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Abstract

Inverse boundary problem for cylindrical geometry and unsteady heat conduction equation was solved in this paper. This solution was presented in a convolution form. Integration of the convolution was made assuming the distribution of temperature T on the integration interval (ti, ti+ Δt) in the form T (x, t) = T (x, ti) Θ + T (z, ti+ Δt) (1 - Θ), where Θ ϵ (0,1). The influence of value of the parameter Θ on the sensitivity of the solution to the inverse problem was analysed. The sensitivity of the solution was examined using the SVD decomposition of the matrix A of the inverse problem and by analysing its singular values. An influence of the thermocouple installation error and stochastic error of temperature measurement as well as the parameter Θ on the error of temperature distribution on the edge of the cylinder was examined.
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Abstract

Direct and inverse problems for unsteady heat conduction equation for a cylinder were solved in this paper. Changes of heat conduction coefficient and specific heat depending on the temperature were taken into consideration. To solve the non-linear problem, the Kirchhoff’s substitution was applied. Solution was written as a linear combination of Chebyshev polynomials. Sensitivity of the solution to the inverse problem with respect to the error in temperature measurement and thermocouple installation error was analysed. Temperature distribution on the boundary of the cylinder, being the numerical example presented in the paper, is similar to that obtained during heating in the nitrification process.
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