The physical and qualitative analysis of fluctuations in air and vapour concentrations in a porous medium

This work presents the development and physical analysis of a sweat transport model that couples the fluctuations in air and vapour concentrations, and temperature, in a one-dimensional porous clothing assembly. The clothing is exposed to inherent time-varying conditions due to variations in the body temperature and ambient conditions. These fluctuations are governed by a coupled system of nonlinear relaxation-transport-diffusion PDEs of Petrovskii parabolic type. A condition for the well-posedness of the resulting system of equations is derived. It is shown that the energy of the diffusion part of the system is exponentially decreasing. The boundedness and stability of the system of equations is thus confirmed. The variational formulation of the system is derived, and the existence and uniqueness of a weak solution is demonstrated analytically. This system is shown to conserve positivity. The difficulty of obtaining an analytical solution due to the complexity of the problem, urges for a numerical approach. A comparison of three cases is made using the Crank-Nicolson finite difference method (FDM). Numerical experiments show the existence of singular coefficient matrices at the site of phase change. Furthermore, the steady-state profiles of temperature, air and vapour concentrations influence the attenuation of fluctuations. Numerical results verify the analytical findings of this work.