Analysis of Surface Temperatures Within Heat Flux Bands During Constant Acceleration Including Deceleration to Halt

Abstract

In the modeling of a uniformly distributed band heat flux region experiencing constant acceleration from rest over a half-space surface, it is found that the maximum surface temperature at the instantaneous speed and the corresponding Peclet number are already well approximated by the long-established steady-state constant-speed models very soon after the moment the flux region clears the overlap of its original footprint at the initiation of motion. During startup when the flux still overlaps its original footprint, maximum temperature at any instant given the level of flux is well approximated by a simple one-dimensional conduction problem with a correspondingly stationary heat flux initiating at time zero. The above acceleration behaviors are observed regardless of whether the uniform flux is constant or Coulombic (proportional to instantaneous speed as frictional heating), though during the initial startup the maximum temperature rise in the Coulombic case is only two-thirds that of the constant flux case. The case of constant deceleration was additionally modeled, where at the eventual instant of halt, the maximum temperature in the case of constant flux was found to be directly proportional to the rate of deceleration to the 1/4 power, whereas in the case of Coulombic flux it was found that maximum temperature was instead inversely proportional to the rate of deceleration.