A finite element method for non-Fourier heat conduction in strong thermal shock environments

Baolin Wang, Jiecai Han

    Research output: Contribution to journalArticlepeer-review


    Non-Fourier effect is important in heat conduction in strong thermal environments. Currently, generally-purposed commercial finite element code for non-Fourier heat conduction is not available. In this paper, we develop a finite element code based on a hyperbolic heat conduction equation, which includes the non-Fourier effect in heat conduction. The finite element space discretization is used to obtain a system of differential equations for the time. The transient responses are obtained by solving the system of differential equations, based on the finite difference, mode superposition, or exact time integral. The code is validated by comparing the numerical results with exact solutions for some special cases. The stability analysis is conducted and it shows that the finite difference scheme is an ideal method for the transient solution of the temperature field. It is found that with mesh refining (decreasing mesh size) and/or high-order elements, the oscillation in the vicinity of sharp change vanishes, and can be essentially suppressed by the finite difference scheme. A relationship between the time step and the space length of the element was identified to ensure that numerical oscillation vanishes.
    Original languageEnglish
    Pages (from-to)226-233
    Number of pages8
    JournalFrontiers of Materials Science in China
    Issue number3
    Early online date26 Jul 2010
    Publication statusPublished - Sep 2010


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