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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 Du Fort–Frankel 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. [ABSTRACT FROM AUTHOR]

The current state of research indicates a necessity of further examination in both numerical and experimental studies related to optimizing shapes of building enclosures for the enhancement of their energy efficiency. The demand for research primarily arises due to the numerical complexities associated with optimizing shapes for this specific purpose. Consequently, the primary objective of this article is to address and bridge these gaps in the field. To achieve this, a two-dimensional steady-state heat diffusion model is assumed to represent the physical processes occurring within building facades of varying shapes. A third type boundary condition is applied to the exterior boundary, encompassing convective and incident short-wave solar radiation effects. The calculation of short-wave radiation accounts for factors such as sunlight exposure and shading, influenced by the surrounding urban environment. The internal boundary interfaces with the indoor ambient air, and thus, a Robin boundary condition is adopted. To tackle the computational demands while ensuring accuracy, the boundary element method (BEM) is employed by discretizing the domain boundary into discrete elements. Then, two heat transfer design objectives are define according to the period of investigations: ones related to enhancing heat transfer and ones focused on thermal insulation problem. Last, a real-world case study is conducted, considering a house wall under varying climate conditions throughout the year. Optimal shapes for the external wall boundary are determined with the constraint that the optimized facade utilizes the same amount of material as the reference flat one. The results demonstrate a substantial increase in energy efficiency compared to the reference flat wall case. • Shape optimization of building facade • Short wave radiation • Steady-state heat transfer • Boundary element method • Energy efficiency [ABSTRACT FROM AUTHOR]