Calculations of Temperature, Conductive Heat Flux, and Heat Wave Velocities Due to Radiant Heating of Opaque Materials

Report No. ARL-TR-5804
Authors: Arthur Cohen
Date/Pages: November 2011; 18 pages
Abstract: The analytic solutions of the one-dimensional Fourier conductive heat flux law and corresponding transient heat transfer equation have been used to calculate temperature, conductive heat flux, and their trajectories due to radiant heating of opaque materials. Heat wave trajectories (and velocities) are defined by the value of a constant temperature or constant conductive heat flux that propagates through the materials. For constant values of zero, the analytic solutions lead to infinite heat wave velocities. For nonzero constant values, the numerical solutions at ultra-short transient times result in other nonphysical velocities (i.e., >3E(10) cm/s). These calculations demonstrate that there are limitations to the validity of the Fourier heat flux law and corresponding heat transfer equation, although they have been used successfully to solve engineering and scientific heat conduction problems for over 180 years.
Distribution: Approved for public release
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Last Update / Reviewed: November 1, 2011