Abstract
The article examines the practical application of the algorithm for solving inverse problems in processing experimental data.
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Abbreviations
- c:
-
volumetric heat capacity
- λ :
-
thermal conductivity
- T:
-
temperature
- x:
-
space coordinate
- τ :
-
time
- τm, b:
-
right-hand boundary value of time and space intervals, respectively
- fi(τ):
-
input temperatures
- I:
-
functional
- θ:
-
temperature increase
- ψ :
-
conjugate variable
- ¯T=(T−To)/Tmax−Tmax):
-
dimensionless temperatures {ie}=λ/λmax, dimensionless thermal conductivity
- nx, {ie}:
-
number of nodes in difference approximation with respect to the space and time coordinates, respectively
- α, β:
-
parameters of the method of conjugate gradients
- p:
-
number of iteration
- min:
-
minimal
- max:
-
maximal value
- 0:
-
initial value
- be:
-
beginning of electrical conductance; meas, measured value
Literature cited
O. M. Alifanov, Identification of Heat Exchange Processes of Aircraft [in Russian], Mashinostroenie, Moscow (1979).
E. A. Artyukhin, “Reconstruction of the temperature dependence of thermal conductivity from the solution of the inverse problem,” Teplofiz. Vys. Temp.,19, No. 5, 963–967 (1981).
E. A. Artyukhin and A. S. Okhapkin, “Determination of the temperature dependence of the thermal conductivity of composite material from the data of non-steady-state experiments,” Inzh.-Fiz. Zh.,44, No. 2, 274–281 (1983).
Yu. G. Narozhnyi, Yu. V. Polezhaev, and V. E. Killikh, “Some results of the investigation of the thermal conductivity of glass-fiber reinforced plastics,” Inzh.-Fiz. Zh.,29, No. 1, 77–80 (1975).
K. G. Omel'chenko, M. V. Savelov, and V. P. Timoshenko, “Investigation of the heat-transfer characteristics in decomposing heat-protection materials,” Inzh.-Fiz. Zh.,29, No. 1, 99–105 (1975).
Yu. V. Polezhaev, V. E. Killikh, and Yu. G. Narozhnyi, “Nonsteady heating of heat-protection materials,” Inzh.-Fiz. Zh.,29, No. 1, 39–44 (1975).
S. B. Stechkin and Yu. N. Subbotin, Splines in Computer Mathematics [in Russian], Nauka, Moscow (1976).
E. Polak, Numerical Methods of Optimization [Russian translation], Mir, Moscow (1974).
A. A. Samarskii, The Theory of Difference Schemata [in Russian], Nauka, Moscow (1977).
V. E. Killikh and Yu. V. Polezhaev, “Temperature measurement inside asbestos-textolite,” in: Thermal Stresses in Structural Elements [in Russian], Issue 10, Naukova Dumka, Kiev (1968), p. 109.
Additional information
Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 45, No. 5, pp. 788–793, November, 1983.
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Artyukhin, E.A., Killikh, V.E. & Okhapkin, A.S. Reconstructing the effective coefficient of thermal conductivity of asbestos-textolite from the solution of the inverse problem. Journal of Engineering Physics 45, 1281–1286 (1983). https://doi.org/10.1007/BF01254734
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DOI: https://doi.org/10.1007/BF01254734