Inverse estimation of unknown thermophysical properties of green facades using the Levenberg-Marquardt algorithm

Abstract

Green facades are becoming increasingly popular in building design, and accurate thermophysical properties of the plant canopy are important to quantitatively evaluate the performance of green facades. The purpose of this paper is to propose an inverse heat conduction problem for estimating the unknown thermophysical properties of building green facades using Maple as the direct solver and the Levenberg Marquardt (LM) algorithm as the inverse method. The proposed method is applied to calculate the thermophysical properties of a green facade with greenery layer thickness of 0.4 m and 0.1 m air gap, and the measured leaf area index is 3.4. The results show that the thermophysical properties of the experimental green facade have no obvious functional dependence on solar radiation (Iglob,90) or ambient air temperature (Ta). The mean values of the thermal conductivity (λ), the density (ρ) and the specific heat (cp) were determined to be 4.4 W/m·K, 6.1 kg/m3 and 7171.2 J/kg·K, respectively. The thermophysical properties calculated in the computational experiment were verified by measured data. The results indicate that the overall trends are similar and show relatively good agreement, but there are still deviations between them, especially during daytime, in the presence of solar radiation. The main influencing factor for errors is the volumetric heat generation (qen). In this study, heat generation is assumed to be the transmitted solar energy totally absorbed by the homogenous layer. This assumption needs be refined in future studies, especially in the presence of higher global solar radiation. The proposed inverse method can be used not only in the analysis of the thermal response of green facades or vertical greenery systems, but also to analyze other building envelopes of unknown thermophysical properties.