On the integral-balance approach to the transient heat conduction with linearly temperature-dependent thermal diffusivity

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• 作者：Antoine Fabre ; Jordan Hristov
• 刊名：Heat and Mass Transfer
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：53
• 期：1
• 页码：177-204
• 全文大小：
• 刊物类别：Engineering
• 刊物主题：Engineering Thermodynamics, Heat and Mass Transfer; Industrial Chemistry/Chemical Engineering; Thermodynamics;
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-1181
• 卷排序：53

文摘

Closed form approximate solutions to nonlinear transient heat conduction with linearly temperature-dependent thermal diffusivity have been developed by the integral-balance integral method under transient conditions. The solutions uses improved direct approaches of the integral method and avoid the commonly used linearization by the Kirchhoff transformation. The main steps in the new solutions are improvements in the integration technique of the double-integration technique and the optimization of the exponent of the approximate parabolic profile with unspecified exponent. Solutions to Dirichlet and Neumann boundary condition problems have been developed as examples by the classical Heat-balance integral method (HBIM) and the Double-integration method (DIM). Additional examples with HBIM and DIM solutions to cases when the Kirchhoff transform is initially applied have been developed.