Stochastic Problem of Viscous Incompressible Fluid Flow with Heat Transfer

Abstract

The paper presented is devoted to the problem of stochastic viscous incompressible fluid flow with heat transfer. The material parameters of the medium are treated as random variables and are defined by use of the first two probabilistic moments. The second order perturbation stochastic second central moment approach is used to improve zeroth, first, and second order differential equations; it makes it possible to compute temperature, pressure, and flow velocity probabilistic moments, i.e. their expected values and cross-covariances. Next the problem is discretized using stochastic finite element method technique, well-known from solid mechanics, and it is illustrated with an example of plane Couette flow.