Overshooting Phenomenon in the Hyperbolic Microscopic Heat Conduction Model

Abstract

The overshooting phenomenon under the effect of the microscopic hyperbolic heat conduction model is investigated. A map tracing the region within which the overshooting phenomenon occurs is presented. The two most important parameters which control the overshooting phenomenon are found to be the first and second time-derivatives of the temperature at t=0. However, in order for the overshooting to appear, a higher initial value of the second time-derivative of the temperature change is required than the initial value of the first time-derivative of the temperature. Overshooting is more likely to appear in the parabolic, rather than in the hyperbolic, microscopic heat conduction model.