On the approximate solution of non-deterministic heat and mass transport problems

Uncertainties inherent to transport processes in realistic heterogeneous media can be described by non-deterministic equations with random coefficients. In this paper, we undertake an analytical study of three classes of heat and mass transfer phenomena described by convection-diffusion reaction continuum models and discrete models: (1) unsteady dispersion in a random filtration velocity field; (2) anomalous diffusion in media with random reaction sites; (3) size effect on thermal conductivity of isotropically disordered solid lattices. Using small perturbation analysis, we solve three non-trivial problems described by differential equations with random coefficients. Although the random part of the parameters is much smaller than the deterministic (weak disorder), the effect of randomness on the behavior of the averaged quantities is both important and counterintuitive.