Specialization of a new flux-based approach to thermal problems. Numerical study of glass façades of buildings with cast shadows

Uneven temperature distributions in the glass panes of building fa & ccedil;ades can induce thermal stresses exceeding material strength, a critical condition usually referred to as "thermal shock". Here, we specialize in architectural glazing a recently-proposed flux-based variational approach to thermal problems, by considering heat exchanges resulting from climatic actions, in particular the variability of environmental temperatures and solar radiation, influenced by the shielding of cast shadows. The finite element implementation is facilitated because the unknown field is the heat displacement, , whose time derivative is the heat flux, which is much smoother than the temperature field, on which the classical approach via Fourier's law is based. A custom in-house-made FEM code is used to determine the effect of size and shape of cast shadows on temperature distribution in monolithic and laminated glass panes, also coupled in insulating glass units. We find that the temperature difference between irradiated and shadowed regions is only mildly influenced by the shape and size of the shadows, but the glass thickness determines the width of the transition zone and, hence, the temperature gradient. Practical rules for the design of glass fa & ccedil;ades are tentatively proposed.