Moisture diffusion due to periodic moisture and temperature boundary conditions—an approximate steady analytical solution with non-constant diffusion coefficients

Abstract

An approximate steady analytical solution is given to the moisture diffusion equation with periodic moisture and temperature boundary conditions, where the moisture flux is determined by both temperature and moisture gradients, specifically F = −D m( ∂m/ ∂x)−D T( ∂T/ ∂x) and which has nonconstant diffusion coefficients. The key physical assumptions made are that the thermal conductivity is constant and that the Fourier number is ⪢1 so that the internal temperature gradient is linear but periodic in response to the periodic temperature boundary conditions. The key mathematical approximation made is to ignore second and higher harmonic terms in the time-dependent part of the solution. The solution agrees with a numerical model over a wide range of parameters to within 10%, and reduces in special cases to well known existing analytical solutions. The solution has applications in a wide number of moisture diffusion problems in building physics.