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.     

板坯加热炉内加热特性的数值分析

以某公司热轧厂常规与双蓄热烧嘴组合供热的板坯加热炉为研究对象,建立该加热炉炉内流动、传热、燃烧和板坯运动吸热过程的三维物理数学模型,运用CFD仿真技术对其进行详细的数值计算,得到炉内稳态的速度场和温度场分布规律、板坯的升温曲线以及板坯温度分布均匀性,计算结果与"黑匣子"实验测量数据吻合良好。本文给出的板坯加热特性计算方法为研究加热炉新工艺、优化板坯加热温度制度提供了科学依据。     

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.     

Shock wave boundary layer interactions in hypersonic flows over a double wedge geometry by using conjugate heat transfer

Shock wave boundary layer interaction phenomena play a critical role in the design of supersonic and hypersonic vehicles. Consequently, this paper mainly focuses on hypersonic flow over a double wedge model, flow fields around concave corners are relatively complicated, and produce several classical viscous flow features depending on the combination of the first and second wedge, and the important characteristic phenomena are mainly the shock‐boundary layer and shock‐shock interaction. For these interactions, aerodynamic heating and pressure loads increase greatly when interactions are present. The conjugate heat transfer (CHT) technique is expected to exactly predict the separation bubble length, heat flux, skin friction coefficient, and pressure distributions in double wedge studies in hypersonic applications. In the present CHT studies, the different wall materials used are thermal insulation, Macor, and SiC, it is clearly shown that while using Macor and thermal insulctation wall material in CHT studies, the interface temperature, skin friction coefficient, heat flux distribution along the length change significantly with increase in simulation time. In comparing the CHT results with the fluid flow solver with the wall, considering isothermal and adiabatic boundary results, it is clearly indicated that the fluid flow solver results are either underpredicting or overpredicting the interface properties, but CHT studies give an accurate prediction of the separation length and interface properties.     

基于步进式加热炉数学模型的氧化烧损预测模拟

针对钢铁企业的氧化烧损问题,用数值模拟的方法进行预测分析。利用CFD流体计算软件建立了炉内流动、燃烧、辐射、钢坯导热和氧化烧损模型,流动模型采用k—ε湍流模型,燃烧采用PDF燃烧模型,辐射换热模型采用离散坐标（DO）辐射模型,热流密度做为钢坯导热的边界条件,模拟钢坯在实际工况下的结果表明,氧化铁皮的快速增长期是在钢坯入炉50～120min之间,位于加热段;在不同均热时间下,钢坯氧化率随均热时间呈线性增长。据此结论,现场操作人员可通过强化加热段加热能力的手段减少钢坯在加热段的停留时间或热装钢坯调整总的在炉时间来降低钢坯氧化烧损率以提高钢坯加热质量。     

连铸连轧辊底式加热炉薄板坯的温度场计算

分析了CSP工艺中辊底式加热炉及炉中板坯的换热特性,建立了板坯换热的二维非稳态数学模型,用差分法计算出了加热炉中不同时刻板坯断面的温度场,给出了板坯在加热炉中的温度变化曲线,为优化加热炉的加热制度提供了理论依据。     

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.     

Study on heating performances of steam generator for solid oxide fuel cell using waste heat from solid particles

This paper reports the heating performances of steam generator for solid oxide fuel cell using waste heat from solid particles. The model of trapezoid-fin-tube heat exchanger was set up by using FLUENT 14.0. The model has been used to investigate the effects of fin tip width (2 mm–4 mm) and fin height (34 mm–46 mm). The fin surface temperature, the particle temperature, the fin total heat flux, the heat recovery efficiency and the heat transfer coefficient were studied. The heating performance of steam generator is improved when the trapezoid-fins are placed on heat transfer tubes, which is conducive to increase the power generation efficiency of solid oxide fuel cell. When the fin height increases from 34 mm to 46 mm, the average temperature of calcined petroleum coke decrease from 414 K to 376 K, the maximum temperature decrease from 498 K to 442 K, the average heat transfer coefficient of internal and external heat exchanger increase 12.4% and 12.7% respectively, the heat recovery efficiency increases 4.3%. When the fin tip width increases from 2 mm to 3 mm, the average temperature reduce 6.7 K and the maximum temperature decrease 7.3 K, the average heat transfer coefficient of internal and external heat exchanger increase 3.8% and 3.7% respectively, the heat recovery efficiency increases 0.88%.     

Heat transfer during pool boiling based on evaporation from micro and macrolayer

An analytical model of heat transfer based on evaporation from the micro and macrolayers to the vapor bubble during pool boiling is developed. Evaporation of microlayer and macrolayer during the growth of individual bubbles is taken care of by using temporal and spatial variation of temperature in the liquid layer. Change of bubble shape during the entire cycle of bubble growth and departure is meticulously considered to find out the rate of heat transfer from the solid surface to the boiling liquid. Continuous boiling curve is developed by considering the bubble dynamics and decreasing thickness of liquid layer along with the increase of dry spot radius. Transient variation of macrolayer and microlayer thickness is predicted along with their effect on CHF. Present model exhibits a good agreement with reported experimental data as well as theories.     

THERMOELASTIC BEHAVIOR OF A COMPOSITE SLAB UNDER A RAPID DUAL-PHASE-LAG HEATING

This work is concerned with the investigation of the thermoelastic response of a composite slab (a two-, thin-, metallic-layered plate) under the effect of an intense rapid heating applied to one side. The dual-phase-lag heat conduction model is used to derive the heat equation in each layer. The heat equations are solved using the Laplace transform technique and the Riemann-sum method. As a result, the thermal behavior, in the form of the temperature distribution along the thickness direction of the slab, is determined. The governing equation of plate deflection is formulated and solved for simply supported edge conditions. As a result, the plate deflections and the thermal stresses are calculated numerically using the finite difference method. Thermal stress distribution is found to depend on the temperature distribution in addition to the difference in the thermal and mechanical properties of the materials that compose the two layers.     

Heat transfer in a directly irradiated solar receiver/reactor for solid–gas reactions

Particle laden solar receivers can be used at high temperatures for efficient heat transfer and fuel generation via chemical reactions. A theoretical analysis of a directly irradiated, particle laden, solar receiver is presented here and compared with experiments. The radiation characteristics of the particles are approximated using a method, which adapts Mie theory to certain cases where a solar receiver is used with seeded particles of variable sizes and shapes. Based on this model carbon black particles whose effective radius, r_p, is less than 100 nm are inefficient in absorbing solar energy and the most suitable particle sizes is in the same range as the wavelengths of the radiation (100 nm < r_p < 1000 nm). The heat transfer coefficient between the particles and the gas was calculated using a refined limiting sphere model developed for the transition regime between molecular and continuum transfer. Previous models assume that there are no gas molecule collisions in the energy transfer layer and the mean free path of the gas molecules is equal to the thickness of this layer. The present model accounts for molecule collisions in the energy transfer layer and therefore enables the thickness of this layer to be larger than one mean free path length. The model was extended to estimate the Nusselt number for gases with several atoms as well as for monatomic gas. A code to simulate the flow and heat transfer in the receiver was developed, utilizing the models for heat transfer from sunlight to the particles and from the particles to the gas. The receiver simulations show good agreement with the wall temperature distribution measured in experiments, but the gas exit temperature in the model was significantly lower than the measured value. This discrepancy could be due to limitations of the simulation code and the particle heat transfer models. The simulation suggests that changing the Nusselt number and particle radius have a small influence on the receiver wall and gas temperatures. Increasing the particle cloud concentration improves the receiver heat transfer up to a threshold value; further increase of the particles concentration has only a marginal influence on the receiver’s heat transfer. This result from the receiver modeling was in a good agreement with solar experiments.     

Numerical and experimental analysis of floor heat storage and release during an intermittent in-slab floor heating process

In this paper, the floor heat storage in the preheating period and the heat release in the intermittent period during an intermittent in-slab floor heating process are investigated. Numerical simulations are used to determine the effect of the design and operating parameters, i.e., the pipe spacing, the filling layer thickness and the pipe water temperature, on the floor heat storage and heat release. The relationship between the intermittent time and the preheating time is also obtained. The results show that pipe spacing has the dominant effect on the preheating time. In the intermittent period, 2 h later, the two-dimensional heat transfer process can be modeled as a one-dimensional vertical heat transfer process, and the filling layer thickness has a relatively large effect on the heat release time. The numerical simulation method is shown to be accurate to at least within 7% of the experimental measurements.     

Periodic heat transfer through a hollow concrete slab: Optimum placement of the air gap

This paper describes an investigation of the periodic heat transfer and optimum placement of the air gap in a hollow concrete slab subjected to solar radiation and atmospheric air on one side and in contact with air at a fixed temperature on the other. The heat conduction equation has been solved using the appropriate boundary conditions at the interfaces. It is found that the presence of an air gap considerably reduces the heat flux through the slab; further, for a given total thickness of concrete the best load levelling is achieved when the thickness of the outer layer of the concrete is least, consistent with structural considerations.     

CSP薄板坯连铸连轧热过程的数值模拟

细致研究了CSP工艺中连铸，均热保温缓冲及其连轧过程对板坯/轧板传热的影响，建立了薄板生产热过程中板坯/轧板温度变化规律的二维非稳态数学模型，通过较精确研究连铸过程中坯壳-结晶器交界面传热，均热热保温过程辐射换热及其连轧过程中轧板-轧辊交界面传热模型，确定板坯/轧板在CSP过程中的复杂边界条件，模型计算结果与邯钢CSP生产线板坯实例数据相吻合。     

Configuration of the micro-layer and characteristics of heat transfer in a narrow gap mini/micro-channel boiling system

Heat transfer measurements were performed in a mini/micro-channel boiling system for water, and the thickness of the micro-layer that formed between the heating surface and the generated vapor under vapor growth was measured by application of the laser extinction method for narrow gaps of 0.5, 0.3 and 0.15 mm. The process of bubble growth was recorded by using a high-speed camera simultaneously. The effects of gap size, the velocity of vapor bubble forefront and the distance from the incipient bubble site were investigated on the micro-layer thickness in a narrow gap mini/micro-channel boiling system and the configuration of the thin liquid micro-layer distributions on the heat transfer surface was clarified. Furthermore, factors that would possibly affect the mechanism and characteristics of heat transfer, such as the position of the generated vapor bubble, the velocity of the vapor forefront, the micro-layer dominant period and the liquid saturation period in the boiling cycle, and so forth, were quantitatively investigated and analyzed on the basis of the measured data. The heat transfer characteristics were analyzed and the data calculated were coincided with the measured data in the boiling curve for the gap size of 0.5 and 0.25 mm measured in the previous report. It was shown that the heat transfer was enhanced due to the micro-layer evaporation.     

Magnetohydrodynamic MgO/CuO‐water hybrid nanofluid flow driven by two distinct geometries

Research regarding the heat transit mechanism of magnetohydrodynamic hybrid nanoliquid flow over contrasting flow profiles is predominantly employed in transpiration, coolants, fiber coatings, heat exchangers, and so on. Owing to this, we intend to dissect the heat transport behavior of MHD hybrid nanofluid flow past a cone as well as a wedge. For the analysis, we take nonlinear radiation and viscous dissipation into consideration with 30% of ethylene glycol and water (or EGW) as base fluid with suspended copper oxide (CuO) and magnesium oxide (MgO) nanoparticles. The Runge‐Kutta method with the shooting technique is utilized to figure out the deduced nonlinear gotverning equations. The influence of the concerned different admissible parameters on similar distributions (cone and wedge) are graphically illustrated and interpreted accordingly via computed numerical values. It is worth noting that the heat transport rate is greater past the cone rather than the wedge. The presence of CuO and MgO hybrid nanoparticles increases the heat transfer rate of the EGW base fluid.     

板坯加热炉内常规燃烧与富氧燃烧数值计算对比分析

以某公司热轧厂板坯加热炉为研究对象,建立该加热炉内流动、传热、燃烧和板坯运动吸热过程的三维物理数学模型,运用CFD仿真技术对其进行详细的数值计算,重点对比分析了常规燃烧和富氧燃烧特性,得到了各自的炉内速度场和温度场分布规律、板坯的升温曲线以及板坯温度分布均匀性,计算结果与“黑匣子”实验测量数据吻合良好.总结出的富氧燃烧...     

Temperature distributions in boreholes of a vertical ground-coupled heat pump system

The objective of this study is to show the temperature distribution development in the borehole of the ground-coupled heat pump systems (GCHPs) with time. The time interval for the study is 48 h. The vertical GCHP system using R-22 as refrigerant has a three single U-tube ground heat exchanger (GHE) made of polyethylene pipe with a 40 mm outside diameter. The GHE was placed in a vertical borehole (VB) with 30 (VB1), 60 (VB2) and 90 (VB3) m depths and 150 mm diameters. The experimental results were obtained in cooling and heating seasons of 2006–2007. A two-dimensional finite element model (FEM) was developed to simulate temperature distribution development in the soil surrounding the GHEs of GCHPs operating in the cooling and the heating modes. The finite element modelling of the GCHP system was performed using the ANSYS code. The FEM incorporated pipes, the grout and the surrounding formation. From the cases studied, this approach appears to be the most promising for estimation the temperature distribution response of GHEs to thermal loading.     

Numerical investigation of natural convection in a square enclosure partially filled with horizontal layers of a porous medium

Two-dimensional buoyancy-induced flow and heat transfer inside a square enclosure partially occupied by copper metallic foam subjected to a symmetric side cooling and constant heat flux bottom heating was tested numerically. Finite Element Method was employed to solve the governing partial differential equations of the flow field and the Local Thermal Equilibrium model was used for the energy equation. The system boundaries were defined as lower heated wall by constant heat flux, cooled lateral walls, and insulated top wall. The three parameters elected to conduct the study are heater length (7 ≤ ζ ≤ 20 cm), constant heat flux (150 ≤ q″ ≤ 600 W m⁻²), and porous material thickness (5 ≤ H ≤ 20 cm). The porous material used was the copper metal foam of porosity = 0.9 and pore density PPI = 10, and saturated with a fluid of Prandtl number = 0.7. On the basis of the results obtained, it was concluded that at the porous layer thickness = 5 cm, the rate of heat transferred was (74.6%) higher than when the layer height was 20 cm (the cavity is fully filled) and at the same thickness it was found that the heat rate is (51.4%) higher than when using the half filling (H = 10 cm). Further, the local and mean Nusselt number is maximum when using the largest heater size and smallest porous layer thickness. Finally, better circulation and convective modes were observed at high values of heat flux.