### Abstract

The paper describes numerical simulations for hyperbolic heat conduction problems involving non-Fourier effects via explicit Lax-Wendroff/Taylor-Galerkin finite element formulations. Various research investigations cite that for cases involving extremely short transient durations or for very low temperatures near absolute zero, the classical Fourier diffusion model for heat conduction breaks down since the wave nature of thermal energy transport becomes dominant; hence, the associated thermal disturbances no longer travel with infinite speeds, but only with a finite speed of propagation. Existing analytical approaches for modeling/analysis of such problems often involve complex mathematical formulations for obtaining closed-form solutions while the major difficulties in numerical simulations include severe oscillatory solution behavior in the vicinity of the propagating shocks. It is in this regard that the present paper seeks to provide an alternate methodology and different computational perspectives for effective modeling/analysis of hyperbolic heat conduction models involving non-Fourier effects. Finite elements are employed as the principal computational tool, and, in conjunction with the proposed formulations, smoothing techniques are incorporated to stabilize the numerical noise and to accurately predict the propagating thermal disturbances. The capability for accurately capturing the propagating thermal disturbances-at characteristic time step values is noteworthy. Numerical test cases are presented to validate the proposed concepts for hyperbolic heat conduction problems.

Original language | English (US) |
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State | Published - Jan 1 1989 |

Event | AIAA 24th Thermophysics Conference, 1989 - Buffalo, United States Duration: Jun 12 1989 → Jun 14 1989 |

### Other

Other | AIAA 24th Thermophysics Conference, 1989 |
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Country | United States |

City | Buffalo |

Period | 6/12/89 → 6/14/89 |

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### Cite this

*Hyperbolic heat conduction problems involving non-fourier effects: Numerical simulations via explicit Lax-Wendroff/Taylor-Galerkin finite element formulations*. Paper presented at AIAA 24th Thermophysics Conference, 1989, Buffalo, United States.