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ARTICLE

Transient Heat Conduction in Materials with Linear Power-Law Temperature-Dependent Thermal Conductivity: Integral-Balance Approach

Antoine Fabre¹, Jordan Hristov^2*, Rachid Bennacer¹

1 Ecole National Superior de Cachan, Universite Paris-Saclay, Paris, France
2 Department of Chemical Engineering, University of Chemical Technology and Metallurgy, Sofia 1756, 8 Kliment Ohridsky, blvd. Bulgária,e-mail: jordan.hristov@mail.bg ; website: http://hristov.com/jordan

Fluid Dynamics & Materials Processing 2016, 12(2), 69-85. https://doi.org/10.3970/fdmp.2016.012.069

Abstract

Closed form approximate solutions to nonlinear transient heat conduction with linear power-law k = k₀(1±βT^m) temperature-dependent thermal diffusivity have been developed by the integral-balance integral method under transient conditions. The solutions use 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 boundary condition problem have been developed as examples by the classical Heat-balance Integral method (HBIM) and the Double-integration method (DIM).

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