Abstract
The temperature proe les that result when a point heat source is swept back and forth along a rod in which heat travels at e nite speed are examined. Green’ s functions are used to solve the hyperbolic heat equation for cases in which the source speed is half, equal to, and double, the natural thermal wave speed of the rod material. Rod temperatures are found to depend on the value of the thermal Mach number that characterizes each heating scenario. For subsonic heating, temperatures decrease smoothly ahead of the source, but drop off sharply in its wake. In supersonic heating, the temperature proe le e ips, moving the sharp drop in rod temperature to the source’ s leading edge. For transonic heating, the temperature proe les have sharp drops on both sides of the source, producing a local spike that grows with time. In all cases, the source generates three distinct wave fronts as it slides along the rod: a primary front moving with the source and two startup fronts traveling at the rod thermal wave speed. These fronts interact to produce local variations in rod temperatures that would not be predicted by Fourier’ s law.
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