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

• Published in: Heat and mass transfer 2015-01, Vol.51 (1), p.143-152
• Main Authors: Zhou, Yang, Wang, Yi-jiang, Wang, Jian-zhou
• Format: Article
• Language: English
• Subjects: Engineering; Engineering Thermodynamics; Heat and Mass Transfer; Industrial Chemistry/Chemical Engineering; Short Communication; Thermodynamics
• ISSN: 0947-7411; 1432-1181
• DOI: 10.1007/s00231-014-1406-1

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.