基于炉气非灰辐射特性的炉膛总括热吸收率动态补偿研究
|
摘要
实现加热炉在线最优控制可以取得明显的经济效益和节能效果。总括热吸收率法将钢坯表面热流简化为炉膛总括热吸收率、钢坯表面温度和炉温的函数,因其算法简单、计算量小,在加热炉在线控制数学模型中已得到广泛应用。然而,研究表明,该方法的关键参数——炉膛总括热吸收率,沿炉长方向的分布并非一组常数,与加热炉内的燃烧、流动和传热密切相关,不仅受炉子等结构参数的影响,也受热工操作等参数的影响。传热是加热炉内发生的最重要过程,加热炉炉膛内的传热以热辐射为主,通常占总热交换量的90%以上。目前,大多数加热炉主要燃烧碳氢气体燃料,作为主要燃烧产物的H2O和CO2气体,具有强烈的非灰辐射特性。因此,本文从加热炉炉膛内的传热机理和炉气的非灰辐射特性出发,对炉膛总括热吸收率进行动态补偿研究,为提高加热炉在线控制数学模型的精度提供理论依据,主要研究内容包括以下六个方面：
(1)对炉气的非灰辐射特性进行研究。采用发射率和吸收率来描述气体的辐射特性,区别了炉气对不同表面的发射率和炉气对不同表面有效辐射中各分量的吸收率。给出吸收性气体对其部分边界平均射线行程的一种反演方法,通过模型检验证实了该方法的可靠性与可行性。分别采用Edwards指数宽带模型和Leckner级数式,计算了水蒸气和二氧化碳发射率,进而计算了典型煤气燃烧产物的发射率。结果表明,在加热炉的温度和压力行程范围内,以Edwards指数宽带模型计算结果为基准,Leckner级数式的最大误差为16%,而Leckner级数式的计算速度约为Edwards指数宽带模型的10倍。
(2)对非灰气体参与的辐射全交换面积进行研究。给出考虑气体非灰特性的辐射全交换面积的两种求解方法：射线跟踪方法和辐射网络图方法。以炉子三元辐射体系为例,应用上述两种方法分别推导了各辐射全交换面积表达式,取得一致的结果,实现了相互印证。在此基础上,计算了连续加热炉各模型段三元辐射体系内的辐射全交换面积,并通过了完整性校验。结果表明：考虑炉气非灰特性的辐射全交换面积已不存在互换性,低温段中尤为明显；随着炉围发射率的增大,钢坯表面段与炉围表面段间的辐射全交换面积增大,而钢坯表面段对自身和对气体段的辐射全交换面积减小。
(3)在上述工作的基础上,建立了考虑炉气非灰辐射特性与引入假想面的加热炉三元数学模型,并采用文献中的实验数据对模型进行验证。分别以实际的换热式和蓄热式加热炉为例,对各辐射全交换面积、钢坯表面热流、炉内温度、炉膛总括热吸收率和炉子热效率等进行数值模拟,并计算了将炉气简化为灰体时的上述变量及其误差。研究了热工操作等参数对炉内热过程的影响,其中有炉围发射率的影响,包括稳态工况和典型动态工况——待轧。本文的稳态研究表明,提高炉围发射率,炉子热效率略有下降,但对待轧的模拟可能出现相反的情况。
(4)建立了区域法数学模型。以实际的换热式和蓄热式加热炉为例,比较了三元模型、引入假想面的三元模型和区域法的计算结果,研究了火焰分布对炉内热过程的影响。
(5)简述炉膛总括热吸收率的辨识方法,为了对炉膛总括热吸收率辨识方法中的断面温差法进行分析,推导了一维、非稳态热传导方程在分布的初始条件和变热流边界条件下的解析解,并导出了钢坯表面热流与钢坯断面温差间的关系式。通过对典型热流分布的分析可知,应用断面温差法对炉膛总括热吸收率进行辨识时,沿炉长方向的任何一点都存在误差,误差的大小取决于钢坯表面热流分布函数。
(6)对炉膛总括热吸收率进行动态补偿研究。应用考虑炉气非灰辐射特性的加热炉数学模型,分别以实际的换热式和蓄热式加热炉为例,研究了热工操作等参数对炉膛总括热吸收率的影响,形成数据库,这样的数据库相当于专家系统的知识库,以备炉膛总括热吸收率动态补偿之用。
Optimization of online control of reheating furnace will bring significant economic and energy saving effects. Total heat exchange factor method simplifies heat flux to slab surface dependant on total heat exchange factor, slab surface temperature and furnace temperature, which has been widely used in online control mathematical models in reheating furnace for its simple algorithm and small computational cost. However, studies showed that the distribution of total heat exchange factor along length of reheating furnace was not a group of constant. Total heat exchange factor which is the key parameter in this method is related to combustion, flowing and heat transfer, and it is dependant on not only structural parameters but also operating parameters. Heat transfer is the most important process, and radiation is the dominant mode in reheating furnace which takes over 90% of the total heat. To date, most reheating furnaces burn mainly gas fuels concluding carbon and hydrogen elements. H2O and CO2 as the main products have strong non-gray radiation properties. In this dissertation, dynamical compensation of total heat exchange factor was carried on considering non-gray radiation properties of gas, aiming at improving the precision of online control mathematical models in reheating furnace. The main work includes the following five aspects of investigations.
(1) Non-gray radiation properties of gas were studied. Emissivities and absorptivities were adopted to describe radiation properties of gas, and emissivities of gas to surfaces and absorptivies of gas to components of effective radiations of surfaces were distinguished. In distinguishing mean beam lengths of gas to parts of its boundary, inverse radiation problems were referred. An inverse method was presented to calculate the mean beam length from absorbing gas to parts of its boundary and it was validated. Edwards exponential wide band model and Leckner series were applied to calculate emissivities of H2O, CO2 as well as combustion products of typical gases. The results show that the maximal error of Leckner series is 16% based on results of Edwards exponential wide band model, but the computational speed of the former is almost 10 times of the latter.
(2) Total radiative exchange areas were studied in non-gray participating media. Considering non-gray radiation properties of gas, two methods called ray tracing method and radiation net-chart method were given to calculate total radiative exchange areas. Expressions of total radiative exchange areas in ternary system in reheating furnace were derived by applying the two methods, and they agreed well with each other. Total radiative exchange areas of a walking beam reheating furnace were calculated and integrity of total radiative exchange areas was validated. The results show that reciprocity of total radiative exchange areas was not existed, especially in low temperature zones. With the increase of wall emissivities, the total radiative exchange areas between slab surface and wall increase, while total radiative exchange areas of slab surface to ifself and to gas decrease.
(3) Advanced mathematical models were developed by introducing imaginary plane into ternary system, including steady and unsteady states, conventional and regenerative reheating furnaces, which were validated by experimental data in the literature. A conventional and a regenerative reheating furnaces were taken as research objects, and total radiative exchange areas, heat flux to slab surface, temperature field, total heat exchange factor along length of reheating furnace coupled with thermal efficiency were simulated, with which results of gray gas were compared. The errors were also given. Effects of operating etc. parameters on heat transfer process were also studied, including the effects of wall emissivities both in steady state and typical unsteady state called delay rolling. The results show that thermal efficiency will decrease when wall emissivity increases in steady state, but it may be different in delay rolling.
(4) Conventional zone method mathematical models were developed in reheating furnace. The conventional and regenerative reheating furnaces were taken as research objects, and the results of ternary model, ternary model by introducing imaginary plane and zone method were compared. Furthermore, effects of flame distribution on heat transfer process were studied.
(5) Three methods for calculation of total heat exchange factor were briefly introduced. An analytical solution of unsteady one-dimensional heat conduction equation with variable/time-dependant heat flux boundary conditions and distributed initial condition was derived, and expressions of cross-section temperature difference of slab were given. By analyzing typical analytical solutions, one can get that the method called cross-section temperature difference will bring errors at any place along length of reheating furnace, and the errors depend on heat flux distribution.
(6) Studies on dynamical compensation of total heat exchange factor were carried on. For the above conventional and regenerative reheating furnaces, effects of operating etc. parameters on total heat exchange factor were investigated based on mathematical models considering non-gray properties of gas, which can be stored and used as experts' knowledge database for compensation of total heat exchange factor in online models.
(1)对炉气的非灰辐射特性进行研究。采用发射率和吸收率来描述气体的辐射特性,区别了炉气对不同表面的发射率和炉气对不同表面有效辐射中各分量的吸收率。给出吸收性气体对其部分边界平均射线行程的一种反演方法,通过模型检验证实了该方法的可靠性与可行性。分别采用Edwards指数宽带模型和Leckner级数式,计算了水蒸气和二氧化碳发射率,进而计算了典型煤气燃烧产物的发射率。结果表明,在加热炉的温度和压力行程范围内,以Edwards指数宽带模型计算结果为基准,Leckner级数式的最大误差为16%,而Leckner级数式的计算速度约为Edwards指数宽带模型的10倍。
(2)对非灰气体参与的辐射全交换面积进行研究。给出考虑气体非灰特性的辐射全交换面积的两种求解方法：射线跟踪方法和辐射网络图方法。以炉子三元辐射体系为例,应用上述两种方法分别推导了各辐射全交换面积表达式,取得一致的结果,实现了相互印证。在此基础上,计算了连续加热炉各模型段三元辐射体系内的辐射全交换面积,并通过了完整性校验。结果表明：考虑炉气非灰特性的辐射全交换面积已不存在互换性,低温段中尤为明显；随着炉围发射率的增大,钢坯表面段与炉围表面段间的辐射全交换面积增大,而钢坯表面段对自身和对气体段的辐射全交换面积减小。
(3)在上述工作的基础上,建立了考虑炉气非灰辐射特性与引入假想面的加热炉三元数学模型,并采用文献中的实验数据对模型进行验证。分别以实际的换热式和蓄热式加热炉为例,对各辐射全交换面积、钢坯表面热流、炉内温度、炉膛总括热吸收率和炉子热效率等进行数值模拟,并计算了将炉气简化为灰体时的上述变量及其误差。研究了热工操作等参数对炉内热过程的影响,其中有炉围发射率的影响,包括稳态工况和典型动态工况——待轧。本文的稳态研究表明,提高炉围发射率,炉子热效率略有下降,但对待轧的模拟可能出现相反的情况。
(4)建立了区域法数学模型。以实际的换热式和蓄热式加热炉为例,比较了三元模型、引入假想面的三元模型和区域法的计算结果,研究了火焰分布对炉内热过程的影响。
(5)简述炉膛总括热吸收率的辨识方法,为了对炉膛总括热吸收率辨识方法中的断面温差法进行分析,推导了一维、非稳态热传导方程在分布的初始条件和变热流边界条件下的解析解,并导出了钢坯表面热流与钢坯断面温差间的关系式。通过对典型热流分布的分析可知,应用断面温差法对炉膛总括热吸收率进行辨识时,沿炉长方向的任何一点都存在误差,误差的大小取决于钢坯表面热流分布函数。
(6)对炉膛总括热吸收率进行动态补偿研究。应用考虑炉气非灰辐射特性的加热炉数学模型,分别以实际的换热式和蓄热式加热炉为例,研究了热工操作等参数对炉膛总括热吸收率的影响,形成数据库,这样的数据库相当于专家系统的知识库,以备炉膛总括热吸收率动态补偿之用。
Optimization of online control of reheating furnace will bring significant economic and energy saving effects. Total heat exchange factor method simplifies heat flux to slab surface dependant on total heat exchange factor, slab surface temperature and furnace temperature, which has been widely used in online control mathematical models in reheating furnace for its simple algorithm and small computational cost. However, studies showed that the distribution of total heat exchange factor along length of reheating furnace was not a group of constant. Total heat exchange factor which is the key parameter in this method is related to combustion, flowing and heat transfer, and it is dependant on not only structural parameters but also operating parameters. Heat transfer is the most important process, and radiation is the dominant mode in reheating furnace which takes over 90% of the total heat. To date, most reheating furnaces burn mainly gas fuels concluding carbon and hydrogen elements. H2O and CO2 as the main products have strong non-gray radiation properties. In this dissertation, dynamical compensation of total heat exchange factor was carried on considering non-gray radiation properties of gas, aiming at improving the precision of online control mathematical models in reheating furnace. The main work includes the following five aspects of investigations.
(1) Non-gray radiation properties of gas were studied. Emissivities and absorptivities were adopted to describe radiation properties of gas, and emissivities of gas to surfaces and absorptivies of gas to components of effective radiations of surfaces were distinguished. In distinguishing mean beam lengths of gas to parts of its boundary, inverse radiation problems were referred. An inverse method was presented to calculate the mean beam length from absorbing gas to parts of its boundary and it was validated. Edwards exponential wide band model and Leckner series were applied to calculate emissivities of H2O, CO2 as well as combustion products of typical gases. The results show that the maximal error of Leckner series is 16% based on results of Edwards exponential wide band model, but the computational speed of the former is almost 10 times of the latter.
(2) Total radiative exchange areas were studied in non-gray participating media. Considering non-gray radiation properties of gas, two methods called ray tracing method and radiation net-chart method were given to calculate total radiative exchange areas. Expressions of total radiative exchange areas in ternary system in reheating furnace were derived by applying the two methods, and they agreed well with each other. Total radiative exchange areas of a walking beam reheating furnace were calculated and integrity of total radiative exchange areas was validated. The results show that reciprocity of total radiative exchange areas was not existed, especially in low temperature zones. With the increase of wall emissivities, the total radiative exchange areas between slab surface and wall increase, while total radiative exchange areas of slab surface to ifself and to gas decrease.
(3) Advanced mathematical models were developed by introducing imaginary plane into ternary system, including steady and unsteady states, conventional and regenerative reheating furnaces, which were validated by experimental data in the literature. A conventional and a regenerative reheating furnaces were taken as research objects, and total radiative exchange areas, heat flux to slab surface, temperature field, total heat exchange factor along length of reheating furnace coupled with thermal efficiency were simulated, with which results of gray gas were compared. The errors were also given. Effects of operating etc. parameters on heat transfer process were also studied, including the effects of wall emissivities both in steady state and typical unsteady state called delay rolling. The results show that thermal efficiency will decrease when wall emissivity increases in steady state, but it may be different in delay rolling.
(4) Conventional zone method mathematical models were developed in reheating furnace. The conventional and regenerative reheating furnaces were taken as research objects, and the results of ternary model, ternary model by introducing imaginary plane and zone method were compared. Furthermore, effects of flame distribution on heat transfer process were studied.
(5) Three methods for calculation of total heat exchange factor were briefly introduced. An analytical solution of unsteady one-dimensional heat conduction equation with variable/time-dependant heat flux boundary conditions and distributed initial condition was derived, and expressions of cross-section temperature difference of slab were given. By analyzing typical analytical solutions, one can get that the method called cross-section temperature difference will bring errors at any place along length of reheating furnace, and the errors depend on heat flux distribution.
(6) Studies on dynamical compensation of total heat exchange factor were carried on. For the above conventional and regenerative reheating furnaces, effects of operating etc. parameters on total heat exchange factor were investigated based on mathematical models considering non-gray properties of gas, which can be stored and used as experts' knowledge database for compensation of total heat exchange factor in online models.
引文
1. Leden B. A control system for fuel optimization of reheating furnace[J]. Scandinavin Journal of metallurgy,1986,15(1),331-336.
2. Sandstrom L, Malmberq D. On-line and in situ monitoring of oxygen concentration and gas temperature in a reheating furnace utilizing tunable diode-laser spectroscopy[J]. Spectrochimica Acta, Part A (Molecular and Biomolecular Spectroscopy),2002,58A(11):2449-2455.
3. Bi C C, Li N, Huang D. Study on billet temperature prediction and furnace temperature optimal setting of regenerative reheating furnace[J]. Acta Automatica Sinica,2004,30(3):476-480.
4.陈海耿.计算传热学在控制算法研究中的应用[J].东北大学学报(自然科学版),2002,23(3)：273-276.
5. Ahmed B, Hmaid B, Mohamed S. Non-gray radiation analysis in participating media with the finite volume method[J]. Turkish Journal of Engineering and Environmental Sciences,2006,30(3):183-192.
6.聂宇宏,陈海耿,姚寿广.非灰系统当量灰吸收系数的反演[J].化工学报,2005,56(6)：1041-1044.
7. Asllanaj Fatmir, Brige Xavier,Jeandel Gerard. Transient combined radiation and conduction in a one-dimensional non-gray participating medium with anisotropic optical properties subjected to radiative flux at the boundaries[J]. Journal of Quantitative Spectroscopy & Radiative Transfer,2007, 107(1):17-29.
8. Wang A, Modest M F. Spectral monte carlo models for nongray radiation analyses in inhomogeneous participating media[J]. International Journal of Heat and Mass Transfer,2007,50(19-20):3877-3889.
9. Mohamed N B, Kamel G and Rachid S. Modeling of radiative heat transfer in 3D complex boiler with non-gray sooting media[J]. International Journal of Heat and Mass Transfer,2007,105(2):167-179.
10. Byun D, Baek S W. Numerical investigation of combustion with non-gray thermal radiation and soot formation effect in a liquid rocket engine[J]. International Journal of Heat and Mass Transfer, 2007;50(3):412-422.
11. Maki A M, Osterman P J, Luomala M J. Numerical study of the pusher-type slab reheating furnace[J], Scandinavian Journal of Metallurgy,2002,31 (2):81-87.
12. Chen Zhigang, Xu Chao, Zhang Bin, et al. Advanced control of walking-beam reheating furnace[J]. Journal of University of Science and Technology Beijing: Mineral Metallurgy Materials(Eng Ed), 2003,10(4):69-74.
13. Jang Y J, Kim S W. An estimation of a billet temperature during reheating furnace operation[J]. International Journal of Control, Automation and Systems,2007,5(1):43-50.
14. Jaklic A, Vode F, Kolenko T. Online simulation model of the slab-reheating process in a pusher-type furnace[J]. Applied Thermal Engineering,2007,27(5-6):1105-1114.
15. Mullikin H F. Evaluation of effective radiant heating surface and application of the Stefan-Boltzmann law to heat absorption in Boiler Furnaces[J]. Transactions of the ASME,1935,57(2):517-529.
16. Donald Q K. Process heat transfer[M]. NewYork: McGraw-Hill, Inc,1950.
17.热经济技术部会加热炉小委会.连续钢片加热炉传热实验计算方法[R].东京：日本钢铁协会,1971.
18. Matsunaga Syogo. Total heat exchange factor of the slab reheating furnace determined in slab reheating experiments[J]. Journal of the Iron and Steel Institute of Japan,1973,59(2):301-307.
19.松永省吾.铁钢业用加热炉の最适操业条件の热工学的研究[D].大阪：日本大阪电气通信大学,1975.转引自：石伟.炉温与炉内总括热吸收率的研究[D].沈阳：东北大学,1994.
20.松永省吾.传热设备中电子计算机的应用[J].东北工学院学报,1984,1：60-69.
21. Trinks W, Manhinner M H. Industrial Furnaces[M]. NewYork: McGraw-Hill, Inc.,1961.
22. Fitgerald F, Sheridan A T. The heating of a slab in a furnace[A]. Proceeding of the conference on mathematical model in metallurgical process development. The iron and steel institute[C]. Tokyo: Japanese Press,1969.18-28.
23. Fitgerald F, Sheridian A T. Prediction of temperature and heat transfer distribution in gas-filled pusher reheating furnace[J].J.Inst.Fuel,1974,7:21-27.
24.陈海耿,杨泽宽,张卫军,等.热轧带钢步进式加热炉计算机优化控制[J].钢铁,1999,34(5)：57-60,33.
25.权芳民,陈海耿.启发式搜索策略在加热炉动态优化控制中的应用[J].钢铁,2000,35(6)：57-60.
26.陈友文.酒钢中板加热炉控制系统[J].武汉理工大学学报,2003,25(11)：80-82.
27.于率浩,姜泽毅,张欣欣,等.钢管调质炉数学模型优化控制研究[J].金属热处理,2005,2：59-62.
28.安月明,温治.步进梁式板坯加热炉数学模型及其仿真系统[J].系统仿真学报,2007,19(12)：2827-2830.
29.石伟,陈海耿,宁宝林.以炉温为基准的炉膛总括热吸收率[J].钢铁,1997,32(4)：69-72.
30.杨小兵,姜泽毅,林林,等.环形加热炉热工过程CFD数值模拟及其应用[J].工业加热,2005,34(6)：27-31.
31.安月明,温治,冯霄红,等.步进梁式连续加热炉总括热吸收率分布规律的实验研究[J].工业 加热,2006,35(5)：24-26.
32. Siegel R, Howell J R. Thermal Radiation Heat Transfer[M]. Second Edition. Washington D C: Hemisphere Publishing Corporation,1981.
33.谈和平,夏新林,刘林华,等.红外辐射特性与传输的数值计算[M].哈尔滨：哈尔滨工业大学出版社,2006.
34. Yunus A. Cengel. Heat transfer[M]. Second Edition. NewYork: McGraw-Hill, Inc.,2003.
35.谭建宇.求解辐射传递方程的无网格法[D].哈尔滨：哈尔滨工业大学,2006.
36. Su M H, Sutton W H. Transient conductive and radiative heat transfer in a silica window[J]. International Journal of Thermophysics and Heat Transfer,1995,9(2):370-373.
37.王中,王宏,孙美.固体火箭发动机红外辐射及抑制技术[J].激光与红外,2003,33(5)：323-324.
38.额日其太,王强,陈渭鹏.两种涡扇发动机排气系统红外辐射特性的比较[J].推进技术,2003,24(4)：334-336.
39.杜朝辉,钟芳源,赵岩.模化比对船用排气红外抑制装置红外辐射特性的影响及修正[J].红外与毫米波学报,2001,20(6)：437-441.
40.孙鸿宾,殷晓静,杨晶.辐射换热[M].北京：冶金工业出版社,1996.
41.聂宇宏.非灰介质参与的辐射换热研究[D].沈阳：东北大学,1997.
42.刘林华.炉膛传热计算方法的发展状况[J].动力工程,2000,20(1)：523-527.
43. Hottel H C, Cohen E S. Radiant heat exchange in a gas-filled enclosure allowance for nonuniformity of gas gemperature[J]. Journal chemical engineering research and development,1958,4:3-14.
44.林立新,陈鸿复,邱夏陶.火焰炉热交换模型—区域法的改进[J].北京钢铁学院学报,1987,9(4)：66-72.
45.岳星火.引入假想面的火焰炉热交换数学模型[D].沈阳：东北大学,1989.
46. Charette A, Larouche A, Kocaefe Y S, et al. Application of the imaginary planes method to three-dimensional systems[J]. International Journal of Heat and Mass Transfer,1990,33(12): 2671-2681.
47. Zhou H C, Chen D L, Cheng Q. A new way to calculate radiative intensity and solve radiative transfer equation through using the monte carlo method[J]. Journal of quantitative spectroscopy and radiative transfer,2004,83:459-481.
48.帅永,董士奎,刘林华,等.双向蒙特卡罗法模拟参与性介质中的辐射换热[J].工程热物理学报,2006,27(1)：109-111.
49. Densmore J D, Urbatsch T J, Evans T M, et al. A hybrid transport-diffusion method for monte-carlo radiative-transfer simulations[J]. Journal of computational physics,2007,222(2):485-503.
50. Chandrasekhar S. Radiative transfer[M]. New York:Dover publications Inc.,1960.
51. Love T J, Grosh R J. Radiative heat transfer in absorbing,emitting and scattering media[J]. International Journal of Heat and Mass Transfer,1965,87:161-166.
52.李本文,周俊虎,李建华,等.辐射换热球面微元对称等分离散坐标法[J].化工学报,2002,53(6)：560-565.
53. Li B W, Liu R X, Tao W Q. Ray effect in ray tracing method for radiative heat transfer[J]. International Journal of Heat and Mass Transfer,1997,40(14):3419-3426.
54.贺志宏.多维辐射传递与耦合换热研究及其在航天技术中的应用[D].哈尔滨：哈尔滨工业大学,2001.
55. Shah N G. New method of computation of radiant heat transfer in combustion chambers[D], University of London, Imperial College,1979.
56.沈九宾,陈海耿,陈婉.用离散传递法求解辐射全交换面积[J].化工学报,2003,54(12)：1674-1677.
57. Raithby G D, Chui E H. A finite-volume method for predicting a radiant heat transfer in enclosures with participating media[J]. International Journal of Heat and Mass Transfer,1990,112:410-415.
58. Trivic D N. Modeling of 3-D non-gray gases radiation by coupling the finite volume method with weighted sum of gray gases model[J]. International Journal of Heat and Mass Transfer,2004,47: 1367-1382.
59. Baek S W, Kim M Y. Analysis of radiative heating of a rocket plume base with the finite volume method[J]. International Journal of Heat and Mass Transfer,1997,40(7):1501-1508.
60. Reddy J N, Murty V D. Finite element solution of integral equations arising in radiative heat transfer and laminar boundary-layer theory[J]. Numerical heat transfer,1978,1:389-401.
61. Fiveland W A, Jessee J P. Finite element formulation of the discrete ordinates method for multidimensional geometries[J]. International Journal of Thermophysics and Heat Transfer,1994,8: 427-433.
62. Qi H, Ruan L, Tan J. Development of a finite element radiation model applied to two-dimensional participating media[J]. Heat transfer-Asian Research,2005,34(6):386-395.
63. Ruan L M, Xie M,Qi H, An W, et al. Development of a finite element model for coupled radiative and conductive heat transfer in participating media. Journal of Quantitative Spectroscopy & Radiative Transfer,2006,102(2):190-202.
64. Maruyama S, Mori Y, Chikira C, et al. Combined nongray radiative and conductive heat transfer in multiple glazing taking into account specular reflection and absorption[J]. Heat transfer-Asian Research,2003,32(8):712-726.
65. Perrone N, Kao R. A general finite difference method for arbitrary meshes[J], Computational structure, 1975,5:45-58.
66. Liu Lin-hua, Tan Jianyu, Li Bing-xi. Meshless Approach for Coupled Radiative and Conductive Heat Transfer in One-Dimensional Graded Index Medium[J]. Journal of Quantitative Spectroscopy and Radiative Transfer,2006,101:237-248.
67. Tan Jianyu, Liu Lin-hua, Li Bing-xi. Least-Squares Collocation Meshless Approach for Coupled Radiative and Conductive Heat Transfer[J]. Numerical heat transfer, Part B,2006,49(2):179-195.
68.杨世铭,陶文铨.传热学[M].第三版.北京：高等教育出版社,1998.
69.余其铮.辐射换热基础[M].北京：高等教育出版社,1990：132-178.
70.尹雪梅,刘林华.高温气体辐射特性计算模型[J].热能动力工程,2007,22(5)：473-479.
71. Pierrot L, Soufiani A, Taine J. Accuracy of narrow-band and global models for radiative transfer in H2O, CO2, and H2O-CO2 mixtures at high temperature[J]. Journal of Quantitative Spectroscopy & Radiative Transfer,1999,6(2):523-548.
72. Marakis J G. Application of narrow and wide band models for radiative transfer in planar media[J]. International Journal of Heat and MassTransfer,2001,44(1):131-142.
73. Okamoto T, Mutou T, Takagi T. Approach for incorporating narrow band nonuniformity into nongray analysis of radiative heat transfer in nonisothermal and nonhomogeneous gas fields[J]. International Journal of Heat and MassTransfer,2001,44:4147-4156.
74. He J, Cheng W L, Buckius R O. Wide band cumulative absorption coefficient distribution model for overlapping absorption in H2O and CO2mixtures[J]. International Journal of Heat and MassTransfer, 2008,51(5-6):1115-1129.
75. Taniguchi H, Kudo K, Otaka M, et al. Development of a monte carlo method for numerical analysis on the radiation energy transfer through nongray gas layer[J]. International Journal for Numerical Method in Engineering,1992,35:883-891.
76. Yuen W W, Ma A. Evaluation of total emittance of an isothermal nongray absorbing, scattering gas-particle mixture based on the concept of absorption mean beam length[J]. International Journal of Heat and Mass Transfer,1992,114:653-658.
77. Tesse L, Dupoirieux F, Zamuner B, ea al. Radiative transfer in real gases using reciprocal and forward Monte Carlo methods and a correlated-k approach[J]. International Journal of Heat and MassTransfer, 2002,45:2797-2814.
78. Zhang H, Shi G. A new approach to solve correlated k-distribution function[J]. Journal of Quantitative Spectroscopy and Radiative Transfer,2005,96:311-324.
79. Ludwig C B, Malkmus W, Reardon J E, et al. Handbook of infrared radiation from combustion gases[M]. Washington D C:National aeronautics and space administration,1973.
80. Soufiani A, Taine J. High temperature gas radiative property parameters of statistical narrow-band model for H2O, CO2 and CO, and correlated-k model for H2O and CO2[J]. International Journal of Heat and MassTransfer,1997,40(4):987-991.
81. Liu F, Smallwood G J, Gulder O L. Application of the statistical narrow-band correlated-k method to low-resolution spectral intensity and radiative heat transfer calculations-effects of the quadrature scheme[J]. International Journal of Heat and Mass Transfer,2000,43:3119-3135.
82. Liu F, Smallwood G J, Gulder O L. Application of the statistical narrow-band correlated-k method to non-grey gas radiation in CO2-H2O mixtures:approximate treatments of overlapping bands[J]. Journal of Quantitative Spectroscopy and Radiative Transfer,2001,68(4):401-417.
83. Liu F, Smallwood G J. An efficient approach for the implementation of the SNB based correlated-k method and its evaluation[J]. Journal of Quantitative Spectroscopy and Radiative Transfer,2004, 84(4):465-475.
84. Levi Di L R, Taine J. A fictive gas-method for accurate computations of low-resolution IR gas transmissivities:application to the 4.3 μm CO2 band[J]. Revue de Physique Appliquee,1986, 21(12):825-831.
85. Caliot C, Maoult Y L, Hafi M E, et al. Remote sensing of high temperature H2O-CO2-CO mixture with a correlated k distribution fictitious gas method and the single-mixture gas assumption[J]. Journal of Quantitative Spectroscopy and Radiative Transfer,2006,102:304-315.
86.刘玉英,张欣欣.箱带模型结合DOM在非灰气体辐射换热计算中的应用[J].热科学与技术,2003,12(2)：336-341.
87. Lallemant N, Sayre A, Weber R.Evaluation of emissivity correlations for H2O-CO2-N2/air mixtures and coupling with solution methods of the radiative transfer equation[J]. Progress in Energy and Combustion Science,1996,22(6):543-574.
88. Strohle J, Coelho P J. On the application of the exponential wide band model to the calculation of radiative heat transfer in one-and two-dimensional enclosures[J]. International Journal of Heat and Mass Transfer,2002,45(10):2129-2139.
89. Modest M F. A simple differential approximation for radiative transfer in nongray gases[J]. International Journal of Heat and Mass Transfer,1979,101:735-736.
90. Modest M F, Sikka K K. The application of the stepwise-gray p1 approximation to molecular gas-particulate mixture[J].Fundamentals of radiation transfer,1991,160:97-103.
91. Komornicki W, Tomeczek J. Modification of the wide band gas radiation model for flame calculation[J]. International Journal of Heat and Mass Transfer,1992,35(7):1667-1671.
92. Marin O, Buckius R O. A simplified wide band model of the cumulative distri-bution function for carton dioxide[J]. International Journal of Heat and MassTransfer,1998,41:3881-3897.
93.聂宇宏,陈海耿.气体辐射宽带关联k模型的修正算法[J].计算物理,2002,19：439-442.
94.尹雪梅,刘林华,李炳熙.水蒸气和CO2混合气体辐射特性宽带k分布模型[J].中国电机工程学报,2008,28(5)：63-68.
95. Dua S S, Cheng P. Muti-dimensional heat transfer in non-isothermal cylindrical media with isothermal boundary walls[J]. International Journal of Heat and MassTransfer,1975,18:245-255.
96. Modest M F. The weighted-sum-of-gray-gases model for arbitrary solution methods in radiative transfer[J]. Transactions of the ASME. Journal of Heat Transfer,1991,113(3):650-656.
97. Kim O J, Song T H. Data base of WSGGM-based spectral model for radiation properties of combustion products[J]. Journal of Quantitative Spectroscopy and Radiative Transfer,2000,64: 379-394.
98. Yu M J, Baek S W, Park J H. An extension of the weighted sum of gray gases non-gray gas radiation model to a two phase mixture of non-gray gas with particles[J]. International Journal of Heat and MassTransfer,2000,43:1699-1713.
99. Leckner B. Spectral and total emissivity of water vapor and carbon dioxide[J].Combustion and flame,1972,19(1).33-48.
100. Zhang H, Modest M F. A muti-scale full-spectrum correlated-k distribution for radiative heat transfer in inhomogeneous gas mixtures[J]. Journal of Quantitative Spectroscopy and Radiative Transfer,2002, 73:349-360.
101. Modest M F. Narrow-band and full-spectrum k-distributions for radiative heat transfer correlated k vs. scaling approximation[J]. Journal of Quantitative Spectroscopy and Radiative Transfer,2003,76: 69-83.
102. Modest M F, Riazzi R. Assemly of full-spectrum k-distributions from a narrow-band database; effects of mixing gases, gases and nongray absorbing particles, and mixtures with nongray scatters in nongray enclosures[J]. Journal of Quantitative Spectroscopy and Radiative Transfer,2005,90:169-189.
103. Modest M F. Radiative heat transfer[M]. NewYork:Mcgraw-Hill Press,2002.
104. Trivic D N, Amon C H. Modeling the 3-D radiation of anisotropically scattering media by two different numerical methods[J]. International Journal of Heat and MassTransfer,2008,51:2711-2732.
105. Modest M F. Radiative Heat Transfer[M]. NewYork: McGraw-Hill Press Inc.,1993.
106. Edwards D K, Balakrishnan A. Slab band absorptance for molecular gas radiation[J]. Journal of Quantitative Spectroscopy and Radiative Transfer,1972,12(10):1379-1387.
107. Wassel A T, Edwards D K. Mean beam lengths for spheres and cylinders[J]. Transactions of the ASME. Journal of Heat Transfer,1976,98(2):308-309.
108.刘林华,余其铮,阮立明,等.煤粉燃烧产物的辐射特性[J].动力工程,1996,16(6)：15-21.
109.沈九宾,陈海耿,陈婉.用离散传递法求解辐射全交换面积[J].化工学报,2003,54(12)：1674-1677.
110.陆钟武.火焰炉[M].北京：冶金工业出版社,1995.
111.欧俭平.高温空气燃烧技术在冶金热工设备上的应用及数值仿真和优化研究[D].长沙：中南大学,2004.
112. Bojic M, Mourdoukoutas P. Energy saving does not yield CO2 emissions reductions:the case of waste fuel use in a steel mill[J]. Applied Thermal Engineering,2000,20:963-975.
113. Bojic M, Tomic M. Effect of refuse-gas fuel use on energy consumption in an industrial pusher furnace[J]. Energy,1998,23(9):767-775.
114. Patankar S V. Computational modeling of flow and heat transfer in industrial applications[J]. International Journal of Heat and MassTransfer,2002,23(3):222-231.
115. Ramirez M, Haber R, Pena V, et al. Fuzzy control of a multiple hearth furnace[J]. Computers in industry,2004,54(1):105-113.
116. Chen W H, Chung Y C, Liu J L. Analysis on energy consumption and performance of reheating furnaces in a hot strip mill[J]. International Communications in Heat and Mass Transfer,2005,32(5): 695-706.
117.李义科,高仲龙,任雁秋,等.加热炉热过程计算机控制的应用与分析[J].工业加热,2000,1：4-6.
118.姜泽毅,汪霞,张欣欣,等.钢(荒)管再加热炉计算机控制数学模型及其应用[J].金属学报,2000,36(4)：429-432.
119.董伟,陈海耿,李瑞阳,等.加热炉热过程动态操作数学模型[J].工程热物理学报,2003,24(2)：295-297.
120.张卫军,吴雪琦,陈海耿.基于机理模型的加热炉在线炉温模糊决策[J].东北大学学报(自然科学版),2005,26(9)：878-881.
121.陈海耿,王子弟,吴彬,等.连续加热炉在线控制系统的仿真研究[J].钢铁,2006,41(12)：75-78.
122.郝小红,温治,安月明,等.连铸坯装炉温度在线实时计算模型及其应用[J].系统仿真学报,2007,19(14)：3324-3326.
123.刘坤,韩仁志,谢国威.蓄热式加热炉内温度场及浓度场的数值模拟[J].冶金能源,2005,24(3)：22-24.
124.宋小飞,刘训良,温治,等.空气单蓄热室状加热炉内传输过程的数值模拟[J].浙江大学学报(工学版),2007,41(10)：1768-1772.
125. Kim M Y. A heat transfer model for the analysis of transient heating of the slab in a direct-fired walking beam type reheating furnace[J]. International Journal of Heat and MassTransfer,2007, 50(19-20):3740-3748.
126. Kung E Y. A Mathematieal Model of Soaking Pits[J]. ISA TRANSACTIONS,1967,6(2):1-10.
127.郝小红,温治.连铸坯凝固传热数学模型的研究[J].铸造技术[J],2007,28(10)：1356-1359.
128.郝小红,温治,安月明,等.连铸坯装炉温度在线实时计算模型及其应用[J].系统仿真学报,2007,19(14)：3324-3326.
129.杨贤荣,马庆芳,原庚新,等.辐射换热角系数手册[M].北京：国防工业出版社,1982.
130. Wiernga J A, Elich J J Ph, Hoogendoorn C J. Spectral effects of radiative heat transfer in high temperature furnaces burning natural gas[J]. Journal of the Institute of Energy,1990,63(456):101-108.
131.白焕炽.高温涂料节能效果分析及其应用前景[J].工业炉,1993,(1)：12-16.
132. Clement J G. High emissivity coatings-a major advanced in furnace technology [J]. Heat treatment of metals,1986,13(3):76-79.
133. Tu P Q, Chen J K, Zhou J C. High emissivity coating and its application for energy-saving[J]. Journal of infrared and millimeter waves,1993,12(6):436-440.
134. Bebellis C L. Evaluation of the high emittance-coating in a large industrial furnace[J]. Industrial heating,1993,60(10):56-60,62.
135. Alexander I C. High reflectivity furnace coatings[J]. Metals and materials,1988,4(1):25-27.
136.欧阳德刚,罗安智.炉壁黑度对火焰炉能耗的影响[J].钢铁研究,1998,(5)：47-49.
137.吴彬,陈海耿,李本文.连续加热炉三元在线控制数学模型[J].工业炉,1999,21(1)：34-37.
138. Elich J J P, Wieringa J A. Temperature effects influencing the spectral and total emissivity of refractories[J]. Experimental thermal and fluid science,1995,10:318-326.
139. Neuer G, Jaroma-Weiland G. Spectral and total emissivity of high-temperature materials[J]. International Journal of Thermophysics,1998,19(3):917-929.
140. Kobayashi M, Ono A, Otsuki M, et al. A database of normal spectral emissivities of metals at high temperatures[J]. International Journal of Thermophysics,1999,20(1):299-308.
141.陈海耿,杨泽宽,张卫军. 热轧带钢步进式加热炉计算机优化控制[J].钢铁,1999,34(5)：57-59.
2. Sandstrom L, Malmberq D. On-line and in situ monitoring of oxygen concentration and gas temperature in a reheating furnace utilizing tunable diode-laser spectroscopy[J]. Spectrochimica Acta, Part A (Molecular and Biomolecular Spectroscopy),2002,58A(11):2449-2455.
3. Bi C C, Li N, Huang D. Study on billet temperature prediction and furnace temperature optimal setting of regenerative reheating furnace[J]. Acta Automatica Sinica,2004,30(3):476-480.
4.陈海耿.计算传热学在控制算法研究中的应用[J].东北大学学报(自然科学版),2002,23(3)：273-276.
5. Ahmed B, Hmaid B, Mohamed S. Non-gray radiation analysis in participating media with the finite volume method[J]. Turkish Journal of Engineering and Environmental Sciences,2006,30(3):183-192.
6.聂宇宏,陈海耿,姚寿广.非灰系统当量灰吸收系数的反演[J].化工学报,2005,56(6)：1041-1044.
7. Asllanaj Fatmir, Brige Xavier,Jeandel Gerard. Transient combined radiation and conduction in a one-dimensional non-gray participating medium with anisotropic optical properties subjected to radiative flux at the boundaries[J]. Journal of Quantitative Spectroscopy & Radiative Transfer,2007, 107(1):17-29.
8. Wang A, Modest M F. Spectral monte carlo models for nongray radiation analyses in inhomogeneous participating media[J]. International Journal of Heat and Mass Transfer,2007,50(19-20):3877-3889.
9. Mohamed N B, Kamel G and Rachid S. Modeling of radiative heat transfer in 3D complex boiler with non-gray sooting media[J]. International Journal of Heat and Mass Transfer,2007,105(2):167-179.
10. Byun D, Baek S W. Numerical investigation of combustion with non-gray thermal radiation and soot formation effect in a liquid rocket engine[J]. International Journal of Heat and Mass Transfer, 2007;50(3):412-422.
11. Maki A M, Osterman P J, Luomala M J. Numerical study of the pusher-type slab reheating furnace[J], Scandinavian Journal of Metallurgy,2002,31 (2):81-87.
12. Chen Zhigang, Xu Chao, Zhang Bin, et al. Advanced control of walking-beam reheating furnace[J]. Journal of University of Science and Technology Beijing: Mineral Metallurgy Materials(Eng Ed), 2003,10(4):69-74.
13. Jang Y J, Kim S W. An estimation of a billet temperature during reheating furnace operation[J]. International Journal of Control, Automation and Systems,2007,5(1):43-50.
14. Jaklic A, Vode F, Kolenko T. Online simulation model of the slab-reheating process in a pusher-type furnace[J]. Applied Thermal Engineering,2007,27(5-6):1105-1114.
15. Mullikin H F. Evaluation of effective radiant heating surface and application of the Stefan-Boltzmann law to heat absorption in Boiler Furnaces[J]. Transactions of the ASME,1935,57(2):517-529.
16. Donald Q K. Process heat transfer[M]. NewYork: McGraw-Hill, Inc,1950.
17.热经济技术部会加热炉小委会.连续钢片加热炉传热实验计算方法[R].东京：日本钢铁协会,1971.
18. Matsunaga Syogo. Total heat exchange factor of the slab reheating furnace determined in slab reheating experiments[J]. Journal of the Iron and Steel Institute of Japan,1973,59(2):301-307.
19.松永省吾.铁钢业用加热炉の最适操业条件の热工学的研究[D].大阪：日本大阪电气通信大学,1975.转引自：石伟.炉温与炉内总括热吸收率的研究[D].沈阳：东北大学,1994.
20.松永省吾.传热设备中电子计算机的应用[J].东北工学院学报,1984,1：60-69.
21. Trinks W, Manhinner M H. Industrial Furnaces[M]. NewYork: McGraw-Hill, Inc.,1961.
22. Fitgerald F, Sheridan A T. The heating of a slab in a furnace[A]. Proceeding of the conference on mathematical model in metallurgical process development. The iron and steel institute[C]. Tokyo: Japanese Press,1969.18-28.
23. Fitgerald F, Sheridian A T. Prediction of temperature and heat transfer distribution in gas-filled pusher reheating furnace[J].J.Inst.Fuel,1974,7:21-27.
24.陈海耿,杨泽宽,张卫军,等.热轧带钢步进式加热炉计算机优化控制[J].钢铁,1999,34(5)：57-60,33.
25.权芳民,陈海耿.启发式搜索策略在加热炉动态优化控制中的应用[J].钢铁,2000,35(6)：57-60.
26.陈友文.酒钢中板加热炉控制系统[J].武汉理工大学学报,2003,25(11)：80-82.
27.于率浩,姜泽毅,张欣欣,等.钢管调质炉数学模型优化控制研究[J].金属热处理,2005,2：59-62.
28.安月明,温治.步进梁式板坯加热炉数学模型及其仿真系统[J].系统仿真学报,2007,19(12)：2827-2830.
29.石伟,陈海耿,宁宝林.以炉温为基准的炉膛总括热吸收率[J].钢铁,1997,32(4)：69-72.
30.杨小兵,姜泽毅,林林,等.环形加热炉热工过程CFD数值模拟及其应用[J].工业加热,2005,34(6)：27-31.
31.安月明,温治,冯霄红,等.步进梁式连续加热炉总括热吸收率分布规律的实验研究[J].工业 加热,2006,35(5)：24-26.
32. Siegel R, Howell J R. Thermal Radiation Heat Transfer[M]. Second Edition. Washington D C: Hemisphere Publishing Corporation,1981.
33.谈和平,夏新林,刘林华,等.红外辐射特性与传输的数值计算[M].哈尔滨：哈尔滨工业大学出版社,2006.
34. Yunus A. Cengel. Heat transfer[M]. Second Edition. NewYork: McGraw-Hill, Inc.,2003.
35.谭建宇.求解辐射传递方程的无网格法[D].哈尔滨：哈尔滨工业大学,2006.
36. Su M H, Sutton W H. Transient conductive and radiative heat transfer in a silica window[J]. International Journal of Thermophysics and Heat Transfer,1995,9(2):370-373.
37.王中,王宏,孙美.固体火箭发动机红外辐射及抑制技术[J].激光与红外,2003,33(5)：323-324.
38.额日其太,王强,陈渭鹏.两种涡扇发动机排气系统红外辐射特性的比较[J].推进技术,2003,24(4)：334-336.
39.杜朝辉,钟芳源,赵岩.模化比对船用排气红外抑制装置红外辐射特性的影响及修正[J].红外与毫米波学报,2001,20(6)：437-441.
40.孙鸿宾,殷晓静,杨晶.辐射换热[M].北京：冶金工业出版社,1996.
41.聂宇宏.非灰介质参与的辐射换热研究[D].沈阳：东北大学,1997.
42.刘林华.炉膛传热计算方法的发展状况[J].动力工程,2000,20(1)：523-527.
43. Hottel H C, Cohen E S. Radiant heat exchange in a gas-filled enclosure allowance for nonuniformity of gas gemperature[J]. Journal chemical engineering research and development,1958,4:3-14.
44.林立新,陈鸿复,邱夏陶.火焰炉热交换模型—区域法的改进[J].北京钢铁学院学报,1987,9(4)：66-72.
45.岳星火.引入假想面的火焰炉热交换数学模型[D].沈阳：东北大学,1989.
46. Charette A, Larouche A, Kocaefe Y S, et al. Application of the imaginary planes method to three-dimensional systems[J]. International Journal of Heat and Mass Transfer,1990,33(12): 2671-2681.
47. Zhou H C, Chen D L, Cheng Q. A new way to calculate radiative intensity and solve radiative transfer equation through using the monte carlo method[J]. Journal of quantitative spectroscopy and radiative transfer,2004,83:459-481.
48.帅永,董士奎,刘林华,等.双向蒙特卡罗法模拟参与性介质中的辐射换热[J].工程热物理学报,2006,27(1)：109-111.
49. Densmore J D, Urbatsch T J, Evans T M, et al. A hybrid transport-diffusion method for monte-carlo radiative-transfer simulations[J]. Journal of computational physics,2007,222(2):485-503.
50. Chandrasekhar S. Radiative transfer[M]. New York:Dover publications Inc.,1960.
51. Love T J, Grosh R J. Radiative heat transfer in absorbing,emitting and scattering media[J]. International Journal of Heat and Mass Transfer,1965,87:161-166.
52.李本文,周俊虎,李建华,等.辐射换热球面微元对称等分离散坐标法[J].化工学报,2002,53(6)：560-565.
53. Li B W, Liu R X, Tao W Q. Ray effect in ray tracing method for radiative heat transfer[J]. International Journal of Heat and Mass Transfer,1997,40(14):3419-3426.
54.贺志宏.多维辐射传递与耦合换热研究及其在航天技术中的应用[D].哈尔滨：哈尔滨工业大学,2001.
55. Shah N G. New method of computation of radiant heat transfer in combustion chambers[D], University of London, Imperial College,1979.
56.沈九宾,陈海耿,陈婉.用离散传递法求解辐射全交换面积[J].化工学报,2003,54(12)：1674-1677.
57. Raithby G D, Chui E H. A finite-volume method for predicting a radiant heat transfer in enclosures with participating media[J]. International Journal of Heat and Mass Transfer,1990,112:410-415.
58. Trivic D N. Modeling of 3-D non-gray gases radiation by coupling the finite volume method with weighted sum of gray gases model[J]. International Journal of Heat and Mass Transfer,2004,47: 1367-1382.
59. Baek S W, Kim M Y. Analysis of radiative heating of a rocket plume base with the finite volume method[J]. International Journal of Heat and Mass Transfer,1997,40(7):1501-1508.
60. Reddy J N, Murty V D. Finite element solution of integral equations arising in radiative heat transfer and laminar boundary-layer theory[J]. Numerical heat transfer,1978,1:389-401.
61. Fiveland W A, Jessee J P. Finite element formulation of the discrete ordinates method for multidimensional geometries[J]. International Journal of Thermophysics and Heat Transfer,1994,8: 427-433.
62. Qi H, Ruan L, Tan J. Development of a finite element radiation model applied to two-dimensional participating media[J]. Heat transfer-Asian Research,2005,34(6):386-395.
63. Ruan L M, Xie M,Qi H, An W, et al. Development of a finite element model for coupled radiative and conductive heat transfer in participating media. Journal of Quantitative Spectroscopy & Radiative Transfer,2006,102(2):190-202.
64. Maruyama S, Mori Y, Chikira C, et al. Combined nongray radiative and conductive heat transfer in multiple glazing taking into account specular reflection and absorption[J]. Heat transfer-Asian Research,2003,32(8):712-726.
65. Perrone N, Kao R. A general finite difference method for arbitrary meshes[J], Computational structure, 1975,5:45-58.
66. Liu Lin-hua, Tan Jianyu, Li Bing-xi. Meshless Approach for Coupled Radiative and Conductive Heat Transfer in One-Dimensional Graded Index Medium[J]. Journal of Quantitative Spectroscopy and Radiative Transfer,2006,101:237-248.
67. Tan Jianyu, Liu Lin-hua, Li Bing-xi. Least-Squares Collocation Meshless Approach for Coupled Radiative and Conductive Heat Transfer[J]. Numerical heat transfer, Part B,2006,49(2):179-195.
68.杨世铭,陶文铨.传热学[M].第三版.北京：高等教育出版社,1998.
69.余其铮.辐射换热基础[M].北京：高等教育出版社,1990：132-178.
70.尹雪梅,刘林华.高温气体辐射特性计算模型[J].热能动力工程,2007,22(5)：473-479.
71. Pierrot L, Soufiani A, Taine J. Accuracy of narrow-band and global models for radiative transfer in H2O, CO2, and H2O-CO2 mixtures at high temperature[J]. Journal of Quantitative Spectroscopy & Radiative Transfer,1999,6(2):523-548.
72. Marakis J G. Application of narrow and wide band models for radiative transfer in planar media[J]. International Journal of Heat and MassTransfer,2001,44(1):131-142.
73. Okamoto T, Mutou T, Takagi T. Approach for incorporating narrow band nonuniformity into nongray analysis of radiative heat transfer in nonisothermal and nonhomogeneous gas fields[J]. International Journal of Heat and MassTransfer,2001,44:4147-4156.
74. He J, Cheng W L, Buckius R O. Wide band cumulative absorption coefficient distribution model for overlapping absorption in H2O and CO2mixtures[J]. International Journal of Heat and MassTransfer, 2008,51(5-6):1115-1129.
75. Taniguchi H, Kudo K, Otaka M, et al. Development of a monte carlo method for numerical analysis on the radiation energy transfer through nongray gas layer[J]. International Journal for Numerical Method in Engineering,1992,35:883-891.
76. Yuen W W, Ma A. Evaluation of total emittance of an isothermal nongray absorbing, scattering gas-particle mixture based on the concept of absorption mean beam length[J]. International Journal of Heat and Mass Transfer,1992,114:653-658.
77. Tesse L, Dupoirieux F, Zamuner B, ea al. Radiative transfer in real gases using reciprocal and forward Monte Carlo methods and a correlated-k approach[J]. International Journal of Heat and MassTransfer, 2002,45:2797-2814.
78. Zhang H, Shi G. A new approach to solve correlated k-distribution function[J]. Journal of Quantitative Spectroscopy and Radiative Transfer,2005,96:311-324.
79. Ludwig C B, Malkmus W, Reardon J E, et al. Handbook of infrared radiation from combustion gases[M]. Washington D C:National aeronautics and space administration,1973.
80. Soufiani A, Taine J. High temperature gas radiative property parameters of statistical narrow-band model for H2O, CO2 and CO, and correlated-k model for H2O and CO2[J]. International Journal of Heat and MassTransfer,1997,40(4):987-991.
81. Liu F, Smallwood G J, Gulder O L. Application of the statistical narrow-band correlated-k method to low-resolution spectral intensity and radiative heat transfer calculations-effects of the quadrature scheme[J]. International Journal of Heat and Mass Transfer,2000,43:3119-3135.
82. Liu F, Smallwood G J, Gulder O L. Application of the statistical narrow-band correlated-k method to non-grey gas radiation in CO2-H2O mixtures:approximate treatments of overlapping bands[J]. Journal of Quantitative Spectroscopy and Radiative Transfer,2001,68(4):401-417.
83. Liu F, Smallwood G J. An efficient approach for the implementation of the SNB based correlated-k method and its evaluation[J]. Journal of Quantitative Spectroscopy and Radiative Transfer,2004, 84(4):465-475.
84. Levi Di L R, Taine J. A fictive gas-method for accurate computations of low-resolution IR gas transmissivities:application to the 4.3 μm CO2 band[J]. Revue de Physique Appliquee,1986, 21(12):825-831.
85. Caliot C, Maoult Y L, Hafi M E, et al. Remote sensing of high temperature H2O-CO2-CO mixture with a correlated k distribution fictitious gas method and the single-mixture gas assumption[J]. Journal of Quantitative Spectroscopy and Radiative Transfer,2006,102:304-315.
86.刘玉英,张欣欣.箱带模型结合DOM在非灰气体辐射换热计算中的应用[J].热科学与技术,2003,12(2)：336-341.
87. Lallemant N, Sayre A, Weber R.Evaluation of emissivity correlations for H2O-CO2-N2/air mixtures and coupling with solution methods of the radiative transfer equation[J]. Progress in Energy and Combustion Science,1996,22(6):543-574.
88. Strohle J, Coelho P J. On the application of the exponential wide band model to the calculation of radiative heat transfer in one-and two-dimensional enclosures[J]. International Journal of Heat and Mass Transfer,2002,45(10):2129-2139.
89. Modest M F. A simple differential approximation for radiative transfer in nongray gases[J]. International Journal of Heat and Mass Transfer,1979,101:735-736.
90. Modest M F, Sikka K K. The application of the stepwise-gray p1 approximation to molecular gas-particulate mixture[J].Fundamentals of radiation transfer,1991,160:97-103.
91. Komornicki W, Tomeczek J. Modification of the wide band gas radiation model for flame calculation[J]. International Journal of Heat and Mass Transfer,1992,35(7):1667-1671.
92. Marin O, Buckius R O. A simplified wide band model of the cumulative distri-bution function for carton dioxide[J]. International Journal of Heat and MassTransfer,1998,41:3881-3897.
93.聂宇宏,陈海耿.气体辐射宽带关联k模型的修正算法[J].计算物理,2002,19：439-442.
94.尹雪梅,刘林华,李炳熙.水蒸气和CO2混合气体辐射特性宽带k分布模型[J].中国电机工程学报,2008,28(5)：63-68.
95. Dua S S, Cheng P. Muti-dimensional heat transfer in non-isothermal cylindrical media with isothermal boundary walls[J]. International Journal of Heat and MassTransfer,1975,18:245-255.
96. Modest M F. The weighted-sum-of-gray-gases model for arbitrary solution methods in radiative transfer[J]. Transactions of the ASME. Journal of Heat Transfer,1991,113(3):650-656.
97. Kim O J, Song T H. Data base of WSGGM-based spectral model for radiation properties of combustion products[J]. Journal of Quantitative Spectroscopy and Radiative Transfer,2000,64: 379-394.
98. Yu M J, Baek S W, Park J H. An extension of the weighted sum of gray gases non-gray gas radiation model to a two phase mixture of non-gray gas with particles[J]. International Journal of Heat and MassTransfer,2000,43:1699-1713.
99. Leckner B. Spectral and total emissivity of water vapor and carbon dioxide[J].Combustion and flame,1972,19(1).33-48.
100. Zhang H, Modest M F. A muti-scale full-spectrum correlated-k distribution for radiative heat transfer in inhomogeneous gas mixtures[J]. Journal of Quantitative Spectroscopy and Radiative Transfer,2002, 73:349-360.
101. Modest M F. Narrow-band and full-spectrum k-distributions for radiative heat transfer correlated k vs. scaling approximation[J]. Journal of Quantitative Spectroscopy and Radiative Transfer,2003,76: 69-83.
102. Modest M F, Riazzi R. Assemly of full-spectrum k-distributions from a narrow-band database; effects of mixing gases, gases and nongray absorbing particles, and mixtures with nongray scatters in nongray enclosures[J]. Journal of Quantitative Spectroscopy and Radiative Transfer,2005,90:169-189.
103. Modest M F. Radiative heat transfer[M]. NewYork:Mcgraw-Hill Press,2002.
104. Trivic D N, Amon C H. Modeling the 3-D radiation of anisotropically scattering media by two different numerical methods[J]. International Journal of Heat and MassTransfer,2008,51:2711-2732.
105. Modest M F. Radiative Heat Transfer[M]. NewYork: McGraw-Hill Press Inc.,1993.
106. Edwards D K, Balakrishnan A. Slab band absorptance for molecular gas radiation[J]. Journal of Quantitative Spectroscopy and Radiative Transfer,1972,12(10):1379-1387.
107. Wassel A T, Edwards D K. Mean beam lengths for spheres and cylinders[J]. Transactions of the ASME. Journal of Heat Transfer,1976,98(2):308-309.
108.刘林华,余其铮,阮立明,等.煤粉燃烧产物的辐射特性[J].动力工程,1996,16(6)：15-21.
109.沈九宾,陈海耿,陈婉.用离散传递法求解辐射全交换面积[J].化工学报,2003,54(12)：1674-1677.
110.陆钟武.火焰炉[M].北京：冶金工业出版社,1995.
111.欧俭平.高温空气燃烧技术在冶金热工设备上的应用及数值仿真和优化研究[D].长沙：中南大学,2004.
112. Bojic M, Mourdoukoutas P. Energy saving does not yield CO2 emissions reductions:the case of waste fuel use in a steel mill[J]. Applied Thermal Engineering,2000,20:963-975.
113. Bojic M, Tomic M. Effect of refuse-gas fuel use on energy consumption in an industrial pusher furnace[J]. Energy,1998,23(9):767-775.
114. Patankar S V. Computational modeling of flow and heat transfer in industrial applications[J]. International Journal of Heat and MassTransfer,2002,23(3):222-231.
115. Ramirez M, Haber R, Pena V, et al. Fuzzy control of a multiple hearth furnace[J]. Computers in industry,2004,54(1):105-113.
116. Chen W H, Chung Y C, Liu J L. Analysis on energy consumption and performance of reheating furnaces in a hot strip mill[J]. International Communications in Heat and Mass Transfer,2005,32(5): 695-706.
117.李义科,高仲龙,任雁秋,等.加热炉热过程计算机控制的应用与分析[J].工业加热,2000,1：4-6.
118.姜泽毅,汪霞,张欣欣,等.钢(荒)管再加热炉计算机控制数学模型及其应用[J].金属学报,2000,36(4)：429-432.
119.董伟,陈海耿,李瑞阳,等.加热炉热过程动态操作数学模型[J].工程热物理学报,2003,24(2)：295-297.
120.张卫军,吴雪琦,陈海耿.基于机理模型的加热炉在线炉温模糊决策[J].东北大学学报(自然科学版),2005,26(9)：878-881.
121.陈海耿,王子弟,吴彬,等.连续加热炉在线控制系统的仿真研究[J].钢铁,2006,41(12)：75-78.
122.郝小红,温治,安月明,等.连铸坯装炉温度在线实时计算模型及其应用[J].系统仿真学报,2007,19(14)：3324-3326.
123.刘坤,韩仁志,谢国威.蓄热式加热炉内温度场及浓度场的数值模拟[J].冶金能源,2005,24(3)：22-24.
124.宋小飞,刘训良,温治,等.空气单蓄热室状加热炉内传输过程的数值模拟[J].浙江大学学报(工学版),2007,41(10)：1768-1772.
125. Kim M Y. A heat transfer model for the analysis of transient heating of the slab in a direct-fired walking beam type reheating furnace[J]. International Journal of Heat and MassTransfer,2007, 50(19-20):3740-3748.
126. Kung E Y. A Mathematieal Model of Soaking Pits[J]. ISA TRANSACTIONS,1967,6(2):1-10.
127.郝小红,温治.连铸坯凝固传热数学模型的研究[J].铸造技术[J],2007,28(10)：1356-1359.
128.郝小红,温治,安月明,等.连铸坯装炉温度在线实时计算模型及其应用[J].系统仿真学报,2007,19(14)：3324-3326.
129.杨贤荣,马庆芳,原庚新,等.辐射换热角系数手册[M].北京：国防工业出版社,1982.
130. Wiernga J A, Elich J J Ph, Hoogendoorn C J. Spectral effects of radiative heat transfer in high temperature furnaces burning natural gas[J]. Journal of the Institute of Energy,1990,63(456):101-108.
131.白焕炽.高温涂料节能效果分析及其应用前景[J].工业炉,1993,(1)：12-16.
132. Clement J G. High emissivity coatings-a major advanced in furnace technology [J]. Heat treatment of metals,1986,13(3):76-79.
133. Tu P Q, Chen J K, Zhou J C. High emissivity coating and its application for energy-saving[J]. Journal of infrared and millimeter waves,1993,12(6):436-440.
134. Bebellis C L. Evaluation of the high emittance-coating in a large industrial furnace[J]. Industrial heating,1993,60(10):56-60,62.
135. Alexander I C. High reflectivity furnace coatings[J]. Metals and materials,1988,4(1):25-27.
136.欧阳德刚,罗安智.炉壁黑度对火焰炉能耗的影响[J].钢铁研究,1998,(5)：47-49.
137.吴彬,陈海耿,李本文.连续加热炉三元在线控制数学模型[J].工业炉,1999,21(1)：34-37.
138. Elich J J P, Wieringa J A. Temperature effects influencing the spectral and total emissivity of refractories[J]. Experimental thermal and fluid science,1995,10:318-326.
139. Neuer G, Jaroma-Weiland G. Spectral and total emissivity of high-temperature materials[J]. International Journal of Thermophysics,1998,19(3):917-929.
140. Kobayashi M, Ono A, Otsuki M, et al. A database of normal spectral emissivities of metals at high temperatures[J]. International Journal of Thermophysics,1999,20(1):299-308.
141.陈海耿,杨泽宽,张卫军. 热轧带钢步进式加热炉计算机优化控制[J].钢铁,1999,34(5)：57-59.