577 0195-928X/03/0300-0577/0 © 2003 Plenum Publishing Corporation International Journal of Thermophysics, Vol. 24, No. 2, March 2003 (© 2003) Note Overshooting Phenomenon in the Hyperbolic Microscopic Heat Conduction Model M. A. Al-Nimr 1, 2 and Mohammad K. Alkam 1 1 Mechanical Engineering Department, Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110, Jordan. 2 To whom correspondence should be addressed. E-mail: malnimr@just.edu.jo Received May 13, 2002 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-deriva- tive 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. KEY WORDS: hyperbolic microscopic model; microscopic heat conduction; overshooting; two-step hyperbolic model; two-step heat conduction model. 1. INTRODUCTION Temperature overshooting is concerned with the excess temperature estab- lished in a conducting medium when two thermal wavefronts meet. The overshooting phenomenon implies the possibility of finding locations within the heated domain which have temperatures higher than the imposed boundary temperature at the wall. This phenomenon may occur in domains exposed to sudden changes in their wall temperature, if the domain has non-zero initial temperature time gradient, “T “t (0, x)=T ˙ o , and if