Abstract
The authors consider the construction of an iterative numerical algorithm and analyze the influence of the location of the temperature sensor on the accuracy of solving the inverse problem.
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Abbreviations
- c:
-
volume heat capacity
- λ :
-
thermal conductivity
- mg :
-
specific mass flow rate
- hg :
-
enthalpy of the gas phase of thermal breakdown products
- T:
-
temperature
- x:
-
three-dimensional coordinate
- τ :
-
time
- τm :
-
right-hand boundary value of the time interval
- fi(τ):
-
input temperatures
- z:
-
concentration of the decomposable component
- A:
-
preexponential factor
- n:
-
order of the breakdown reaction
- E/R:
-
activation energy
- kT :
-
limiting value of the coke number
- ρ0 :
-
density of the original material
- Tr :
-
temperature at the start of thermal breakdown
- b:
-
right-hand boundary value of the three-dimensional interval
- I:
-
functional
- ϑ :
-
temperature increment
- ψ :
-
conjugate variable
- i:
-
three-dimensional subscript
- Tmin :
-
minimum value of temperature
- Tmax :
-
maximum value of temperature
- λmax :
-
maximum value of thermal conductivity
Literature cited
B. M. Pankratov, Yu. V. Polezhaev, and A. K. Rud'ko, Interaction of Materials with Gas Flows [in Russian], Mashinostroenie, Moscow (1976).
Yu. V. Polezhaev, V. E. Killikh, and Yu. G. Narozhnyi, “Unsteady heating of thermally insulating materials,” Inzh.-Fiz. Zh.,29, No. 1, 39 (1975).
E. A. Artyukhin, “Determination of thermal diffusivity from experimental data,” Inzh.-Fiz. Zh.,29, No. 1, 87 (1975).
O. M. Alifanov, E. A. Artyukhin, and S. V. Rumyantsev, “Solution of boundary and co-efficient inverse problems by iterative methods,” in:Heat and Mass Transfer IV [in Russian], Vol. 9, ITMO Akad. Nauk BSSR (1980), p. 106.
E. A. Artyukhin, “Recovery of the thermal conductivity from solution of a nonlinear in-verse problem,” Inzh.-Fiz. Zh.,41, No. 1, 587 (1981).
E. A. Artyukhin and A. S. Okhapkin, “Determination of the temperature dependence of the thermal conductivity of a composite material from the data of an unsteady experiment,” Inzh.-Fiz. Zh.,44, No. 2, 274 (1983).
S. B. Stechkin and Yu. N. Subbotin, Splines in Computational Mathematics [in Russian], Nauka, Moscow (1976).
O. M. Alifanov, Identification of Aircraft Heat Transfer Processes [in Russian], Mashinostroenie, Moscow (1979).
E. Polak, Numerical Methods of Optimization [Russian translation], Mir, Moscow (1974).
F. P. Vasil'ev, Methods of Solving Extremal Problems [in Russian], Nauka, Moscow (1981).
A. A. Samarskii, Theory of Difference Schemes [in Russian], Nauka, Moscow (1977).
N. V. Muzylev, “Uniqueness theorems for some inverse heat-conduction problems,” Zh. Vychisl. Mat. Mat. Fiz.,20, No. 2, 388 (1980).
O. M. Alifanov and S. V. Rumyantsev, “Stability of iterative methods of solving linear incorrectly posed problems,” Dokl. Akad. Nauk SSSR,248, No. 6, 1289 (1979).
Additional information
Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 45, No. 5, pp. 781–788, November, 1983.
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Artyukhin, E.A., Okhapkin, A.S. Parametric analysis of the accuracy of solution of a nonlinear inverse problem of recovering the thermal conductivity of a composite material. Journal of Engineering Physics 45, 1275–1281 (1983). https://doi.org/10.1007/BF01254733
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DOI: https://doi.org/10.1007/BF01254733