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.     

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.     

A numerical analysis of slab heating characteristics in a walking beam type reheating furnace

Numerical analysis of slab heating characteristics in a reheating furnace has been accomplished using FLUENT, a commercial software. The phenomena in the furnace are periodically transient because the slabs are transported toward a rolling mill with every time interval controlled. Unsteady calculation has been performed to obtain a periodically transient solution. A User-Defined Function (UDF) program has been developed to process the movement of slabs because FLUENT cannot handle the movement using its default functions. When the mean temperature of a slab emitted to the rolling mill does not change, calculation is considered to have converged and is stopped. This convergence criterion is appropriate for achieving an analytical solution. With the boundary and initial conditions given, over 55 new slabs are inserted to get a converged solution. Skid posts and beams are included in the calculation because they disturb radiation heat transfer from hot combustion gas to the slabs. This article examines what the slabs experience in the furnace before they are emitted to the rolling mill and whether a slab emitted to the rolling mill satisfies the required slab conditions, such as target temperature and skid severity.     

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.     

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.     

Estimation of slab surface radiative emissivities by solving an inverse coupled conduction,convection, and radiation problem

Slab surface radiative emissivities severely affect the radiative heat transfer in a reheating furnace, as well as the slabs’ coupled conduction, convection, and radiation. Accurate evaluation of these parameters is of significance to ensure the high accuracy of the mathematical model for a reheating furnace, which is beneficial to the energy saving. However, it is difficult to directly and accurately measure these parameters. In this article, slab surface radiative emissivities in a reheating furnace are estimated by solving a nonlinear inverse problem, which is an inverse coupled conduction, convection, and radiation problem. An efficient and accurate gradient method, i.e., Levenberg–Marquardt algorithm, is applied to obtain the solution of the inverse problem. First, a finite difference method and the complex-variable-differentiation method are used for sensitivity analysis, and the inversion accuracy coupled with the efficiency is demonstrated. Then, effects of initial guesses, measurement errors, and measurement locations on estimated slab surface radiative emissivities are investigated in detail. Finally, conclusions are drawn based on the results and analysis.     

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.     

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.     

Online simulation model of the slab-reheating process in a pusher-type furnace

This paper presents an online simulation model of the slab-reheating process in a pusher-type furnace in Acroni d.o.o. in Slovenia. The simulation model is connected to the information system of a hot-processing plant that provides online measuring and charging data of the furnace. The simulation model considers the exact geometry of the furnace enclosure, including the geometry of the slabs inside the furnace. A view-factor matrix of the furnace enclosure was determined using the Monte Carlo method. The heat exchange between the furnace gas, the furnace wall and the slab’s surface is calculated using a three-temperature model. The heat conduction in the slabs is calculated using the 3D finite-difference method. The model was validated using measurements from trailing thermocouples positioned in the test slabs during the reheating process in the furnace.A graphical user interface (GUI) was developed to ensure a user-friendly presentation of the simulation-model results.     

Mathematical modeling and optimization of hydrogen distribution network used in refinery

In the present investigation, mathematical models have been developed to optimize hydrogen distribution in the refinery. Five models, Model-0, Model-1, Model-2, Model-3 and Model-4, have been formulated to determine the optimal hydrogen network. Amongst these, Model-0 and Model-1 are NLP networks, whereas the remaining three are MINLP networks. The NLP models are improved gradually to develop MINLP models which incorporate new compressor and PSA. The model considers pressure constraints, source flow balance, sink flow balance, compressor flow balance, sink purity constraint, operating cost, capital cost associated with new equipment, payback period and export cost. Amongst five models, Model-4 is predicted as optimal network which is MINLP model incorporating new compressor and PSA. It predicts reduction in hydrogen by 21.74% and annual profit of $ 16.57 million. The present work selects the optimal type of new compressor based on different capital cost functions. Further, the reliability of the present work is checked through comparison of its results with published models.     

Optimum residence time analysis for a walking beam type reheating furnace

A 3D unsteady numerical simulation of a reheating furnace was performed to obtain the optimal slab residence time. Too long residence time decrease the efficiency of the reheating furnace, whereas too short residence time cannot satisfy the required heating quality of a slab. The total five cases of residence times – 6032 s, 6496 s, 6960 s, 7424 s and 7888 s – were investigated for the optimum residence time analysis with the two slab requirements, those of emission temperature and uniformity. In this study, the slab emission temperature should be in the range between 1373 K and 1573 K. The skid mark severity of an emitted slab should be lower than 50 K to satisfy the uniformity requirement. The numerical analysis was done for the identical geometry and operating condition of the reheating furnace using FLUENT. Slabs were assumed to move very quickly that it took no time for them to move next positions. The quick movements of slabs were processed with the own developed User-Defined Function program. Among the five cases of residence times, the residence time of 7427 s turned out to be most efficient.     

加热炉钢坯加热质量的数值模拟研究

处理不同入炉温度的钢坯需采用合理的加热时间和工艺,针对此问题,采用数值模拟的方法研究人炉温度分别为200,400,600,700℃的钢坯最佳加热时间和加热质量。通过利用Fluent流体计算软件建立了钢坯非稳态导热模型和氧化烧损模型,模拟结果表明：在相同的加热工艺下,钢坯人炉温度为27℃,炉内停留时间为180min时,位于预热段的第5块钢坯表面受到的辐射热流最大,达到92kW／m^2,出炉钢坯氧化率为1．419％;钢坯入炉温度为200℃时,合理的炉内停留时间为150min,出炉温度达到1183℃,出炉钢坯氧化率为1．307％。     

Onset of convection in a vertical slab of saturated porous media between two impermeable conducting blocks

The onset of natural convection in a vertically oriented, finite thin slab of saturated porous material is considered. The slab is embedded between two impermeable conducting blocks of finite dimension. A vertical temperature difference is imposed between the upper and lower horizontal surfaces of the slab and blocks, and a linear temperature distribution is imposed on the outer vertical surfaces of the blocks. This configuration is used to model convection in a saturated, fractured rock zone like that associated with faulting. A linear stability analysis is developed for both convection in the slab and conduction in the block. The objective of the study is to obtain the critical Rayleigh number and mode of convection in the slab. When the block and the slab widths are both small compared to the other two dimensions one finds a large number of tall, narrow, three-dimensional cells. In contrast, a block of relatively large width promotes the formation of longer wavelength, weakly three-dimensional cells in the slab at a much lower Rayleigh number. The difference is related to the character of the temperature distribution in the solid block.     

Horizontal concrete slabs as passive solar collectors

Natural convection, radiation and conduction heat transfer on horizontal concrete slab systems is experimentally studied. The system was a 0.78 m long, 0.40 m wide and 0.10 m thick concrete slab. A heat source was used to impose a constant heat flux which could be varied from about 200 to 700 W/m². Temperatures at various points and heat flux by natural convection at the horizontal surface were measured. Using various assumptions, the system was also analyzed theoretically. It is found that the mathematical model to study the transient heat transfer in the slab system was satisfactory to predict its thermal behavior in various conditions. An empirical correlation for natural convection on the horizontal concrete slab was derived and used in the analysis. The results showed that the incident energy on the concrete slab was not a parameter affecting strongly the absorbed heat by the slab, the radiation heat losses made about 60% while those by natural convection 40%, and the major energy storage–restitution was taking place during the first 3 to 4 h. The optimization of energy storage density and the thermal performance was also discussed and various parameters affecting them were defined.     

Maximum thermal load levelling in a double hollow wall/roof

The effect of a metal sheet in the middle of a hollow concrete slab, on the thermal performance of the concrete slab has been studied; one face of the wall/roof is exposed to solar radiation and ambient air and the other is in contact with room air at constant temperature. the optimum distribution of inside and outside concrete thicknesses for maximum thermal load levelling has been obtained; it is seen that this is achived when the outer concrete thickness is as small as possbile. These result have also been compared with the results corresponding to single hollow and double hollow concrete slabs.     

Performance of various design of solar air heaters for crop drying applications

Different heat sources are employed for the drying of agricultural products. However, in many rural locations in most developing countries, supplies of non-renewable sources of energy are either unavailable, unreliable or, for many farmers, too expensive. In renewable energy sources, solar energy is the most appropriate for drying systems. This energy allows independent systems to be constructed and possesses a thermal conversion mode which necessitates a simple technology which is adapted to the rural regions for crop drying applications. These systems are all based on the air heating flat plate solar collectors.Therefore, six different types of natural circulation air heating solar collectors (Model-1: single plastic glazing, black painted hardboard absorber and front-pass; Model-2: single plastic glazing, black painted flat plate absorber and front-pass; Model-3: single plastic glazing, black painted zigzag plate absorber and front-pass; Model-4: single plastic glazing, black painted flate plate absorber and back-pass; Model-5: single plastic glazing, black painted zigzag plate absorber and back-pass; Model-6: double plastic glazing, black painted flat plate absorber and back-pass) were designed, constructed and analysed for their performance in this study. Each collector mainly consisted of a frame constructed from hardboard, vent holes, hardboard insulation, absorbing surface made of black coated aluminium sheet and clear plastic glazing.All solar air heaters were mounted on a stand facing south at an inclination angle, and they were tested simultaneously under the same environmental conditions. The experimental setup was instrumented for the measurement of solar radiation, temperature and relative humidity of the atmosphere air, outlet air temperature, surface temperature of the back and edge insulator and absorber plate, air speed and wind velocity.It is understood from the results of the investigation that the performances of Model-1, Model-2, Model-3, Model-4, Model-5 and Model-6 are 42.11, 45.88, 44.23, 39.76, 39.05 and 36.94% respectively, and the performance of the most efficient collector (Model-2) is aproximately 9% more than the least efficient one (Model-6). In addition, it is seen that unlike number of glazing sheet and air pass method, the effect of the shape of the absorbing surface on the performance is considerably less.     

Time-varying heat transfer from adjacent slab-on-grade floors

A steady-periodic solution for the heat conduction problem under a slab-on-grade floor adjacent to another slab is presented. The two slabs can be uninsulated or uniformally insulated. A water table is assumed to exist at finite depth from the soil surface. The interzone temperature profile estimation technique is used to develop a semi-analytical solution for the heat conduction equation in the ground medium. The soil temperature field, and the total slab heat loss are obtained and analysed in detail. The effect of the distance that separates the adjacent slabs on the mean and amplitude of total slab heat loss is discussed. © 1998 John Wiley & Sons, Ltd.     

导流板式煤粉燃烧器解决炉内结渣的数值试验

用投影法计算喷口出口和炉内空气动力场。用蒙特卡洛法计算了炉内的辐射换热，用有限差分法计算了对流换热和导热，最后求解出炉内的温度分布。数值试验结果表明，采用了导流板式煤粉燃烧器，可有效减小炉内切圆直径，降低水冷壁附近的温度水平，防止炉内结渣的发生。在某300MW机组上的成功应用，验证了本数值试验的正确性。该方法的提出为解决大型电站锅炉内结渣问题提供了一条行之有效的途径。     

Periodic heat transfer through inhomogeneous media. Part 1. Slab

The paper presents exact analytical solutions of one-dimensional periodic heat conduction through an inhomogeneous slab for a certain class of thermal conductivity profiles (including linear and exponential). The exact analytical solutions for some of these profiles have been compared with those obtained by considering the slab to be made up of a number of homogeneous layers with different thermal conductivities varying from layer to layer and using the layered structure (or matrix multiplication) method. The numerical results arrived at by the layered-structure method converge rapidly (with increasing number of layers considered) to the values obtained from the exact analytical solutions. This gives confidence in the application of the layered-structure method to periodic heat conduction through inhomogeneous slabs. The numerical results have been presented in the form of elements of a 2 × 2 matrix, relating the sinusoidal steady-state temperature and heat flux on the two sides of the slab.     

木材在火灾环境中热解行为的数值模拟

建立了火灾环境中木材热解行为的数学物理模型，模型包含瞬态热传导、对流传热、热解过程的热效应和非线性边界条件热解过程中炭表面的收缩情况。对影响木材热解过程的物理参数进行了讨论，并利用211工程建设的火灾早期特性实验台对较大尺寸的木板在模拟火灾条件下的热解过程进行了实验研究，和模型计算的结果比较，两者相符较好。