Analytical solution for nonlinear infinite line source problem with temperature-dependent thermal properties

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• 作者：Yang Zhou (1) (2)
  Yi-jiang Wang (1) (2)
  Jian-zhou Wang (1) (2)
  
  1. State Key Laboratory for Geomechanics and Deep Underground Engineering ; China University of Mining and Technology ; Xuzhou ; 221116 ; Jiangsu ; China
  2. School of Mechanics and Civil Engineering ; China University of Mining and Technology ; Xuzhou ; 221116 ; Jiangsu ; China
  
• 刊名：Heat and Mass Transfer
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：51
• 期：1
• 页码：143-152
• 全文大小：558 KB
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• 刊物类别：Engineering
• 刊物主题：Engineering Thermodynamics and Transport Phenomena
  Industrial Chemistry and Chemical Engineering
  Thermodynamics
  Physics and Applied Physics in Engineering
  Theoretical and Applied Mechanics
  Engineering Fluid Dynamics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1181

文摘

A nonlinear infinite line source problem with temperature-dependent thermal properties is investigated. By dividing the temperature range into number of subintervals and assuming that the thermal properties within each subinterval are constant, the problem is transformed to a cylindrical multiphase Stefan problem with no latent heat at the moving boundaries. An analytical solution is constructed by the similarity transformation technique. In most situations, the final solution is an approximate one. In order to verify the accuracy of the approximate solution, a group of exact solutions for special cases are also developed and compared. The general accuracy of the approximate solution increases as the number of subintervals increases. The results show that dividing the temperature range into the subintervals having same successive ratio of the thermal property can be an effective strategy. The number of subintervals required to keep the root mean square error in the temperature estimate under certain level is also discussed.