Open AccessSolution and analysis of non-Fourier heat conduction in a plane slab under arbitrary periodic surface thermal disturbance
Author(s) -
Zhao Wei-Tao,
Wu Jiu-Hui
Publication year - 2013
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.62.184401
Subject(s) - superposition principle , thermal conduction , heat flux , slab , fourier transform , fourier series , plane (geometry) , heat equation , harmonic , mechanics , materials science , fourier analysis , physics , heat transfer , mathematical analysis , thermodynamics , geometry , mathematics , geophysics , quantum mechanics
In this paper, the non-Fourier heat conduction in a plane slab under arbitrary periodic surface thermal disturbance is solved analytically. Hyperbolic heat conduction equation is employed to describe this problem involving high-rate change of temperature. Firstly, when the plane slab surface is subjected to a sudden heat flux change or a harmonic heat flux change, the analytic solution of this problem is found by using the separation of variables method and Duhamel’s principle. On this basis, when the plane slab surface is subjected to an arbitrary periodic heat flux change, the analytic solution of temperature field is obtained by using the Fourier series and the principle of superposition. Using the obtained analytical solution, the temperature profiles of the plane slab are analyzed, and the differences between the temperature response obtained by using non-Fourier heat conduction model and that obtained by using Fourier model are discussed. This solution can be applied to more realistic periodic boundary conditions in technology.