The inverse geometric problem of thermal conductivity for determining the thickness of scale in steam boiler pipes

A. N. Soloviev^ab, M. A. Shevchenko^b, M. S. Germanchuk<sup>c

a</sup> Crimean Engineering and Pedagogical University the Name Fevzi Yakubov, Simferopol, Russia
^b Southern Federal University, Rostov-on-Don, Russia
^c V. I. Vernadsky Crimean Federal University, Simferopol, Russia

Abstract: The paper considers a nonstationary nonlinear problem of thermal conductivity in a steam boiler pipe, on the inner surface of which there is calcined scale. In the inverse geometric problem, the thickness of this scale is determined by the temperature change at the outer surface of the tube. Three cases of movement of water and steam in a tube are considered: only water, water and steam, and only steam. The problem is solved on the cross section of the structural element, the movement of water and steam is modeled by the presence of distributed heat extraction in them, when steam is formed, heat extraction at the phase boundary is taken into account, which is set by the boiling point. As a result of solving the problem by the finite element method, for the three cases under consideration, the dependence of the temperature at the outer boundary on the thickness of the scale layer is constructed. These dependencies serve as the basis for solving the inverse geometric problem of identifying scale parameters.

Keywords: inverse geometric problem of thermal conductivity, water–steam phase transition, finite element method.

UDC: 51-7, 519.6

DOI: 10.22363/2413-3639-2024-70-3-487-497

 English version: Journal of Mathematical Sciences, 2024, 287:4, 664–672