uses entirely FLUENT along with a user-defined function, which has been developed to account for the movement of slabs. The results obtained from both models have a maximum temperature difference of 2.25%, whereas the computational time for the first model is 3 h and that for the second model is approximately 100 h.     

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…     

Simultaneous radiation and conduction heat transfer in a graded index semitransparent slab with gray boundaries

The simultaneous radiation and conduction heat transfer in a semitransparent slab of absorbing-emitting gray medium is solved in this paper. The refractive index of the medium spatially varies in a linear relationship, and the two boundary walls are diffuse and gray. A curved ray tracing technique in combination with a pseudo-source adding method is employed to deduce the radiative intensities on gray walls. Resorting to some of the results presented by Ben Abdallah and Le Dez, an exact expression of the radiative flux in medium is deduced. The influences on the temperature and radiative flux fields are examined, which are caused by the refractive index distribution, absorbing coefficient, thermal conductivity and the boundary wall emissivities. The results display the significant influences of the refractive index distribution and boundary wall emissivities on the radiative flux and temperature in medium.     

Improved social spider optimization algorithms for solving inverse radiation and coupled radiation–conduction heat transfer problems

A novel bio-inspired swarm algorithm, social spider optimization (SSO), is introduced to solve the inverse transient radiation and coupled radiation–conduction problems for the first time. Based on the original model, five improved SSO (ISSO) algorithms are developed to enhance search ability and convergence velocity. The sensitivity analysis of measured signals with respect to the physical parameters of the medium are described. After which, the SSO and ISSO algorithms are applied to solve the inverse estimation problems in a one-dimensional participating medium. Two cases concerns radiative transfer problems are investigated, in which the radiative source term, extinction coefficient, scattering albedo, and scattering symmetry factor are reconstructed. Furthermore, the coupled radiation–conduction heat transfer model is considered and the main parameters such as the conduction–radiation parameter, boundary emissivity, and scattering albedo are retrieved. All retrieval results show that SSO-based algorithms are robust and effective in solving inverse estimation problems even with measurement errors. Findings also show that the proposed ISSO algorithms are superior to the original SSO model in terms of computational accuracy and convergence velocity.     

燃烧产物辐射特性的误差对炉内辐射传热计算精度的影响

本文用离散坐标法对含吸收散射性介质矩形空腔内的３维辐射传递过程进行了模拟，并编写了相应的数值计算程序。利用该程序分析了介质的吸收系数、散射系数、相函数、光谱特性及壁面灰渣沉积层黑度的不确定性对矩形燃烧室内烟气温度及热流计算精度的影响。结果表明计算精度很大程度上取决于燃烧产物辐射特性的取值精度，特别是壁面灰渣沉积层黑度的取值精度。在煤粉燃烧室中，介质的散射不宜忽略。     

Experimental investigation on simultaneous measurement of temperature distributions and radiative properties in an oil-fired tunnel furnace by radiation analysis

The paper reports experimental investigations on simultaneous measurement of temperature distribution and radiative properties in an oil-fired tunnel furnace by radiation analysis. Two color CCD cameras were used to obtain visible thermal radiation in the furnace. A radiation imaging model was established by the calculation of radiative transfer equation in the furnace. The temperature distribution and radiative properties can be obtained from the inversion of the radiative imaging model. The validity of radiative imaging model was verified by the numerical analysis of cavity radiation and isothermal system radiation, and the accuracy of reconstruction method was validated by simulation reconstruction. The experimental analysis was divided into two parts. Firstly, the temperatures of wall surface were calculated from the radiative image of refractory wall and compared with the measured temperature of a thermocouple. The difference between the two methods was only about 20 K. Secondly, the temperature distributions in the furnace, absorption coefficients of combustion medium, and emissivities of refractory wall were reconstructed. Because of a single burner in the tunnel furnace, the temperature distributions in the XY vertical sections in the furnace were with temperature higher in the center and lower near the refractory wall surface, and the temperatures decreased along the length of the tunnel furnace. The measured emissivity of refractory wall showed that the refractory material of RPA-MC30 is with high reflectivity in visible spectrum.     

燃烧室内三维温度场的辐射反问题

本文提出了一种在介质辐射特性已知的条件下,由壁面入射辐射热流的测量值反演燃烧室内三维温度场的方法。该方法是在辐射传递方程离散坐标近似的基础上,用求目标函数极小值的共轭梯度法进行反演计算。通过对吸收系数、散射不对称因子、反照率、壁面黑度和燃烧室大小尺寸等参数对反演精度影响的分析,结果表明,即使存在随机测量误差,这些参数对温度场反演精度的影响也不大,本文所提出的方法可较精确地反演燃烧室内三维温度场。     

Comparisons of different heat transfer models of a walking beam type reheat furnace

Four different heat transfer models (Model-1 to -4) for the prediction of temperature of the slabs of a walking beam type reheat furnace have been compared. The models are classified based on the solution methodology and simplifications. In the first three models (Model-1 to -3), the furnace is modelled as radiating medium with spatially varying known temperature. Model-1 solves the 3D transient conduction in the slab and radiation in the furnace separately and is coupled via the boundary condition. In the second model, both radiation in the furnace and conduction in the slab are solved simultaneously. A user defined function (UDF) programme has been developed to process the movement of the slabs. Model-3 is similar to Model-2 but it includes additionally the skid support systems for the slabs. In the Model-4, convection in the furnace has been included in addition to all the features considered in Model-3. The convection has been modelled with the consideration of flow of hot gas through the inlet of the burners. All the models have been compared for their performance and computational time. Model-1 has been found to be quite economical and accurate. The inclusion of skid supporting system has little effect in the temperature distribution in the slab.     

Radiative slab heating analysis for various fuel gas compositions in an axial-fired reheating furnace

A transient radiative slab heating analysis was performed to investigate the effect of various fuel mixtures on the performance of an axial-fired reheating furnace. The various fuel mixtures tested were assumed to be attained by mixing COG (coke oven gas) and BFG (blast furnace gas), which are the two main byproduct gases found in the integrated steel mill industry. The numerical prediction of radiative heat transfer was calculated using an FVM radiation solving method, which is a well-known and efficient method for curvilinear coordinates. The WSGGM (weighted sum of gray gas model) was also adopted to calculate the radiative heat transfer in composition dependent media. The entire furnace was divided into fourteen sub-zones to calculate the radiative thermal characteristics of the furnace without flow field calculations. Each sub-zone was assumed to have homogeneous media and wall temperatures. All of the medium and wall temperatures were computed by calculating the overall heat balance using some relevant assumptions. The overall heat balance was satisfied when the net heat input equaled the three sources of heat loss in each sub-zone, wall loss, skid loss, and slab heating loss.     

Inverse boundary design of a radiant furnace with diffuse-spectral design surface

An optimization technique is applied to inverse design of radiative furnaces with diffuse-spectral surfaces. The variation of emissivity with respect to the wavelength is approximated by considering a set of spectral bands with constant emissivities and then the radiative transfer equation is solved by the net radiation method for each band. The conjugate gradient method is used for estimation of temperatures over reflector and heater surfaces. The sensitivity problem is approximated by differentiation of the radiative transfer equation with respect to the unknown variables. The performance of the present method is evaluated by comparing the results with the results obtained by considering a diffuse-gray design surface.     

Entropy Generation due to Combined Natural Convection and Thermal Radiation within a Rectangular Enclosure

ABSTRACT

The present work investigates entropy production due to coupled natural convection/radiation heat transfer phenomenon in an inclined rectangular enclosure, isothermally heated from the bottom side and isothermally cooled from the other sides. The discrete-ordinate method is used in modeling the radiative transport equation while the statistical narrow band correlated-k model is adopted to deduce the radiative properties of the medium. The influence of pertinent parameters such as aspect ratio, inclination angle and walls emissivities on entropy generation is studied. It is found that the volumetric entropy generation is reduced when increasing the inclination angle of the enclosure. Moreover, it is shown that the minimum entropy production due to radiation heat transfer in participating media occurs at aspect ratio equal to unity.     

A Coupled Numerical Study of Slab Temperature and Gas Temperature in the Walking-Beam-Type Slab Reheating Furnace

In the present study, a three-dimensional simulation is performed for the turbulent reactive flow and radiactive heat transfer in the walking-beam-type slab reheating furnace using STAR-CD software. The geometric model takes care of all components of the furnace. To obtain a steady solution, the walking beams are assumed fixed in the furnace and the slab is modeled as a laminar flow having a very high viscosity and thus moving at a nearly constant speed. The temperature distributions of the slab and the gas mixture are obtained through a coupled calculation. The simulation results successfully predict the temperature distribution inside the slab and the heat flux on the slab surfaces, providing an opportunity for a full exploration of the influence of the walking beam system on the skid marks. The simulation results show that the radiative shielding by the static beams is the main cause of the skid marks. The heat loss through the skid button to the cooling system worsens the skid marks.     

Inverse Boundary Design Problem of Turbulent Forced Convection Between Parallel Plates With Surface Radiation Exchange

The inverse methodology is employed to estimate the unknown heat flux distribution over the heater surface of a channel formed by two parallel plates with forced convection and surface radiation exchange, from the knowledge of the desired temperature and heat flux distributions over a given design surface. The energy and radiative transfer equations are solved by the finite-volume method and the net radiation method, respectively. The conjugate gradient method is used for minimization of an objective function, which is expressed by the sum of square residuals between estimated and desired heat fluxes over the design surface. The performance and accuracy of the present method for solving inverse problems are evaluated by some numerical experiments.     

On the treatment of non-optimal regularization parameter influence on temperature distribution reconstruction accuracy in participating medium

The choice of the regularization parameter plays a very important role in the inverse radiation problem of temperature distribution in participating medium and in practice the regularization parameter is not easy to determine accurately, which can directly affect the reconstruction accuracy and introduce errors into reconstruction results. This paper presents the alleviation of non-optimal regularization parameter influence on the temperature distribution reconstruction accuracy in participating medium using coupled methods, i.e., two kinds of regularization method (least square QR decomposition (LSQR) method and truncated singular value decomposition (TSVD) method) coupled with genetic algorithm (GA). The radiative heat transfer was described by the backward Monte Carlo method for its efficiency. Two kinds of temperature distributions with one peak and two peaks are considered. The results show that GA can still improve the accuracy of solutions even though the optimal regularization parameters are used in the coupled methods (LSQR-GA and TSVD-GA). GA can also reduce the temperature reconstruction errors due to the non-optimal choice of the regularization parameter and improve the accuracy of the reconstruction results in the coupled methods. Moreover, the coupled methods can even reach the same or better solutions accuracy for some samples with non-optimal regularization parameter, compared with the accuracy of solutions obtained by the single LSQR method or TSVD method with the optimal regularization parameter. This study demonstrates that the coupled method can alleviate non-optimal regularization parameter influence and obtain more accurate results for the inverse radiation problem of temperature distribution in participating medium.     

Inverse radiation analysis of a one-dimensional participating slab by stochastic particle swarm optimizer algorithm

A stochastic particle swarm optimizer (SPSO) algorithm, which can guarantee the convergence of the global optimization solution with probability one, is adopted to estimate the parameters of radiation system. To illustrate the performance of this algorithm, three cases are investigated, in which the source term, the extinction coefficient, the scattering coefficient, and the non-uniform absorption coefficients in a one-dimensional slab are retrieved. The directional radiative intensity, reflectance and transmittance, radiative flux simulated by discrete ordinate method (DOM) are served as input for the inverse analysis, respectively. By SPSO algorithm presented, all these radiative parameters could be estimated accurately, even with noisy data. In conclusion, the SPSO algorithm is proved to be fast and robust, which has the potential to be implemented in various fields of inverse radiation problem.     

A probabilistic study of the influence of parameter uncertainty on thermal radiation heat transfer

The influence of uncertainty in the boundary conditions on the solution of the radiative transfer equation is studied using probabilistic methods. We consider the problem of a heated slab, the surfaces and volume of which are at fixed temperatures. The basic problem stemmed from the need to study a hypothetical accident scenario in a fast breeder nuclear reactor in the cover gas region which may contain a sodium aerosol. The emissivities of the surface of such a region will be uncertain and estimates must be made. We demonstrate how the uncertainties in these data parameters are transmitted to the solution of the associated transfer equation and define sensitivity coefficients for the configuration factors. We also consider a number of different material surfaces, the emissivities of which are only known within certain limits, and obtain sensitivity coefficients for them as well as mean values, variances and, in some cases, the probability distribution of the configuration factors. A variational method is used to solve the basic equation, but for more general problems where such methods are inapplicable we describe a technique based on polynomial chaos theory.     

Investigation of the slab heating characteristics in a reheating furnace with the formation and growth of scale on the slab surface

In this work, the development of a mathematical heat transfer model for a walking-beam type reheating furnace is described and preliminary model predictions are presented. The model can predict the heat flux distribution within the furnace and the temperature distribution in the slab throughout the reheating furnace process by considering the heat exchange between the slab and its surroundings, including the radiant heat transfer among the slabs, the skids, the hot combustion gases and the furnace wall as well as the gas convection heat transfer in the furnace. In addition, present model is designed to be able to predict the formation and growth of the scale layer on the slab in order to investigate its effect on the slab heating. A comparison is made between the predictions of the present model and the data from an in situ measurement in the furnace, and a reasonable agreement is found. The results of the present simulation show that the effect of the scale layer on the slab heating is considerable.