Stochastic modelling of the heat and moisture transfer in a porous medium

Abstract

A multi-phase and multi-component flow model with inherent stochastic terms is derived and is used to study the heat and moisture transfer in a fibrous porous medium. The materials’ porosity, velocity derived from Darcy’s law and ambient temperature at the external boundary are treated as white Gaussian noises. An effective multistep implicit splitting finite difference method (FDM) is adopted to solve the strongly coupled non-linear water, energy, vapour and air equations. The existence of a unique solution is analysed through the Lipschitz, monotonicity, growth, hemicontinuity and coercivity conditions. The notion of better thermal comfort arises from the results, as fluctuations are seen to dissipate on approaching the inner boundary (human body). Also, attention is drawn to the significance of considering all necessary uncertain variables in the system of equations. Four scenarios are considered in order to investigate the degree of contribution of the fluctuating terms. Clearly, ignoring certain vital stochastic elements can influence the results. Consequently, a combination of the stochastic porosity, velocity and ambient temperature incorporated into the same multi-phase and multi-component flow model is expected to provide more realistic results.