  A fully coupled transient heat and moisture transport in a masonry structure
is examined in this paper. Supported by several successful applications in
civil engineering the nonlinear diffusion model proposed by K\"{u}nzel is
adopted in the present study. A strong material heterogeneity together with a
significant dependence of the model parameters on initial conditions as well as
the gradients of heat and moisture fields vindicates the use of a hierarchical
modeling strategy to solve the problem of this kind. Attention is limited to
the classical first order homogenization in a spatial domain developed here in
the framework of a two step (meso-macro) multi-scale computational scheme (FE^2
problem). Several illustrative examples are presented to investigate the
influence of transient flow at the level of constituents (meso-scale) on the
macroscopic response including the effect of macro-scale boundary conditions. A
two-dimensional section of Charles Bridge subjected to actual climatic
conditions is analyzed next to confirm the suitability of algorithmic format of
FE^2 scheme for the parallel computing.
