Invariant for one-dimensional heat conduction in dielectrics and metals

¹ Department of Mechanical Engineering, University of Houston - 4726 Calhoun Road, Houston, TX 77204, USA
² Institut Pprime, CNRS, Université de Poitiers, ISAE-ENSMA - F-86962 Futuroscope Chasseneuil, France
³ School of Information Technology and Mathematical Sciences University of South Australia - GPO Box 2471, Adelaide, SA 5001, Australia

^(a) jose.ordonez@cnrs.pprime.fr (corresponding author)
^(b) hghasemi@central.uh.edu (corresponding author)

Received: 4 April 2017
Accepted: 12 June 2017

Abstract

We theoretically and experimentally demonstrate that the one-dimensional heat conduction in dielectrics and metals is ruled by the invariant , where T is the temperature and z an arbitrary position within the heated material of length L. This is achieved using the integral expressions predicted by the Boltzmann transport equation, under the gray relaxation time approximation, for the steady-state temperature and heat flux, and measuring the temperature at three equidistant positions in rods of Si, Cu, and Fe-C excited with temperatures much smaller than their corresponding Debye ones. The obtained temperature invariant for symmetrical positions could be applied to describe the heating of materials supporting one-dimensional heat conduction.