An efficient two-dimensional heat transfer model for building envelopes

TL;DR

This paper introduces an efficient two-dimensional heat transfer model for building envelopes that improves accuracy over traditional one-dimensional models, accounting for environmental factors like shading and wind effects, validated through comparisons and sensitivity analysis.

Contribution

The paper presents a novel explicit 2D heat transfer model that balances high accuracy with computational efficiency, incorporating complex boundary conditions and environmental influences.

Findings

The model shows good agreement with analytical solutions and standard schemes.

Significant discrepancies are found between 1D and 2D models in high solar and wind regions.

The sensitivity analysis highlights the impact of boundary condition modeling on results.

Abstract

A two-dimensional model is proposed for energy efficiency assessment through the simulation of heat transfer in building envelopes, considering the influence of the surrounding environment. The model is based on the \DF ~approach that provides an explicit scheme with a relaxed stability condition. The model is first validated using an analytical solution and then compared to three other standard schemes. Results show that the proposed model offers a good compromise in terms of high accuracy and reduced computational efforts. Then, a more complex case study is investigated, considering non-uniform shading effects due to the neighboring buildings. In addition, the surface heat transfer coefficient varies with wind velocity and height, which imposes an addition non-uniform boundary condition. After showing the reliability of the model prediction, a comparison over almost $120$ cities in France is carried out between the two- and the one-dimensional approaches of the current building simulation programs. Important discrepancies are observed for regions with high magnitudes of solar radiation and wind velocity. Last, a sensitivity analysis is carried out using a derivative-based approach. It enables to assess the variability of the solution according to the modeling of the two-dimensional boundary conditions. Moreover, the proposed model computes efficiently the solution and its sensitivity to the modeling of the urban environment.