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Heat and Mass Transfer

, Volume 31, Issue 3, pp 105–111 | Cite as

A semi-numerical method for solving inverse heat conduction problems

  • J. Taler
Originals

Abstract

A semi-numerical method is presented for solving the inverse heat conduction problems in homogeneous and composite bodies. The presented solution does not require both the initial temperature distribution in the body and the whole temperature-time history at the temperature sensor locations. Sample calculations confirm that this approach produces stable and accurate results for both exact and noisy data. The extension of the method presented to two or three dimensions is straightforward.

Keywords

Temperature Distribution Fluid Dynamics Heat Conduction Apply Physic Initial Temperature 
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.

Nomenclature

Bi

Biot number (=hx/k)

c

specific heat (J/kg K)

E

distance from exposed surface to temperature sensor, m

Fo

Fourier number (=αt/L2)

f

measured temperature (K)

h

heat transfer coefficient (W/m2K)

k

thermal conductivity (W/mK)

L

thickness of the plate (m)

M

number of nodal points

N

number of time measurement points

q

heat flux (W/m2)

qE

heat flux atx=E(W/m2)

qN

nominal value of the heat flux (W/m2)

S

least squares function (K2)

T

temperature (K)

T0

initial temperature (K)

T

fluid temperature (K)

t

time (s)

x

coordinate

Greek symbols

α

thermal diffusivity (m2/s)

Δt

time step(s)

Δx

grid size (thickness of the control volume) (m)

δ

layer thickness (m)

ɛ

random error (K)

ρ

density (kg/m3)

σf

standard deviation of the measurement errors (K)

Seminumerische Methode zur Lösung inverser Wärmeleitungsprobleme

Zusammenfassung

Eine seminumerische Methode zur Lösung inverser Wärmeleitungsprobleme in homogenen und mehrschichtigen Körpern wird dargestellt. Weder die anfängliche Temperaturverteilung, noch der gesamte zeitliche Verlauf der gemessenen Temperatur gehen in das Berechnungsverfahren ein. Die in der Arbeit dargestellten Beispiele bestätigen, daß die Methode stabile und genaue Ergebnisse bringt und sich auf zwei- und dreidimensionale Probleme in einfacher Weise erweitern läßt.

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References

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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • J. Taler
    • 1
  1. 1.Institute for Process and Power EngineeringCracow University of TechnologyKrakowPoland

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