An efficient two-dimensional heat transfer model for building envelopes

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.