Year: 2026
Type: article
Abstract: The paper considers a linear boundary inverse heat conduction problem in a two-dimensional axisymmetric spatial domain. The problem of determining the spati-otemporal density of heat flux in processes of external heating of cylindrical workpieces is formulated. The method of modal identification, based on the application of integral transforms to the temperature state distributed in two spatial coordinates and time, as well as to the identified function depending on one spatial argument and time, is applied to solve it. The Laplace transform in time and a finite integral transform in the variable on which the desired function depends are applied sequentially. This leads to a modal representation of the analyzed characteristics in the form of their expansions into series of the same dimension. The expansion coefficients of the temperature, which have the meaning of modal components, are determined based on experimental temperature information obtained from several measuring devices. The number of sensors corresponds to the number of modes considered in the expansion. The obtained coefficients are related to the corresponding expansion coefficients of the boundary action based on a modal representation in the form of a system of differential equations written in Laplace transforms. This approach leads to the implementation of a set of independent loops for identifying the time modes of the function to be identified. Subsequent accounting of the obtained modes of the boundary action in the form of a finite-dimensional series leads to the reconstruction of the desired function.Preliminary solution of the optimal experimental design problem for determining the coordinates of temperature monitoring points significantly improves the accuracy of solving the problem and provides identification quality that is satisfactory for engineering applications.
Authors: Anna N. Diligenskaya, Irina S. Bochkareva
Institution: Samara State Technical University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7203612781