Abstract
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.
Highlights
It is increasingly being acknowledged that urban sustainability requires a comfortable and healthy environment
Numerical solutions of the green wall model are strongly related to the plant parameters that define the thermal energy transport, mass transport and storage behaviour, empirical relations involved in modelling heat and Energies 2021, 14, 4422 moisture fluxes, crop transpiration, choosing the relevant different stems of the plants, and characteristics of the canopy, etc
The numerical simulation tool governing the transport phenomena in green roofs [11] was modified in such a way as to be able to estimate the transport of heat and moisture in vegetated vertical walls
Summary
It is increasingly being acknowledged that urban sustainability requires a comfortable and healthy environment. The structural support, including the bare wall, insulation layer and soil, was regarded as an unsaturated homogeneous porous medium for which the heat and moisture transport are interlinked and coupled It is governed quantitatively by a set of coupled nonlinear partial differential equations (PDEs). Numerical solutions of the green wall model are strongly related to the plant parameters that define the thermal energy transport, mass transport and storage behaviour, empirical relations involved in modelling heat and Energies 2021, 14, 4422 moisture fluxes, crop transpiration, choosing the relevant different stems of the plants, and characteristics of the canopy, etc. It goes on to describe the finite difference and the boundary element methods used to solve the canopy and porous solid transport equations, respectively Based on this model, three numerical examples of increasing complexity are discussed: a two-layer greenery system (canopy-brick wall), a four-layer greenery system (canopy-ICB-mortar-concrete wall), and a five-layer greenery system (canopy-substrate-ICB-mortar-concrete wall).
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