Advertisement

Forschung im Ingenieurwesen

, Volume 64, Issue 11, pp 296–306 | Cite as

A new space marching method for solving inverse heat conduction problems

  • J. Taler
Originalarbeiten — Research Papers

Abstract

A new space marching method is presented for solving the one-dimensional nonlinear inverse heat conduction problems. The temperature-dependent thermal properties and boundary condition on an accessible part of the boundary of the body are known. Additional temperature measurements in time are taken with a sensor located in an arbitrary position within the solid, and the objective is to determine the surface temperature and heat flux on the remaining part of the unspecified boundary. The temperature distribution throughout the solid, obtained from the inverse analysis, is then used for the computation of thermal stresses in the entire domain, including the boundary surfaces. The proposed method is appropriate for on-line monitoring of thermal stresses in pressure components. The three presented example show that the method is stable and accurate.

Keywords

Heat Flux Heat Transfer Coefficient Thermal Stress Hollow Sphere Surface Heat Flux 
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.

Eine neue Methode zur Lösung inverser Wärmeleitungsprobleme

Zusammenfassung

In der vorliegenden Arbeit wird ein Verfahren zur Lösung der eindimensionalen inversen Wärmeleitungsprobleme dargestellt. Temperaturabhängige Stoffwerte und eine Randbedingung an der leicht zugängigen Außenoberfläche des Körpers sind bekannt. Die Temperatur und die Wärmestrodichte an der Innenoberfläche werden aus dem gemessenen zeitlichen Temperaturverlauf im inneren Punkt der Wand bestimmt. Aus der Lösung des inversen Problems erhält man die Temperaturverteilung in der Wand, die zur Berechnung der Wärmespannungen übert Ort und Zeit verwendet wird. Die Berechnung der Temperatur und Spannungsverteilung nach dem vorgeschlagenen Verfahren ist nicht aufwendig und kann online durchgeführt werden. Drei Beispiele bestätigen, daß die vorgeschlagene Methode stabile und genaue Ergebnisee bringt und sich auf zwei- und dreidimensionale Probleme in einfacher Weise erweitern läßt.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Taler J (1996) XVI Polish Numerical method for the solution of nonlinear transient inverse heat conduction problems. Conference on Thermodynamics, Koszalin-Kołobrzeg, Conference Proceedings, Vol. 2, pp. 425–433, (in Polish)Google Scholar
  2. 2.
    Taler J (1995) Theory and practice of the identification of heat transfer problems. Ossolineum, Wrocław, (in Polish)Google Scholar
  3. 3.
    Beck JV, Blackwell B, Jr CRS (1985) Inverse heat conduction. Wiley, New YorkMATHGoogle Scholar
  4. 4.
    Alifanov OM (1995) Inverse heat transfer problems. Springer-Verlag, BerlinMATHGoogle Scholar
  5. 5.
    D’Souza N (1974) Numerical solution of one-dimensional inverse transient heat conduction by finite difference method. ASME Paper No. 75-WA/HT-81Google Scholar
  6. 6.
    Weber CF (1981) Analysis and solution of the ill-posed inverse heat conduction problem. Int. J. Heat Mass Transfer 24, 1783–1792MATHCrossRefGoogle Scholar
  7. 7.
    Hensel E, Hills RG (1986) An initial value approach to the inverse heat conduction problem. ASME J. Heat Transfer 108, 248–256Google Scholar
  8. 8.
    Raynaud M, Beck JV (1988) Methodology for comparison of inverse heat conduction methods. ASME Journal of Heat Transfer 110, 30–37CrossRefGoogle Scholar
  9. 9.
    Vogel J, Sara L, Kerjci L (1993) A simple inverse heat conduction method with optimization. Int. J. Heat Mass Transfer 36, 4215–4220CrossRefGoogle Scholar
  10. 10.
    Taler J (1996) A semi-numerical method for solving inverse heat conduction problems. Heat and Mass Transfer 31, 105–111CrossRefGoogle Scholar
  11. 11.
    Stefan J (1889) Über die Theorie der Eisbildung im Polarmeere. Sitzungsberichte der Kaiserlichen Akademie Wiss. Wien, Math.- Natur. 98/2a, 965–983Google Scholar
  12. 12.
    Burggraf OR (1964) An exact solution of the inverse problem in heat conduction theory and applications. ASME J. Heat Transfer 86/3, 373–382Google Scholar
  13. 13.
    Taler J, Zima W (1999) Solution of inverse heat conduction problems using control volume approach. Int. J. Heat Mass Transfer (in Press)Google Scholar
  14. 14.
    Korn GA, Korn TM (1968) Mathematical Handbook. McGraw, New YorkGoogle Scholar
  15. 15.
    Mannesmann-Röhren-Werke (1985) Warmfeste und hochwarmfeste Stähle. DüsseldorfGoogle Scholar

Copyright information

© Springer-Verlag 1999

Authors and Affiliations

  • J. Taler
    • 1
  1. 1.Institut for Process and Power EngineeringCracow University of TechnologyCracowPoland

Personalised recommendations