The present paper reports the simulation of unsteady coupled moisture and heat transport through a multi-layer porous solid. The governing partial-differential transport equations are written and solved simultaneously for the continuous driving potentials, i.e. relative humidity and temperature. The coupled equations are solved numerically using a singular boundary integral representation of the governing equations. The multi-layer porous solid building elements under study are submitted to convective heat and mass exchange with the surrounding environment and exposed to solar heat flux. The integral equations are discretized using mixed-boundary elements and a multidomain method also known as the macro-elements technique (Brebbia, 1984 [1], Popov et al., 2007 [2]). The numerical model uses quadratic approximation over space and linear approximation over time for all field functions, which provides highly accurate numerical results. (C) 2017 Elsevier Ltd. All rights reserved.