@ARTICLE{Joachimiak_Magda_Non-linear_2017, author={Joachimiak, Magda and Ciałkowski, Michał}, number={No 2}, journal={Archives of Thermodynamics}, pages={81-100}, howpublished={online}, year={2017}, publisher={The Committee of Thermodynamics and Combustion of the Polish Academy of Sciences and The Institute of Fluid-Flow Machinery Polish Academy of Sciences}, 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.}, type={Artykuły / Articles}, title={Non-linear unsteady inverse boundary problem for heat conduction equation}, URL={http://www.journals.pan.pl/Content/105642/PDF/04_paper.pdf}, doi={10.1515/aoter-2017-0011}, keywords={inverse problem, sensitivity of solution to inverse problem, application of Chebyshev polynomials}, }