TY - EJOU
AU - Fabre, Antoine
AU - Hristov, Jordan
AU - Bennacer, Rachid
TI - Transient Heat Conduction in Materials with Linear Power-Law Temperature-Dependent Thermal Conductivity: Integral-Balance Approach
T2 - Fluid Dynamics \& Materials Processing
PY - 2016
VL - 12
IS - 2
SN - 1555-2578
AB - Closed form approximate solutions to nonlinear transient heat conduction with linear power-law *k = k*_{0}(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).
KW - Non-linear heat conduction
KW - integral-balance solutions
KW - temperature-dependent thermal diffusivity
DO - 10.3970/fdmp.2016.012.069