Title: Investigation of the accuracy of an approximate solution of the initial boundary value problem of thermal conductivity with boundary conditions of the third kind

Authors: Alexandra S. Nikolaeva; Maxim A. Evtushenko; Luiza A. Manukyan

Addresses: Department of Theoretical Mechanics, Samara National Research University, Moskovskoe shosse, 34, Samara, Russia ' Training Laboratory of Ground Testing of Aviation Vehicles, Samara National Research University, Moskovskoe shosse, 34, Samara, Russia ' Department of Space Engineering, Samara National Research University, Moskovskoe shosse, 34, Samara, Russia

Abstract: The paper compares two approximations of the solution of the initial boundary value problem of thermal conductivity with boundary conditions of the third kind for the case of a temperature shock of a homogeneous thin plate. A second-order approximation with respect to the plate thickness is obtained. The results of the numerical simulation are compared with the known first-order approximation with respect to the plate thickness. The results obtained demonstrate good convergence. They can be used in controlling the motion of a small spacecraft with elastic structural elements. It is necessary to level out the effect of temperature shock disturbances on the angular motion of a small spacecraft.

Keywords: thermal conductivity problem; boundary conditions of the third kind; temperature shock; thin plate.

DOI: 10.1504/IJMMNO.2025.145634

International Journal of Mathematical Modelling and Numerical Optimisation, 2025 Vol.15 No.1, pp.52 - 63

Received: 06 Feb 2025
Accepted: 13 Feb 2025
Published online: 09 Apr 2025 *