On the influence of random environmental factors on heat transfer processes in aircrafts
S.A. Gusev1,2, V.N. Nikolaev3
1Institute of Computational Mathematics and Mathematical Geophysics of Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russia
2Novosibirsk State Technical University, Novosibirsk, Russia
3Siberian Scientific Research Institute of Aviation named after S.A. Chaplygin, Novosibirsk, Russia
Keywords: heat transfer, boundary value problem, random disturbances, mathematical modeling
Abstract
The main goal of the work is to simulate heat transfer in structural elements of an aircraft under random temperature changes on its outer surface due to rapid changes in environmental parameters. In this case, to model the heat transfer a one-dimensional boundary value problem of the third kind is taken for the heat conduction equation. Random disturbances are specified at the boundary corresponding to the outer surface. The numerical solution is based on an application of the Galerkin method. Modeling the random disturbances of the external environment is carried out using a Wiener integral in a system of differential equations written in integral form. Calculations for a problem with a known exact solution show that when moving away from the boundary with random disturbances, the numerical solution of the boundary value problem with disturbances converges to the known exact solution of the unperturbed boundary value problem. Based on an expansion of the solution to the boundary value problem in trigonometric functions, theoretical estimates are obtained for the influence of a disturbance on the outer surface as a function of the wall thickness and the disturbance magnitude.
|
