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

  • Henry J. Petroski
  • Morris Stern
Original Papers

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.

Keywords

Thermal Conductivity Heat Conductor Response Function Cauchy Problem Mathematical Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Zusammenfassung

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

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References

  1. [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. [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. [3]
    R. Courant andD. Hilbert,Methods of Mathematical Physics, Vol. II (Interscience, New York 1962).Google Scholar
  4. [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. [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. [6]
    H. J. Petroski andD. E. Carlson,Controllable States of Rigid Heat Conductors, Z. angew. Math. Phys.19, 372–376 (1968).Google Scholar
  7. [7]
    I. G. Petrovsky,Lectures on Partial Differential Equations (Interscience, New York 1954).Google Scholar
  8. [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. [9]
    C. Truesdell andR. A. Toupin,The Classical Field Theories, Handb. Phys.III/1 (Ed. S. Flügge, Springer, Berlin 1960).Google Scholar
  10. [10]
    A. G. Webster,Partial Differential Equations of Mathematical Physics, 2nd corr. ed. (Hafner, New York 1950).Google Scholar

Copyright information

© Birkhäuser Verlag 1972

Authors and Affiliations

  • Henry J. Petroski
    • 1
  • Morris Stern
    • 1
  1. 1.Dept. of Aerospace Eng. and Eng. MechanicsThe University of Texas at AustinUSA

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