Skip to main content
SpringerLink
Log in

On the approximation of the thermal conductivity of rigid heat conductors as a Cauchy Problem

  • Original Papers
  • Published:
Zeitschrift für angewandte Mathematik und Physik ZAMP Aims and scope Submit manuscript

Summary

It is shown that the material response function of a nonlinear rigid heat conductor may be viewed as the solution to a Cauchy Problem. The measurements necessary to determine sufficient initial and characteristic data are indicated.

Zusammenfassung

Der Näherungswert von nichtlinearem Wärmeleitungsvermögen eines starren Körpers wird äquivalent mit der Lösung eines Cauchy-Problems bewiesen.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. B. D. Coleman andV. J. Mizel,Thermodynamics and Departures from Fourier's Law of Heat Conduction, Arch. rat. Mech. Analysis13, 245–261 (1963).

    Google Scholar 

  2. B. D. Coleman andW. Noll,The Thermodynamics of Elastic Materials with Heat Conduction and Viscosity, Arch. rat. Mech. Analysis13, 167–178 (1963).

    Google Scholar 

  3. R. Courant andD. Hilbert,Methods of Mathematical Physics, Vol. II (Interscience, New York 1962).

    Google Scholar 

  4. H. J. Petroski,On the Insufficiency of Controllable States to Characterize a Class of Rigid Heat Conductors, Z. angew. Math. Mech.51, 481–482 (1971).

    Google Scholar 

  5. H. J. Petroski,On the Use of Steady Linear Temperature Fields to Characterize a Class of Rigid Heat Conductors, Arch. rat. Mech. Analysis35, 342–350 (1969).

    Google Scholar 

  6. H. J. Petroski andD. E. Carlson,Controllable States of Rigid Heat Conductors, Z. angew. Math. Phys.19, 372–376 (1968).

    Google Scholar 

  7. I. G. Petrovsky,Lectures on Partial Differential Equations (Interscience, New York 1954).

    Google Scholar 

  8. C. Truesdell andW. Noll,The Non-Linear Field Theories of mechanics, Handb. Phys.III/3 (Ed. S. Flügge, Springer, Berlin 1965).

    Google Scholar 

  9. C. Truesdell andR. A. Toupin,The Classical Field Theories, Handb. Phys.III/1 (Ed. S. Flügge, Springer, Berlin 1960).

    Google Scholar 

  10. A. G. Webster,Partial Differential Equations of Mathematical Physics, 2nd corr. ed. (Hafner, New York 1950).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Aerospace Eng. and Eng. Mechanics, The University of Texas at Austin, USA

    Henry J. Petroski & Morris Stern

Authors
  1. Henry J. Petroski
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Morris Stern
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Petroski, H.J., Stern, M. On the approximation of the thermal conductivity of rigid heat conductors as a Cauchy Problem. Journal of Applied Mathematics and Physics (ZAMP) 23, 270–276 (1972). https://doi.org/10.1007/BF01593091

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01593091

Keywords

Search

Navigation