Numerical Study of the Influence of Random Environmental Factors on the Heat Transfer Processes of Aircrafts

The paper considers numerical simulation of heat transfer in the skin of an aircraft moving in flight in order to study the influence of random perturbations on its heat exchange with the external environment. Heat transfer is described by a one-dimensional boundary value problem of the third kind. The Galerkin method is used to approximate the solution of the boundary value problem. To simulate the random perturbations of the external environment, the Wiener integral is inserted into the resulting system of ordinary differential equations, written in the integral form. This transformation of the system is equivalent to adding in the boundary condition the white noise in the generalized sense. The obtained system of stochastic differential equations is numerically solved by the Euler-Maruyama method. To estimate the influence of the random perturbations, in numerical experiments, a boundary value problem with a known exact solution is used. These experiments allow you to determine the influence of random disturbances at various distances from the border.