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Invariant for one-dimensional heat conduction in dielectrics and metals

Journal Article


Abstract


  • We theoretically and experimentally demonstrate that the one-dimensional heat conduction in dielectrics and metals is ruled by the invariant T4 (z) + T4 (L-z) = constant, 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.

UOW Authors


  •   Hill, James (external author)

Publication Date


  • 2017

Published In


  • EPL  Journal

Citation


  • Sajadi, S. M., Ordonez-Miranda, J., Hill, J. M., Ezzahri, Y., Joulain, K., & Ghasemi, H. (2017). Invariant for one-dimensional heat conduction in dielectrics and metals. EPL, 118(3). doi:10.1209/0295-5075/118/34001

Scopus Eid


  • 2-s2.0-85024118504

Volume


  • 118

Issue


  • 3

Place Of Publication


Abstract


  • We theoretically and experimentally demonstrate that the one-dimensional heat conduction in dielectrics and metals is ruled by the invariant T4 (z) + T4 (L-z) = constant, 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.

UOW Authors


  •   Hill, James (external author)

Publication Date


  • 2017

Published In


  • EPL  Journal

Citation


  • Sajadi, S. M., Ordonez-Miranda, J., Hill, J. M., Ezzahri, Y., Joulain, K., & Ghasemi, H. (2017). Invariant for one-dimensional heat conduction in dielectrics and metals. EPL, 118(3). doi:10.1209/0295-5075/118/34001

Scopus Eid


  • 2-s2.0-85024118504

Volume


  • 118

Issue


  • 3

Place Of Publication