Evaluation of effective conductivities for masonry with interfaces

Evaluation of effective or macroscopic coefficients of thermal conductivity under steady state conditions is presented. In computational homogenization there are three levels at which the field quantities are to be averaged. Solving a set of problem equations on micro-scale (at the porous or microscopic level) provides us with the up-scaled equations for the homogenization on meso-scale. At this meso-structural or mesoscopic level masony is treated as a composition of stone blocks or bricks and mortar (joint) and its homogenization produces the macroscopic equations which may be used when analyzing a masonry building and/or a bridge as a whole (macroscopic analysis). The main koncern of this contribution is the modeling of transport phenomena on meso-scale. Special attention is paid to the description of heat transport across interfaces between stone blocks (bricks) and mortar, which in classical models is mostly not dealt with. These phenomena especially gain on importance in the regions situated in the immediate vicinity of surfaces of bulky structures exposed to thermal radiation of the sun. The paper first gives a detailed summary on the solution of a simple steady state heat conduction problem with an emphasis on various types of boundary conditions applied to the representative volume element a periodic unit cell. Next, a comment on treating internal interfaces, when materials with substantially different porosities are expected, is provided.