Abstract
An interaction scheme is considered for the solution of a nonlinear inverse heat-conduction problem with the results of measuring the temperature at an arbitrary number of points within the body taken into account.
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Abbreviations
- n:
-
number of temperature measurement points
- τ, t:
-
time
- τp, tp :
-
length of the time interval
- x:
-
a space coordinate
- Xi(t):
-
\(i = \overline {1,n} \) coordinates of the temperature measurement points
- T(x, t):
-
temperature
- C(T):
-
bulk specific heat of the material
- λ(T):
-
coefficient of material heat conduction
- T(x, 0):
-
initial temperature distribution
- q:
-
heat flux density
- fi(t):
-
\(i = \overline {1,n} \), temperature measurement
- Ψi(zi, t):
-
\(i = \overline {1,n} \), conjugate variable
- ϑi(zi, t):
-
\(i = \overline {1,n} \), temperature variation
- α, β, p:
-
parameters of the conjugate gradient method
- s:
-
number of iteration
- l :
-
number of points in a discrete representation of the time function
- ɛ:
-
an error estimate
Literature cited
O. M. Alifanov, Identification of Heat-Transfer Processes of Flying Vehicles [in Russian], Mashinostroenie, Moscow (1979).
O. M. Alifanov and V. V. Mikhailov, “Solution of a nonlinear inverse problem by an iteration method,” Inzh.-Fiz. Zh.,35, No. 6, 1123–1129 (1978).
O. M. Alifanov and S. V. Rumyantsev, “On a method of solving incorrectly posed problems,” Inzh.-Fiz. Zh.,34, No. 2, 328–331 (1978).
Additional information
Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 45, No. 5, pp. 776–781, November, 1983.
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Alifanov, O.M., Mikhailov, V.V. Solution of the inverse boundary-value problem of heat conduction in an overdefined formulation. Journal of Engineering Physics 45, 1270–1274 (1983). https://doi.org/10.1007/BF01254732
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DOI: https://doi.org/10.1007/BF01254732