On probabilistic viscous incompressible flow of some composite fluids

Abstract

The perturbation-based stochastic finite element formulation for the viscous incompressible fluid flow with heat transfer is proposed below. Analyzed viscoelastic fluid contains elastic spherical particles with randomly treated radii and total number in the fluid volume; these random variables are defined using their expected values and variances. Starting from these parameters and statistically described fluid viscosity, the probabilistic moments of the effective viscosity for a fluid with these suspensions are derived thanks to the second order perturbation second central probabilistic moment approach. So defined random effective fluid is next studied in the incompressible isobaric Couette flow between parallel plates, where the heat transfer effects are included. Defining boundary velocities and temperatures by their first two moments, the expected values and cross-covariances of the relevant homogenized fluid state functions are calculated. The engineering application of the approach can be modeling of polymers in fluid state (during their processing), reinforced with rubber particles to strengthen the entire composite as well as in general computational simulation of the composite fluids. The stochastic methodology applied to fluids with random solid suspensions can be extended on random flows with stochastic bubbles as well as multiphase coupled flow problems, where partially saturated media are considered [7], too. The main value of the stochastic approach is that it creates the opportunity to determine reliability indices, quite analogously to the research in the domain of solids and structures made of composites.