Green roof heat and mass transfer mathematical models: A review

Quezada–García, S.; Espinosa-Paredes, Gilberto; Polo-Labarrios, M.A.; Espinosa-Martínez, Erick-Gilberto; Escobedo-Izquierdo, M. Azucena

doi:10.1016/j.buildenv.2019.106634

Cited by 22 publications

(19 citation statements)

References 74 publications

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“…Most studies agree that evapotranspiration is one of the main factors that affect the thermal behaviour of green roofs (see [4,7] and the references therein). Evapotranspiration is a combination of soil evaporation and plant transpiration.…”

Section: Introductionmentioning

confidence: 90%

“…During the last few decades, green roofs have been studied from different points of view. Several mathematical models of heat transfer or heat and mass transfer for green roofs have been proposed (see [4] for a review of this type of models). Two of the most representative green roof mathematical models were proposed by del Barrio [5] and Sailor [6].…”

Section: Introductionmentioning

confidence: 99%

“…Most of these energy balance models are one-dimensional models, that is, they consider the substratum and the canopy as homogeneous. See [4] for a review of green roof mathematical models.…”

Section: Introductionmentioning

confidence: 99%

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On the Existence of Solutions of a Two-Layer Green Roof Mathematical Model

Tello

Vilar

2020

Mathematics

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The aim of this article is to fill part of the existing gap between the mathematical modeling of a green roof and its computational treatment, focusing on the mathematical analysis. We first introduce a two-dimensional mathematical model of the thermal behavior of an extensive green roof based on previous models and secondly we analyze such a system of partial differential equations. The model is based on an energy balance for buildings with vegetation cover and it is presented for general shapes of roofs. The model considers a vegetable layer and the substratum and the energy exchange between them. The unknowns of the problem are the temperature of each layer described by a coupled system of two partial differential equations of parabolic type. The equation modeling the evolution of the temperature of the substratum also considers the change of phase of water described by a maximal monotone graph. The main result of the article is the proof of the existence of solutions of the system which is given in detail by using a regularization of the maximal monotone graph. Appropriate estimates are obtained to pass to the limit in a weak formulation of the problem. The result goes one step further from modeling to validate future numerical results.

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Section: Introductionmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

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On the Existence of Solutions of a Two-Layer Green Roof Mathematical Model

Tello

Vilar

2020

Mathematics

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“…In order to properly model the energy performance of buildings provided with green roofs (considered as passive components), some reliable, yet simplified, mathematical procedures have been implemented and are available in literature. An extensive review of them is well presented in (Quezada-García, Espinosa-Paredes, Polo-Labarrios, Espinosa-Martínez, & Escobedo-Izquierdo, 2020). Among these, the one developed by Sailor (Sailor, 2008) has also been implemented in one of the most widely used building energy simulation software, i.e., EnergyPlus (EnergyPlus).…”

Section: An Insight Into the Energy Modelling Of Green Roofs And On Some Of Its Currents Gapsmentioning

confidence: 99%

Covering the Gap for an Effective Energy and Environmental Design of Green Roofs: Contributions from Experimental and Modelling Researches

Cirrincione

Peri

2021

Future City

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Green roofs are components of the building envelope that have become increasingly popular in urban contexts because other than providing numerous environmental benefits they are also capable of reducing building energy consumption, especially in summer. However, despite all these advantages, green roofs are still affected by some limitations. Specifically, there are some gaps affecting the energy modelling consisting in the absence of a proper database, information (growth stage, leaf area index, and coverage ratio) relative to the different green roof plant species, which technicians could use in case of lack of actual field data to perform energy analysis of buildings equipped with green roofs. These gaps concern also environmental and economic assessments of such technology. In fact, the currently available green roof LCA and LCC studies seem to underestimate the role of the substrate on the overall environmental impact and the role of the disposal phase on the life cycle cost of the green roof. In this chapter, all these aspects are addressed, and contributions to their solution, which arose from both experimental and modelling research, carried out by the authors are presented.

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“…The mathematical methods for analysis, modeling and optimization are increasingly used in the sewing and textile technologies [1][2][3][4]. This allows avoiding the subjective factor and creates real conditions for automation of the processes.…”

Section: Introductionmentioning

confidence: 99%

Approximation of a function describing a quality criterion of the thermo-mechanical fusible interfacing process

Andonova¹,

Baeva²

2020

cdatp

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The present work aims to investigate the function describing the relationship between a quality criterion and input factors of the thermo-mechanical fusible /TMF/ interfacing process and to derive its effective approximation. An approximation by interpolation was applied for the purpose of the study. A numerical realization of a linear and exponential approximation of the mathematical model describing the TMF interfacing process was performed. An effective linear approximation of the function connecting the quality criterion with the input factors of the TMF interfacing process was found. This creates conditions for replacing the relatively complex function (describing the TMF interfacing process) with its linear approximation. The linear approximation gives the possibility easier and faster to determine the relationships between the input factors and the quality criterion. This created conditions for ignoring the subjective factor and for optimizing and automating the studied technological process.

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Green roof heat and mass transfer mathematical models: A review

Cited by 22 publications

References 74 publications

On the Existence of Solutions of a Two-Layer Green Roof Mathematical Model

On the Existence of Solutions of a Two-Layer Green Roof Mathematical Model

Covering the Gap for an Effective Energy and Environmental Design of Green Roofs: Contributions from Experimental and Modelling Researches

Approximation of a function describing a quality criterion of the thermo-mechanical fusible interfacing process

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