Prediction of the effective parameters of the nanofluids using the generalized stochastic perturbation method

The paper presents the results concerning a new problem of homogenization of the fluids filled with a random volume fraction of nanoparticles. We use a variety of probabilistic and statistical methods applied for numerical determination of the effective physical properties of different fluids filled with nanoparticles. The new probabilistic approach in the form of a higher order stochastic perturbation method is employed here, which is based on a higher order Taylor expansion of input random quantities and the resulting homogenized parameters using a general order series with random coefficients; it is contrasted with the Monte Carlo simulation and analytical symbolic integration. All computer methods are used to determine up to the fourth probabilistic moments and coefficients for effective specific heat, viscosity, heat conductivity and mass density for some nanofluids of modern technological importance. The volume fraction of the nanoparticles is treated in this study as the input Gaussian parameter truncated to the positive values and uniquely defined by the expectation, where its coefficient of variation is an additional parameter in our analysis. Computational experiments are performed here using computer algebra system MAPLE and they demonstrate a very good agreement of the probabilistic characteristics computed using analytical, perturbation and simulation methods.