高温电加热过程模拟分析
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摘要
工业电炉是普遍使用的加热设备,对其进行优化设计的研究具有重要意义。本文对电阻炉核心加热元件的传热特性进行了较细致的模拟计算和分析,具体研究工作有以下几个方面:
1、对电加热体材料的研究。本文从电热体结构、尺寸、表面温度三个方面对电加热体进行研究,得出圆管状的电热体的内外温度分布比较均匀。当电热体的直径D>5cm时,棒状及方棒电加热体的内外温差比较高,而管状电加热体则相对比较低。电加热体外表面温度对电加热体的影响也比较明显,半径一定时,温差与电热体外表面温度近似成平方关系,当外表面温度一定时,电加热体温差随着半径的增大而升高。
2、高温电加热条件下,对于含有大分子碳化硅杂质颗粒的石墨电加热材料进行三维稳态模拟,得知电流对碳化硅颗粒与石墨电加热体之间的温差影响最大,当电流密度达到20A/mm2时,温差达到35℃。而且,碳化硅颗粒的存在,也使石墨体的温度升高,碳化硅颗粒粒度越大,石墨体内部升温越高。
3、研究了非稳态情况下各种电加热元件的传热特性。对于管状电热元件,内部绝热材料的压紧对应着密度的变化,它对电热体升温及内部温度分布都有很大的影响,压紧的绝热材料比未压紧的升温快而且内部温差较低。对于J GQ型电加热元件,在压紧的状态下加热元件外表面达到70℃所用的时间明显少于未压紧状态下所用的时间。另外,在未压紧时加热元件内部的温度明显高于压紧情况下的温度对于石墨电热体。研究了石墨体非稳态电加热升温过程中,电加热体的升温速率与石墨体的密度有直接关系,根据模拟得知在电加热过程中石墨体温度分布均匀,因此反推出升温速率与电热体密度的关系,关系式为:,当密度较小时计算结果与模拟结果相吻合。对于有裂纹存在的棒状及管状石墨电热体,裂纹的存在对石墨电加热体升温过程中的影响非常严重,由于裂纹的存在,棒状石墨电热体升温速率下降,对于10mm的棒状电加热体,对于直径为10mm的棒状电加热体,无裂纹时,1s钟后的温度为524.95℃,而有裂纹时的最高温度才为434.587℃,并且温度的最高点和最低点都集中在裂缝附近,这就会在裂缝处产生很大的热应力。对于厚度为10mm管状电热体由于裂纹的存在,使电热体温度分布极不均匀,电热体温度为1000℃左右时,裂纹处的温度就已经达到2400℃,这样继续加热下去,石墨体未达到工作温度,就会超过石墨体熔点,造成石墨体的烧结。在辐射和热传导耦合情况下模拟了直径随轴向逐渐减小石墨体的温度场和应力场分布状况,结果表明,直径越小升温速率越高,但是轴向上温度梯度却是逐渐减小的。
Industrial furnace is commonly used heating equipment, it is very important to design and optimize the furnace. In this paper, it simulates and optimize the heat transfer characteristics of the core of the resistance furnace detailed. Specific studies in the following areas:
1 the research of the electric heater
This article studies the electric heating from the electric structure, size, and the surface temperature of the three aspects. The inside and outside temperature is distributing more uniform, when the cross-section of the electric heating is the circular ring. When D>5cm, the internal and external difference in temperature of circle rods and square rods is higher, but tube electricity heat body stand opposite each other lower. The surface temperature affects the electric heating rods obviously. When radius is a certain value, it is the approximate to last square relation between with difference in temperature and external surface temperature. When the outer surface temperature is a certain temperature, the heating temperature difference with a radius of the increasing rise
2 Under the conditions of high temperature electric heating three-dimensional steady-state simulate the macromolecular particles containing impurities in the graphite heating materials. It’s finding that the current is greatest impact the heat of the graphite containing impurities. For silicon carbide particles, the greater the current, the greater the temperature difference between the particles, and temperature difference is directly proportional to the square with the current relations. When the current is 20 A/mm2,the temperature difference has reached 35℃. In addition to Current, the impurities in the size of particles also directly affect the temperature of the electric distribution. In addition to Current, the size of particles also directly affects the temperature of the electric distribution.
3 This paper studies the heat transfer characteristics of variety of electric heating elements, under the unsteady-state status. For the Tubular electric heating elements, internal insulation materials affect the velocity of calefactive and the inner distribution of temperature on the electric heating. For J GQ style tubular electric heating elements, pinched heating elements under the surface reached to 70℃, the time spent significantly less than the state did not pinched , another is the temperature of loosen heating elements is higher obviously than that pinched circumstances. For the graphite electric element, at the condition of radiating outside of heat, the temperature of the graphite electric element is absent quickly. The heating rate is relative to the density. According to simulation, the temperature distributed equality, so receive the relative is: When the density is small, the result of calculation and simulation result are identical. For the graphite electric element which has crack on the surface, the exist of the crack are effect the heat rate very much, the exist of the crack causes the decline of the heat rate. a 10mm- diameter graphite electric element, a second latter, the temperature reach 524.95℃if there is no a crack .But it highest temperature is 434.587℃when there is a crack. At the round of the crack the temperature is smaller than the main body of the graphite electric element. There is a big difference in temperature, which result the heat stress. The existence of the crack in tubular graphite electric element result the un-equality of the element temperature For a 10mm-deepth tubular graphite electric element, when the temperature of the crack achieve to the work temperature, the temperature of the body is at only a small point(about500℃).So if continues to heat the temperature of the body has not reach the work temperature, the crack temperature has exceed the melting point.
1、对电加热体材料的研究。本文从电热体结构、尺寸、表面温度三个方面对电加热体进行研究,得出圆管状的电热体的内外温度分布比较均匀。当电热体的直径D>5cm时,棒状及方棒电加热体的内外温差比较高,而管状电加热体则相对比较低。电加热体外表面温度对电加热体的影响也比较明显,半径一定时,温差与电热体外表面温度近似成平方关系,当外表面温度一定时,电加热体温差随着半径的增大而升高。
2、高温电加热条件下,对于含有大分子碳化硅杂质颗粒的石墨电加热材料进行三维稳态模拟,得知电流对碳化硅颗粒与石墨电加热体之间的温差影响最大,当电流密度达到20A/mm2时,温差达到35℃。而且,碳化硅颗粒的存在,也使石墨体的温度升高,碳化硅颗粒粒度越大,石墨体内部升温越高。
3、研究了非稳态情况下各种电加热元件的传热特性。对于管状电热元件,内部绝热材料的压紧对应着密度的变化,它对电热体升温及内部温度分布都有很大的影响,压紧的绝热材料比未压紧的升温快而且内部温差较低。对于J GQ型电加热元件,在压紧的状态下加热元件外表面达到70℃所用的时间明显少于未压紧状态下所用的时间。另外,在未压紧时加热元件内部的温度明显高于压紧情况下的温度对于石墨电热体。研究了石墨体非稳态电加热升温过程中,电加热体的升温速率与石墨体的密度有直接关系,根据模拟得知在电加热过程中石墨体温度分布均匀,因此反推出升温速率与电热体密度的关系,关系式为:,当密度较小时计算结果与模拟结果相吻合。对于有裂纹存在的棒状及管状石墨电热体,裂纹的存在对石墨电加热体升温过程中的影响非常严重,由于裂纹的存在,棒状石墨电热体升温速率下降,对于10mm的棒状电加热体,对于直径为10mm的棒状电加热体,无裂纹时,1s钟后的温度为524.95℃,而有裂纹时的最高温度才为434.587℃,并且温度的最高点和最低点都集中在裂缝附近,这就会在裂缝处产生很大的热应力。对于厚度为10mm管状电热体由于裂纹的存在,使电热体温度分布极不均匀,电热体温度为1000℃左右时,裂纹处的温度就已经达到2400℃,这样继续加热下去,石墨体未达到工作温度,就会超过石墨体熔点,造成石墨体的烧结。在辐射和热传导耦合情况下模拟了直径随轴向逐渐减小石墨体的温度场和应力场分布状况,结果表明,直径越小升温速率越高,但是轴向上温度梯度却是逐渐减小的。
Industrial furnace is commonly used heating equipment, it is very important to design and optimize the furnace. In this paper, it simulates and optimize the heat transfer characteristics of the core of the resistance furnace detailed. Specific studies in the following areas:
1 the research of the electric heater
This article studies the electric heating from the electric structure, size, and the surface temperature of the three aspects. The inside and outside temperature is distributing more uniform, when the cross-section of the electric heating is the circular ring. When D>5cm, the internal and external difference in temperature of circle rods and square rods is higher, but tube electricity heat body stand opposite each other lower. The surface temperature affects the electric heating rods obviously. When radius is a certain value, it is the approximate to last square relation between with difference in temperature and external surface temperature. When the outer surface temperature is a certain temperature, the heating temperature difference with a radius of the increasing rise
2 Under the conditions of high temperature electric heating three-dimensional steady-state simulate the macromolecular particles containing impurities in the graphite heating materials. It’s finding that the current is greatest impact the heat of the graphite containing impurities. For silicon carbide particles, the greater the current, the greater the temperature difference between the particles, and temperature difference is directly proportional to the square with the current relations. When the current is 20 A/mm2,the temperature difference has reached 35℃. In addition to Current, the impurities in the size of particles also directly affect the temperature of the electric distribution. In addition to Current, the size of particles also directly affects the temperature of the electric distribution.
3 This paper studies the heat transfer characteristics of variety of electric heating elements, under the unsteady-state status. For the Tubular electric heating elements, internal insulation materials affect the velocity of calefactive and the inner distribution of temperature on the electric heating. For J GQ style tubular electric heating elements, pinched heating elements under the surface reached to 70℃, the time spent significantly less than the state did not pinched , another is the temperature of loosen heating elements is higher obviously than that pinched circumstances. For the graphite electric element, at the condition of radiating outside of heat, the temperature of the graphite electric element is absent quickly. The heating rate is relative to the density. According to simulation, the temperature distributed equality, so receive the relative is: When the density is small, the result of calculation and simulation result are identical. For the graphite electric element which has crack on the surface, the exist of the crack are effect the heat rate very much, the exist of the crack causes the decline of the heat rate. a 10mm- diameter graphite electric element, a second latter, the temperature reach 524.95℃if there is no a crack .But it highest temperature is 434.587℃when there is a crack. At the round of the crack the temperature is smaller than the main body of the graphite electric element. There is a big difference in temperature, which result the heat stress. The existence of the crack in tubular graphite electric element result the un-equality of the element temperature For a 10mm-deepth tubular graphite electric element, when the temperature of the crack achieve to the work temperature, the temperature of the body is at only a small point(about500℃).So if continues to heat the temperature of the body has not reach the work temperature, the crack temperature has exceed the melting point.
引文
[1]江尧忠著.工业电炉.北京:清华大学出版社, 1993年12月第1版3～5
[2]陈爱中.硫酸厂气体电加热炉技术的进展.硫酸工业,1998年第4期14～17
[3]陈懋雍.大型热处理电阻炉的五大发展趋势.中国科技信息,1994年04期16
[4]张仲怀.电阻炉的温度最优控制.工业电炉,1984年第05期35-41
[5]陈常及.节能热处理电阻炉.工业电炉,1984年第04期26～29
[6]舒克炎.电阻炉改炉节能.工业加热,1988年第04期40～46
[7]李爱东.电阻炉的节能改造.机车车辆工艺,1994年第04期41
[8]何汉机.开工加热炉盘管技术改造.大氮肥,1996年第01期31～34
[9]俞祥九戚洪明.循环式电加热其设计及应用.广东化工,1998年第04期55～56
[10]郑远碳.纤维生产技术和工业应用.石化技术与应用, 1995年04期255～259
[11]陈耀庭,周明义,王国全,俞炯,谷晓昱,者东梅等.碳纤维/聚合物复合材料的导电性及电磁屏蔽性能的研究.塑料科技, 1997年06期4～7
[12]朱波,曹伟伟,王延相,王成国等.新型碳纤维电加热辐射管的开发.工业加热, 2005年02期32～35
[13] E.G.Acherica.America,US Patent No.492767,1893
[14] Kuriakose,Areekattuthazhayil K.United States Patent No4419336,1983
[15]朱兴宏等.等直径硅碳棒工业试验.轻合金加工技术[J],1997,25(4).18～19
[16] Lee.G.Carbide and Nitride Ceramics by Carboththermal Reduction of silica Diss Asber InT.B,1976,37(7):1379
[17]商跃进.有限元原理与ANSYS应用指南.北京:清华大学出版社,2005,165～180
[18]博嘉科技编著.有限元分析软件——ANSYS融会与贯通.中国水利水电出版社,2002,219-220
[19]美国ANSYS公司,ANSYS非线性分析指南
[20]美国ANSYS公司,ANSYS耦合场分析指南
[21]堂兴伦等. ANSYS工程应用教程.热与电磁学篇.北京:铁道出版社, 2003
[22]龚曙光.ANSYS基础应用及范例解析.北京:机械工业出版社, 2003 , 5
[23]孔祥伟,李壬龙,王秉新,王国栋,刘相华.轧辊温度场及轴向热凸度有限元计算.钢铁研究学报,2000 , 12 (9) 25～29
[24]赵永忠,朱启建,李谋渭.中厚板控冷过程有限元模拟及在生产中的应用.冶金设备, 2002 , 12 (6) 31～36
[25]龚涛,杨海西,邓康.连铸过程中结晶器内流体流动和温度传输的数值模拟.计算物理, 2000 , 17 (6) 43～47
[26]许光明,李兴刚,崔建忠.液固相铝2不锈钢板复合轧制温度场的模拟计算.钢铁研究学报, 2002 , 12
[27]杨庆祥,李艳丽,赵言辉,姚枚.堆焊金属残余应力场的计算机模拟.焊接学报( Transactions of theChina Welding Institution) , 2001 , 3 (22)
[28]吴祥兴,胡伦骥,杜汉斌,胡席远1在激光焊接温度场数值模拟中的应用.电焊机, 2002 , 32 (9)
[29]薛勇,张建勋.基于ANSYS软件的焊接变形工程预测.焊接技术, 2002 , 30 (增刊)
[30]朱援祥,张小飞,杨兵,李晓梅.基于有限元的多次补焊焊接残余应力的数值模拟.焊接学报( Transactions of the China Welding Institution ) ,2002 , 1 (23)
[31] A1P1Amosov and A1F1Fedotov , Finite2Element Plane Model of Thermal Conditions in Self2Progragating High2Temperature Synthesis of Blanks in a Friable Shell ,Journal of Engineering Physics and Thermo physics ,Vol174 , No15 , 20011
[32] J1Drescher , R1Schmidt , H12J1Hardtke , Finite2Ele2 Ment2Modellierung und Simulation Des Menschlichen Trommelfells , HNO , 1998246 : 129～134
[33] Y1H1Mu , N1P1Hung and K1A1Ngoi , Optimizations Design of a Piezoelectric Micro pump Int Adv ManufTechnol (1999) 15 : 573～576
[34] S1Yilmaz , FEM2Untersuchung des thermodynamisch2en und thermoses christens Verhaltens bei der Erstar2rung Von einem Stahlgubteil , Forschung im Ingenieur2 wesen , 2002 (67) : 117～122
[35] M1S1Kim , J1C1Choi , Y1H1Kim , G1J1Huh and C1Kim , An automated Process Planning and Die DesignSystem for Quasi2Axisymmetric Cold Forging Products ,Int J Adv Manuf Technol , 2002 (20) : 201～213
[36]刘岩,杨海天.基于时域精细算法的EFG/ FE2EFG方法求解热传导问题.应用基础与工程科学学报[A] 2002 308-317
[37]邱海鹏,郭全贵,宋永忠,翟更太,刘朗.原料配比对石墨材料热传导性能的影响材料科学与工艺第10卷第3期2 0 0 2年9月225～230
[38]刘忠杰,刘中兴,陈俊俊.稀土电解槽用石墨高温导热系数的测定.稀土第23卷第3期2002年6月48～51
[39] [日]Masakazu Adachi, Hiroshi,Shioyama,Masaki Narisawa等. 900-2800K多晶硅石墨电阻率与温度关系.碳素技术. 1991 N4
[40]梁训裕.碳化硅耐火材料.北京:科学出版社,1981年5月第1版265～316
[41]谢有赞.炭石墨材料工艺.1988年8月第1版
[42]甄永杰,师晋生,刘振义,高启军.管状电加热元件的不稳定态导热数值模拟节能,2004年第7期,14～17
[43] S. V.帕坦卡.传热与流体流动的数值计算[M] .北京:科学出版社,1984.
[44] Yang Haitian. A new approach of time stepping for solving transfer problems [ J ] . Communications in Numerical Method in Engineering , 1999 , 15 : 325～334
[45] Belytschko T , Lu Y Y, Gu L. Element free gale kin methods [J ] . International Journal for Numerical Methods in Engineering , 1994 , 37 : 229～256
[46] Keller,K.,Hoffinann,M.,Zorneer,E.,and Bumenberg,J.,“Application of High Temperature Multilayer Insulations,”Aetna Astronaut,VOI.26,No.6,1992,PP 451一458
[47]沈远胜,杨中喜,王冬至,陶珍东,任丽.电阻炉电热元件使用寿命问题的热工方案的研究[J]工业加热,第35卷2006年第4期31～34
[48]史光梅,刘朝.工业炉内辐射换热模型研究进展[J].工业加热, 2004,34(5): 9～12.
[49] ModestM F. Radiative Heat Transfer [M ]. New York: McGraw Hill Inc, 1993. 713～715.
[50]孙世梅张红.热管换热器传热性能及温度场数值模拟[M].化工学报,第55卷第3期472-475
[51] Tarzia D A. Determination of the Unknown Coefficience in the Lame2clapcyron Problem Corond2phase Seft Stefan Prob2lem. Autocracies in Appl Math , 1983 , 3 : 74～82
[52]郭宏伟,葛仕福.新型空气电加热器的牲能研究.化工时刊,2001年第2期29～31
[53]赵升吨张立军柳伟化春键.棒料热应力预制V型槽尖端理想裂纹的可行性研究,塑性工程学报,2006年10月,第13卷第5期,51～57
[54]马振宁,高明.金属材料裂纹尖端温度场和热应力场的数值模拟,沈阳师范大学学报(自然科学版) ,2006年1月,第24卷第1期,35～37
[55]龚曙光. ANSYS工程应用实例解析[M] .北京:机械工业出版社. 2003. 278～327
[56]付宇明,白象忠,许志强·带有中间裂纹载流薄板放电瞬间耦合场的数值模拟[J ]·固体力学学报, 2002 ,23 (3),307～311·
[57]胡宇达,白象忠·含半无限长裂纹导电板的热电止裂问题[J ]·应用基础与工程科学学报, 2001 ,9 (1) ,64～67·
[58]郑丽娟,付宇明,白象忠,田振国·带有裂纹的金属薄板构件裂尖处电热应力的数值分析[J ]·机械工程学报,2002 ,38 (3) ,90～93·
[59]董玉平,邓波,申树云,孙启新.基于ANSYS的U形波纹管热应力分析节能技术2007年1月,第25卷,总第141期, 38～41
[60]白晨,蒋国璋,李公法耐火材料制品的温度和热应力分析研究.湖北工业大学学,第21卷第3期80～82
[61]吉野良一. Improvement of Plate Brick Shape for SlideGate Valve [ J ] . Shinagawa Technical Report , 1997(40) : 35～39.
[62] Michael W. Maupin. Finite2Element Study of A De2gasser Bottom And Throat Area [ J ] .
[63] National Steel ,1997 :369 - 378.Gasser A , Boisse P. Experimental and Numerical An2 alyses of Thermo mechanical Ref rectory Lining Behav2iour [J ] . Proc Instant Mech Engrs , 2001 (215) : 41～53.
[64]陈勇,练章华等.界面存在微间隙的热采井井筒热应力分析。石油机械, 2008年,第36卷,第1期7～10
[2]陈爱中.硫酸厂气体电加热炉技术的进展.硫酸工业,1998年第4期14～17
[3]陈懋雍.大型热处理电阻炉的五大发展趋势.中国科技信息,1994年04期16
[4]张仲怀.电阻炉的温度最优控制.工业电炉,1984年第05期35-41
[5]陈常及.节能热处理电阻炉.工业电炉,1984年第04期26～29
[6]舒克炎.电阻炉改炉节能.工业加热,1988年第04期40～46
[7]李爱东.电阻炉的节能改造.机车车辆工艺,1994年第04期41
[8]何汉机.开工加热炉盘管技术改造.大氮肥,1996年第01期31～34
[9]俞祥九戚洪明.循环式电加热其设计及应用.广东化工,1998年第04期55～56
[10]郑远碳.纤维生产技术和工业应用.石化技术与应用, 1995年04期255～259
[11]陈耀庭,周明义,王国全,俞炯,谷晓昱,者东梅等.碳纤维/聚合物复合材料的导电性及电磁屏蔽性能的研究.塑料科技, 1997年06期4～7
[12]朱波,曹伟伟,王延相,王成国等.新型碳纤维电加热辐射管的开发.工业加热, 2005年02期32～35
[13] E.G.Acherica.America,US Patent No.492767,1893
[14] Kuriakose,Areekattuthazhayil K.United States Patent No4419336,1983
[15]朱兴宏等.等直径硅碳棒工业试验.轻合金加工技术[J],1997,25(4).18～19
[16] Lee.G.Carbide and Nitride Ceramics by Carboththermal Reduction of silica Diss Asber InT.B,1976,37(7):1379
[17]商跃进.有限元原理与ANSYS应用指南.北京:清华大学出版社,2005,165～180
[18]博嘉科技编著.有限元分析软件——ANSYS融会与贯通.中国水利水电出版社,2002,219-220
[19]美国ANSYS公司,ANSYS非线性分析指南
[20]美国ANSYS公司,ANSYS耦合场分析指南
[21]堂兴伦等. ANSYS工程应用教程.热与电磁学篇.北京:铁道出版社, 2003
[22]龚曙光.ANSYS基础应用及范例解析.北京:机械工业出版社, 2003 , 5
[23]孔祥伟,李壬龙,王秉新,王国栋,刘相华.轧辊温度场及轴向热凸度有限元计算.钢铁研究学报,2000 , 12 (9) 25～29
[24]赵永忠,朱启建,李谋渭.中厚板控冷过程有限元模拟及在生产中的应用.冶金设备, 2002 , 12 (6) 31～36
[25]龚涛,杨海西,邓康.连铸过程中结晶器内流体流动和温度传输的数值模拟.计算物理, 2000 , 17 (6) 43～47
[26]许光明,李兴刚,崔建忠.液固相铝2不锈钢板复合轧制温度场的模拟计算.钢铁研究学报, 2002 , 12
[27]杨庆祥,李艳丽,赵言辉,姚枚.堆焊金属残余应力场的计算机模拟.焊接学报( Transactions of theChina Welding Institution) , 2001 , 3 (22)
[28]吴祥兴,胡伦骥,杜汉斌,胡席远1在激光焊接温度场数值模拟中的应用.电焊机, 2002 , 32 (9)
[29]薛勇,张建勋.基于ANSYS软件的焊接变形工程预测.焊接技术, 2002 , 30 (增刊)
[30]朱援祥,张小飞,杨兵,李晓梅.基于有限元的多次补焊焊接残余应力的数值模拟.焊接学报( Transactions of the China Welding Institution ) ,2002 , 1 (23)
[31] A1P1Amosov and A1F1Fedotov , Finite2Element Plane Model of Thermal Conditions in Self2Progragating High2Temperature Synthesis of Blanks in a Friable Shell ,Journal of Engineering Physics and Thermo physics ,Vol174 , No15 , 20011
[32] J1Drescher , R1Schmidt , H12J1Hardtke , Finite2Ele2 Ment2Modellierung und Simulation Des Menschlichen Trommelfells , HNO , 1998246 : 129～134
[33] Y1H1Mu , N1P1Hung and K1A1Ngoi , Optimizations Design of a Piezoelectric Micro pump Int Adv ManufTechnol (1999) 15 : 573～576
[34] S1Yilmaz , FEM2Untersuchung des thermodynamisch2en und thermoses christens Verhaltens bei der Erstar2rung Von einem Stahlgubteil , Forschung im Ingenieur2 wesen , 2002 (67) : 117～122
[35] M1S1Kim , J1C1Choi , Y1H1Kim , G1J1Huh and C1Kim , An automated Process Planning and Die DesignSystem for Quasi2Axisymmetric Cold Forging Products ,Int J Adv Manuf Technol , 2002 (20) : 201～213
[36]刘岩,杨海天.基于时域精细算法的EFG/ FE2EFG方法求解热传导问题.应用基础与工程科学学报[A] 2002 308-317
[37]邱海鹏,郭全贵,宋永忠,翟更太,刘朗.原料配比对石墨材料热传导性能的影响材料科学与工艺第10卷第3期2 0 0 2年9月225～230
[38]刘忠杰,刘中兴,陈俊俊.稀土电解槽用石墨高温导热系数的测定.稀土第23卷第3期2002年6月48～51
[39] [日]Masakazu Adachi, Hiroshi,Shioyama,Masaki Narisawa等. 900-2800K多晶硅石墨电阻率与温度关系.碳素技术. 1991 N4
[40]梁训裕.碳化硅耐火材料.北京:科学出版社,1981年5月第1版265～316
[41]谢有赞.炭石墨材料工艺.1988年8月第1版
[42]甄永杰,师晋生,刘振义,高启军.管状电加热元件的不稳定态导热数值模拟节能,2004年第7期,14～17
[43] S. V.帕坦卡.传热与流体流动的数值计算[M] .北京:科学出版社,1984.
[44] Yang Haitian. A new approach of time stepping for solving transfer problems [ J ] . Communications in Numerical Method in Engineering , 1999 , 15 : 325～334
[45] Belytschko T , Lu Y Y, Gu L. Element free gale kin methods [J ] . International Journal for Numerical Methods in Engineering , 1994 , 37 : 229～256
[46] Keller,K.,Hoffinann,M.,Zorneer,E.,and Bumenberg,J.,“Application of High Temperature Multilayer Insulations,”Aetna Astronaut,VOI.26,No.6,1992,PP 451一458
[47]沈远胜,杨中喜,王冬至,陶珍东,任丽.电阻炉电热元件使用寿命问题的热工方案的研究[J]工业加热,第35卷2006年第4期31～34
[48]史光梅,刘朝.工业炉内辐射换热模型研究进展[J].工业加热, 2004,34(5): 9～12.
[49] ModestM F. Radiative Heat Transfer [M ]. New York: McGraw Hill Inc, 1993. 713～715.
[50]孙世梅张红.热管换热器传热性能及温度场数值模拟[M].化工学报,第55卷第3期472-475
[51] Tarzia D A. Determination of the Unknown Coefficience in the Lame2clapcyron Problem Corond2phase Seft Stefan Prob2lem. Autocracies in Appl Math , 1983 , 3 : 74～82
[52]郭宏伟,葛仕福.新型空气电加热器的牲能研究.化工时刊,2001年第2期29～31
[53]赵升吨张立军柳伟化春键.棒料热应力预制V型槽尖端理想裂纹的可行性研究,塑性工程学报,2006年10月,第13卷第5期,51～57
[54]马振宁,高明.金属材料裂纹尖端温度场和热应力场的数值模拟,沈阳师范大学学报(自然科学版) ,2006年1月,第24卷第1期,35～37
[55]龚曙光. ANSYS工程应用实例解析[M] .北京:机械工业出版社. 2003. 278～327
[56]付宇明,白象忠,许志强·带有中间裂纹载流薄板放电瞬间耦合场的数值模拟[J ]·固体力学学报, 2002 ,23 (3),307～311·
[57]胡宇达,白象忠·含半无限长裂纹导电板的热电止裂问题[J ]·应用基础与工程科学学报, 2001 ,9 (1) ,64～67·
[58]郑丽娟,付宇明,白象忠,田振国·带有裂纹的金属薄板构件裂尖处电热应力的数值分析[J ]·机械工程学报,2002 ,38 (3) ,90～93·
[59]董玉平,邓波,申树云,孙启新.基于ANSYS的U形波纹管热应力分析节能技术2007年1月,第25卷,总第141期, 38～41
[60]白晨,蒋国璋,李公法耐火材料制品的温度和热应力分析研究.湖北工业大学学,第21卷第3期80～82
[61]吉野良一. Improvement of Plate Brick Shape for SlideGate Valve [ J ] . Shinagawa Technical Report , 1997(40) : 35～39.
[62] Michael W. Maupin. Finite2Element Study of A De2gasser Bottom And Throat Area [ J ] .
[63] National Steel ,1997 :369 - 378.Gasser A , Boisse P. Experimental and Numerical An2 alyses of Thermo mechanical Ref rectory Lining Behav2iour [J ] . Proc Instant Mech Engrs , 2001 (215) : 41～53.
[64]陈勇,练章华等.界面存在微间隙的热采井井筒热应力分析。石油机械, 2008年,第36卷,第1期7～10