内融冰式蓄冰管三维传热性能动态模拟
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摘要
随着世界能源危机的深化,冰蓄冷空调系统以其简单的结构和显著的社会经济效益得到了日益广泛地应用。特别是在我国电力极度紧张的局面下,冰蓄冷空调系统具有显著的调峰作用,对于缓解我国目前的电力紧张局面有着十分重要的重用,同时也对我国经济的科学发展有着积极的意义。在目前应用的多种蓄冰系统中,内融冰式蓄冰系统具有可靠性高,结冰融冰比较迅速等优点,从而得到了广泛的应用。因此,对蓄冰管的蓄冰、融冰特性进行深入的研究有现实的理论意义与实际的工程价值。本文出于这一目的,对内融冰式蓄冰管的传热性能展开理论研究。
本文应用焓法,建立了内融冰式蓄冰管单管蓄冰过程的物理数学模型,理论分析了该过程的传热特性,同时也分析了低温冷媒的流速、入口温度、蓄冰管管径、蓄冰管外水的初始温度四个蓄冰前的初始因素对蓄冰性能的影响,为正确合理的设计蓄冰系统提供理论指导。
同时,应用焓法,分别在考虑自然对流和忽略自然对流两种情况下,建立了内融冰式蓄冰管融冰时的物理数学模型,理论分析了对应过程的传热特性,同时也分析了高温热媒的流速、入口温度、蓄冰管管径、蓄冰管外冰的初始温度四个融冰前的初始因素对自然对流强度和融冰性能的影响,为正确进行系统优化、参数匹配等提供了理论指导。
Along with the world energy crisis turning deeply, the ice storage system is applied more and more widely because of its simple design and obviously economy. Especially under the extreme nervous situation of the electric power in our country , the ice storage system has the special and important function of alleviating the nervous situation of the current electric power, and also has the aggressive meaning to the scientific development of the economy of our country.Among all the ice storage systems, internal-melt ice-on-tube has been widely used because of its high reliability and relatively high charging and discharging rate. Therefore, it is important to investigate the mechanism of freezing and meting about ice-on-tube. For this purpose a research of the performance of heat transfer of internal-melt ice-on-tube is carried out theoretically.
Through enthalpy method, a three-dimension heat transfer mathematical model for the ice-on-tube with freezing is established. Based on the model the influences of the velocity in the tube, the inlet temperature of flow, the diameter of tube and the initial temperature of the water on the heat transfer characteristics of freezing are analyzed. It provides theoretical instruction of designing ice-on-tube.
Besides, under the two circumstances with nature convection and without nature convection, a three-dimension heat transfer mathematical model for the ice-on-tube with melting is established. Based on the model the influences of the velocity in the tube, the inlet temperature of flow, the diameter of tube and the initial temperature of the ice on the natural convection of the melted water and the heat transfer characteristics of melting are analyzed. It provides theoretical instruction of optimizing system and matching parameters.
本文应用焓法,建立了内融冰式蓄冰管单管蓄冰过程的物理数学模型,理论分析了该过程的传热特性,同时也分析了低温冷媒的流速、入口温度、蓄冰管管径、蓄冰管外水的初始温度四个蓄冰前的初始因素对蓄冰性能的影响,为正确合理的设计蓄冰系统提供理论指导。
同时,应用焓法,分别在考虑自然对流和忽略自然对流两种情况下,建立了内融冰式蓄冰管融冰时的物理数学模型,理论分析了对应过程的传热特性,同时也分析了高温热媒的流速、入口温度、蓄冰管管径、蓄冰管外冰的初始温度四个融冰前的初始因素对自然对流强度和融冰性能的影响,为正确进行系统优化、参数匹配等提供了理论指导。
Along with the world energy crisis turning deeply, the ice storage system is applied more and more widely because of its simple design and obviously economy. Especially under the extreme nervous situation of the electric power in our country , the ice storage system has the special and important function of alleviating the nervous situation of the current electric power, and also has the aggressive meaning to the scientific development of the economy of our country.Among all the ice storage systems, internal-melt ice-on-tube has been widely used because of its high reliability and relatively high charging and discharging rate. Therefore, it is important to investigate the mechanism of freezing and meting about ice-on-tube. For this purpose a research of the performance of heat transfer of internal-melt ice-on-tube is carried out theoretically.
Through enthalpy method, a three-dimension heat transfer mathematical model for the ice-on-tube with freezing is established. Based on the model the influences of the velocity in the tube, the inlet temperature of flow, the diameter of tube and the initial temperature of the water on the heat transfer characteristics of freezing are analyzed. It provides theoretical instruction of designing ice-on-tube.
Besides, under the two circumstances with nature convection and without nature convection, a three-dimension heat transfer mathematical model for the ice-on-tube with melting is established. Based on the model the influences of the velocity in the tube, the inlet temperature of flow, the diameter of tube and the initial temperature of the ice on the natural convection of the melted water and the heat transfer characteristics of melting are analyzed. It provides theoretical instruction of optimizing system and matching parameters.
引文
1巨永平,孙志荣.空调工程中的蓄冷技术.暖通空调. 1995, (6):38~44
2樊栓狮,谢应明等.蓄冷空调及气体水合物蓄冷技术.化工学报. 2003, (S1):131~135
3陈光明.日本蓄热空调现状.暖通空调. 1998, (4):33~35
4张永铨.国内外冰蓄冷技术的发展与应用.制冷技术. 1999, (2):21~24
5张国强,龚光彩等.能源、环境与空调制冷.制冷学报. 2000 , (3):1~6
6 D. Arnold. Dynamic Simulation of Encapsulated Ice Stores-Part1: Model Development and Validation. ASHRAE Transfer. 1990, 96:566~571
7 D. Arnold. Dynamic Simulation of Encapsulated Ice Stores-Part2: Model Development and Validation. ASHRAE Transfer. 1994,100:1245~1254
8 Jerold W. Jones. Evaluation of RP-459 Algorithms for Modeling External Melt, Ice-on-Pipe Thermal Storage System Components. ASHRAE Transfer. 1995,101:1342~1351
9 Akio Saito. Recent Advances in Research on Cold Thermal Energy Storage. International Journal of Refrigeration. 2002, (25):177~189
10 R. K. Strand, C. D. Peterson, G.. N. Coleman. Development of Direct and Indirect Ice Storage Models for Energy Analysis Calculations. Trans ASHRAE Transfer. 1994,100(1):1230~1244
11 M. Landy, C. D. Noble. Case Study of Cost-effective Low-temperature Air Distribution, Ice Storage. ASHRAE Transfer. 1991,97(1):854~859
12 Elleson. High-qualitity Air-conditioning with Cold Air Distribution. ASHRAE Transfer. 1991,97(1):839~842
13潘雨顺,吴建国,贾燕芳.冰蓄冷低温送风空调技术研究现状与发展优势.低温与特气. 2001, (5):1~4
14 Robert A. Potter, Jr., Douglas P. Weitzel, Dion J. King, Daisie D. Boettner. Study of Operational Experience with Thermal Storage Systems. ASHRAE Transfer. 1995,101:549~557
15 Brousseau P, Lacroix M. Study of The Thermal Performance of A Multi-layer PCM Storage Unit. Energy Convers. Mgmt. 1996,37(5):599~609
16 G. A. Lane. PCM Science and Technology: The Essential Connection. ASHRAE Transfer. 1985,91:1897~1910
17 S. L. Chen. Analysis of Cool Storage for Air Conditioning. Int. Journal of Energy Research. 1992, (16):553~563
18 Wilie D. Evaluation and Selecting Thermal Energy Storage. Energy Eng.1990,87(6):128~132
19 Charles E D, James S E. Design Guide for Cool Thermal Storage. ASHRAE Transfer. 1993,99(II):798~804
20 Akbari H, Mertol A. Thermal Energy Storage for Cooling of Commercial Buiding. Kilkis S. Energy Storage Systems. 1989:315~347
21张永铨.中国蓄冷技术应用的新进展.制冷. 2000, (1):33~37
22张奕,黄虎,张小松.盘管冰蓄冷装置管外结冰过程研究.哈尔滨工业大学学报. 2004, (10):1310~1313
23赵贤兵,李芳芹.空调冰球蓄冷传热过程数值模拟.建筑热能通风空调. 2002,(3):26~29
24晏刚等.冰蓄冷球内凝固的实验研究.制冷与空调. 2002, (4):22~24
25杜恩杰等.壳管式蓄冰槽蓄冷特性的试验研究.流体机械. 2004, (10):42~45
26王茜,徐士鸣.冰蓄冷系统研究新进展.节能. 2003, (11):4~8
27李金平等.蓄冷空调技术及其发展方向探讨.能源技术. 2003,24(3):119~121
28吴喜平.蓄冷技术和蓄热电锅炉在空调中的应用.同济大学出版社. 2000
29顾念祖等.储冰桶性能的测定A .第八届全国余热制冷与热泵技术学术会议论文集C. 1997:102– 105
30 Charles E D ,James S E. Design Guide for Cool Thermal Storage J . ASHRAE Trans. 1993 ,99(II):798– 804
31 Tran N , Kreider J F, Brothers P. Field Measurement of Chilled Water Storage thermal Performance J. ASHRAE Trans. 1989 ,95(I):1106 - 1112
32 Hensel E C, Robinson N L , Buntain J. Chilled Water Storage System Performance MonitoringJ . ASHRAE Trans. 1991 ,97(I):1151 - 1160
33许建俊,华泽钊. Na SO·10H O溶液的特性及其在蓄冷空调技术中的应用.制冷学报. 1997,19(1):1 -6
34 Douglas A A. Thermal Energy Forum: Eutectic Cool Storage: Current DevelopmentsJ . ASHRAE J . 1990, (4):46 - 50
35 Douglas A A. Thermal Energy Forum: The past , Pre2sent and Future of Eutectic Salt Storage System J . ASHRAEJ. 1989,5:26 - 28
36郭开华,舒碧芬.空调蓄冷及气体水合蓄冷技术.制冷学报. 1995,53(3):15 - 21
37邹进,黄素逸.相变热传导的计算.能源技术. 2000, (1):11~14
38张宴平等.相变贮能—理论和应用.中国科学技术大学出版社. 1996
39郭宽良等.计算传热学.中国科学技术大学出版社. 1988
40 L. S. Yao,W. Cherney. Transient Phase-change Around A Horizontal Cylinder. Int. J. Heat Mass Transfer. 1981,24(12):1971~1981
41 Alex H. W.,Jerold W. Jones. Modeling of An Ice-on-coil Thermal Energy Storage System. Energy Convers. Mgmt. 1996,37(10):1493~1507
42王华生等.圆环形腔内凝固问题的热阻法近似解.西安交通大学学报. 2001,35(3):255~260
43 Stephan K,Holzknecht B. Die Asymptotische Losungen Fur Vorgange Des Erstarrens. Int. J. Heat Mass Transfer. 1976,19:597
44 Shamsunder N. Heat Transfer in Thermal Storage System, Design Procedures for Latent Heat Storage. Energy Research and Development Administration. 1978
45 Poots G.. An Approximate Treatment of Heat Conduction Problem Involving A Two-dimensional Solidification Front. Int. J. Heat Mass Transfer. 1962,5:339
46 Budhia H,Kreith F. Heat Transfer with Melting or Freezing in A Wedge. Int. J. Heat Mass Transfer. 1973,16:195
47 Crank J,Gupta RJ. A Moving Boundary Problem Arising from the Diffusion of Oxygen in Absorbing Tissue. J. Inst. Math. 1972,10:19
48 Labdon M B,Guceri S I. Heat Transfer of Phase Change Materials in Two-dimensional Cylindrical Coordinates. AIAA Paper No. 1981
49 Fox L. Moving Boundary Problems. Oxford:Clarendon Press. 1975
50 Hushemi H T, Sliepcevich C M. A Numerical Method for Solving Two-dimensional Problems of Heat Conduction with Change of Phase. Chem. EngProg. Symp. Ser. 1971,63(79):29~41
51 Meyer G H. Multidimensional Stefan Problems. SIAMJ. Numerical Anal. 1973,10:522
52 Caldwell J,Date A. W. Implicit Enthalpy Formulation of Phase-change Problems on Unstructured Grid. Comm. on Num. Meth. Engineering. 2003,19(11):865~875
53 Landan G H. Heat Conduction in A Melting Solid. Q. Appl. Math. 1951, (8):81~94
54 Duda J L,Malone M F,Notter R H,Vrentas J S. Analysis of Two-dimensional Diffusion Controlled Moving Boundary Problems. Int. J. Heat Mass Transfer. 1975,18:901~910
55 Saitoh T. Numerical Method for Multidimensional Phase-change Problem with Arbitrary Geometry. J. Heat Transfer. 1987,5:47~54
56 Hsu C E,Sparrow E M,Patankar S V. Numerical Solution of Moving Boundary Problems by Boundary Immobilization and Control-volume-based Finite-difference Scheme. Int. J. Heat Mass Transfer. 1981,24(8):1335~1343
57 Sparrow E M.,Hsu C E. Analysis of Two-dimensional Freezing on the Outside of ACoclant Carrying Tube. Int. J. Heat Mass Transfer. 1981,24(8):1345~1357
58 Crank J,Gupta R S. Isotherm Migration Method in Two Dimensions. Int. J. Heat Mass Transfer. 1975,18:1101
59 S. Srinivas Shastri,R. M. Allen. Method of Lines and Enthalpy Method for Solving Moving Boundary Problems. Int. Comm. Heat Mass Transfer. 1998,25(4):531~540
60 Yiding Cao, Amir Faghri, Won Soon Chang. A Numerical Analysis of Stefan Problems for Generalized Multi-dimensional Phase-change Structures Using the Enthalpy Model. Int. J. Heat Mass Transfer. 1989,32(7):1289~1298
61冯亦步等.对流换热边界条件冰球蓄冰时间的焓法计算.天津商学院学报. 2003,23(3):1~4
62张文群,陈林根,张振山.圆环腔内有相变非稳态传热的数值分析.锅炉技术. 2003,34(4):30~34
63 B. Ghasemi,M. Molki. Melting of Unfixed Solids in Square Cavities. Int. J. Heat Fluid Flow. 1999,20(4):446~452
64 J. M. Khodadadi,Y. Zhang. Effects of Buoyancy-driven Convection on Melting within Spherical Containers. Int. J. Heat Mass Transfer. 2001,44(8):1605~1618
65 Shamsundar N,Sparrow E M. Analysis of Multidimensional Conduction Phase Change via the Enthalpy Modal. J. Heat Transfer. 1975,97:333~340
66 Commi G,Del Guidices,Lewis R W,Zienkiewicy O C. Finite Element Solution of Nonlinear Heat Conduction Problem with Special Reference to Rhase Change. Int. J. Num. Meth. Engineering. 1974,8:613
67 Ronel J,Baliga B R. A Finite Element Method for Unsteady Heat Conduction in Materials with and without Phase Change. American Society of Mechanical Engineers. 1979
68 Lynch D R,O’Nell K. Continuously Deforming Finite Elements for the Solution of Parabolic Problems with and without Phase Change. Int. J. Num. Meth. Engineering. 1981,17(1):81~96
69陶文铨.数值传热学.西安交通大学出版社. 2001
70 Gray D D,Giorgin A. The Validity of the Boussinesq Approximation for Liquids and Gases. Int. J. Heat Mass Transfer. 1976,19:549~551
71 V. R. Voller , C. Prakash. A Fixed Grid Numerical Modeling Methodology for Convection-diffusion Mushy Region Phase-change Problems. Int. J. Heat Mass Transfer. 1987,30(8):1709~1719
2樊栓狮,谢应明等.蓄冷空调及气体水合物蓄冷技术.化工学报. 2003, (S1):131~135
3陈光明.日本蓄热空调现状.暖通空调. 1998, (4):33~35
4张永铨.国内外冰蓄冷技术的发展与应用.制冷技术. 1999, (2):21~24
5张国强,龚光彩等.能源、环境与空调制冷.制冷学报. 2000 , (3):1~6
6 D. Arnold. Dynamic Simulation of Encapsulated Ice Stores-Part1: Model Development and Validation. ASHRAE Transfer. 1990, 96:566~571
7 D. Arnold. Dynamic Simulation of Encapsulated Ice Stores-Part2: Model Development and Validation. ASHRAE Transfer. 1994,100:1245~1254
8 Jerold W. Jones. Evaluation of RP-459 Algorithms for Modeling External Melt, Ice-on-Pipe Thermal Storage System Components. ASHRAE Transfer. 1995,101:1342~1351
9 Akio Saito. Recent Advances in Research on Cold Thermal Energy Storage. International Journal of Refrigeration. 2002, (25):177~189
10 R. K. Strand, C. D. Peterson, G.. N. Coleman. Development of Direct and Indirect Ice Storage Models for Energy Analysis Calculations. Trans ASHRAE Transfer. 1994,100(1):1230~1244
11 M. Landy, C. D. Noble. Case Study of Cost-effective Low-temperature Air Distribution, Ice Storage. ASHRAE Transfer. 1991,97(1):854~859
12 Elleson. High-qualitity Air-conditioning with Cold Air Distribution. ASHRAE Transfer. 1991,97(1):839~842
13潘雨顺,吴建国,贾燕芳.冰蓄冷低温送风空调技术研究现状与发展优势.低温与特气. 2001, (5):1~4
14 Robert A. Potter, Jr., Douglas P. Weitzel, Dion J. King, Daisie D. Boettner. Study of Operational Experience with Thermal Storage Systems. ASHRAE Transfer. 1995,101:549~557
15 Brousseau P, Lacroix M. Study of The Thermal Performance of A Multi-layer PCM Storage Unit. Energy Convers. Mgmt. 1996,37(5):599~609
16 G. A. Lane. PCM Science and Technology: The Essential Connection. ASHRAE Transfer. 1985,91:1897~1910
17 S. L. Chen. Analysis of Cool Storage for Air Conditioning. Int. Journal of Energy Research. 1992, (16):553~563
18 Wilie D. Evaluation and Selecting Thermal Energy Storage. Energy Eng.1990,87(6):128~132
19 Charles E D, James S E. Design Guide for Cool Thermal Storage. ASHRAE Transfer. 1993,99(II):798~804
20 Akbari H, Mertol A. Thermal Energy Storage for Cooling of Commercial Buiding. Kilkis S. Energy Storage Systems. 1989:315~347
21张永铨.中国蓄冷技术应用的新进展.制冷. 2000, (1):33~37
22张奕,黄虎,张小松.盘管冰蓄冷装置管外结冰过程研究.哈尔滨工业大学学报. 2004, (10):1310~1313
23赵贤兵,李芳芹.空调冰球蓄冷传热过程数值模拟.建筑热能通风空调. 2002,(3):26~29
24晏刚等.冰蓄冷球内凝固的实验研究.制冷与空调. 2002, (4):22~24
25杜恩杰等.壳管式蓄冰槽蓄冷特性的试验研究.流体机械. 2004, (10):42~45
26王茜,徐士鸣.冰蓄冷系统研究新进展.节能. 2003, (11):4~8
27李金平等.蓄冷空调技术及其发展方向探讨.能源技术. 2003,24(3):119~121
28吴喜平.蓄冷技术和蓄热电锅炉在空调中的应用.同济大学出版社. 2000
29顾念祖等.储冰桶性能的测定A .第八届全国余热制冷与热泵技术学术会议论文集C. 1997:102– 105
30 Charles E D ,James S E. Design Guide for Cool Thermal Storage J . ASHRAE Trans. 1993 ,99(II):798– 804
31 Tran N , Kreider J F, Brothers P. Field Measurement of Chilled Water Storage thermal Performance J. ASHRAE Trans. 1989 ,95(I):1106 - 1112
32 Hensel E C, Robinson N L , Buntain J. Chilled Water Storage System Performance MonitoringJ . ASHRAE Trans. 1991 ,97(I):1151 - 1160
33许建俊,华泽钊. Na SO·10H O溶液的特性及其在蓄冷空调技术中的应用.制冷学报. 1997,19(1):1 -6
34 Douglas A A. Thermal Energy Forum: Eutectic Cool Storage: Current DevelopmentsJ . ASHRAE J . 1990, (4):46 - 50
35 Douglas A A. Thermal Energy Forum: The past , Pre2sent and Future of Eutectic Salt Storage System J . ASHRAEJ. 1989,5:26 - 28
36郭开华,舒碧芬.空调蓄冷及气体水合蓄冷技术.制冷学报. 1995,53(3):15 - 21
37邹进,黄素逸.相变热传导的计算.能源技术. 2000, (1):11~14
38张宴平等.相变贮能—理论和应用.中国科学技术大学出版社. 1996
39郭宽良等.计算传热学.中国科学技术大学出版社. 1988
40 L. S. Yao,W. Cherney. Transient Phase-change Around A Horizontal Cylinder. Int. J. Heat Mass Transfer. 1981,24(12):1971~1981
41 Alex H. W.,Jerold W. Jones. Modeling of An Ice-on-coil Thermal Energy Storage System. Energy Convers. Mgmt. 1996,37(10):1493~1507
42王华生等.圆环形腔内凝固问题的热阻法近似解.西安交通大学学报. 2001,35(3):255~260
43 Stephan K,Holzknecht B. Die Asymptotische Losungen Fur Vorgange Des Erstarrens. Int. J. Heat Mass Transfer. 1976,19:597
44 Shamsunder N. Heat Transfer in Thermal Storage System, Design Procedures for Latent Heat Storage. Energy Research and Development Administration. 1978
45 Poots G.. An Approximate Treatment of Heat Conduction Problem Involving A Two-dimensional Solidification Front. Int. J. Heat Mass Transfer. 1962,5:339
46 Budhia H,Kreith F. Heat Transfer with Melting or Freezing in A Wedge. Int. J. Heat Mass Transfer. 1973,16:195
47 Crank J,Gupta RJ. A Moving Boundary Problem Arising from the Diffusion of Oxygen in Absorbing Tissue. J. Inst. Math. 1972,10:19
48 Labdon M B,Guceri S I. Heat Transfer of Phase Change Materials in Two-dimensional Cylindrical Coordinates. AIAA Paper No. 1981
49 Fox L. Moving Boundary Problems. Oxford:Clarendon Press. 1975
50 Hushemi H T, Sliepcevich C M. A Numerical Method for Solving Two-dimensional Problems of Heat Conduction with Change of Phase. Chem. EngProg. Symp. Ser. 1971,63(79):29~41
51 Meyer G H. Multidimensional Stefan Problems. SIAMJ. Numerical Anal. 1973,10:522
52 Caldwell J,Date A. W. Implicit Enthalpy Formulation of Phase-change Problems on Unstructured Grid. Comm. on Num. Meth. Engineering. 2003,19(11):865~875
53 Landan G H. Heat Conduction in A Melting Solid. Q. Appl. Math. 1951, (8):81~94
54 Duda J L,Malone M F,Notter R H,Vrentas J S. Analysis of Two-dimensional Diffusion Controlled Moving Boundary Problems. Int. J. Heat Mass Transfer. 1975,18:901~910
55 Saitoh T. Numerical Method for Multidimensional Phase-change Problem with Arbitrary Geometry. J. Heat Transfer. 1987,5:47~54
56 Hsu C E,Sparrow E M,Patankar S V. Numerical Solution of Moving Boundary Problems by Boundary Immobilization and Control-volume-based Finite-difference Scheme. Int. J. Heat Mass Transfer. 1981,24(8):1335~1343
57 Sparrow E M.,Hsu C E. Analysis of Two-dimensional Freezing on the Outside of ACoclant Carrying Tube. Int. J. Heat Mass Transfer. 1981,24(8):1345~1357
58 Crank J,Gupta R S. Isotherm Migration Method in Two Dimensions. Int. J. Heat Mass Transfer. 1975,18:1101
59 S. Srinivas Shastri,R. M. Allen. Method of Lines and Enthalpy Method for Solving Moving Boundary Problems. Int. Comm. Heat Mass Transfer. 1998,25(4):531~540
60 Yiding Cao, Amir Faghri, Won Soon Chang. A Numerical Analysis of Stefan Problems for Generalized Multi-dimensional Phase-change Structures Using the Enthalpy Model. Int. J. Heat Mass Transfer. 1989,32(7):1289~1298
61冯亦步等.对流换热边界条件冰球蓄冰时间的焓法计算.天津商学院学报. 2003,23(3):1~4
62张文群,陈林根,张振山.圆环腔内有相变非稳态传热的数值分析.锅炉技术. 2003,34(4):30~34
63 B. Ghasemi,M. Molki. Melting of Unfixed Solids in Square Cavities. Int. J. Heat Fluid Flow. 1999,20(4):446~452
64 J. M. Khodadadi,Y. Zhang. Effects of Buoyancy-driven Convection on Melting within Spherical Containers. Int. J. Heat Mass Transfer. 2001,44(8):1605~1618
65 Shamsundar N,Sparrow E M. Analysis of Multidimensional Conduction Phase Change via the Enthalpy Modal. J. Heat Transfer. 1975,97:333~340
66 Commi G,Del Guidices,Lewis R W,Zienkiewicy O C. Finite Element Solution of Nonlinear Heat Conduction Problem with Special Reference to Rhase Change. Int. J. Num. Meth. Engineering. 1974,8:613
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