A mathematical model that governs unsteady coupled moisture and heat energy transport through an exterior wall covered with vegetation is described. The unknown temperature and moisture content of the plants and canopy air are represented by a system of nonlinear ordinary differential equations (ODEs). The transport of moisture and heat through the support structure, which includes insulation and soil layers, is defined in a series of nonlinear partial differential equations (PDEs). After setting out the model, this article presents and discusses a set of numerical applications. First, a simplified system consisting of a brick wall covered with climbing vegetation is used to study the role of individual variables (e.g., wind speed, minimum stomatal internal leaf resistance, leaf area index, and short-wave extinction coefficient) on the hygrothermal behaviour of the green wall. Thereafter, more complex green wall systems comprising a bare concrete wall, mortar, cork-based insulation (ICB), soil and vegetation are used to evaluate the influence of the thermal insulation and substrate layers on the heat flux distribution over time at the interior surface of the wall, and on the evolution of the relative humidity, water content, and temperature throughout the cross section of the green wall. The numerical experiments proved that vegetation can effectively reduce exterior facade surface temperatures, heat flux through the building envelope and daily temperature fluctuations.
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