## 1 Introduction
These studies [6, 8, 10] underscore the complexity of assessing overall wall thermal performance, pointing to significant deviations from standard predictions under varied conditions. Over recent decades, the design of building envelope systems has seen significant changes. Though still in use, traditional heavy materials like brick or concrete have increasingly given way to lighter construction techniques [11]. These modern methods, such as timber [12] and lightweight steel-framed (LSF) constructions [13, 14], are favoured for their speedier build times and less bulky structures, especially in low-rise and residential buildings [15]. Simultaneously, the capacity for system integration within wall thickness, along with minimized and recyclable construction waste, significantly reduces structural load and, consequently, construction costs [14, 16, 17]. This shift reflects a broader trend towards efficiency and practicality in building practices. However, from the energy efficiency and thermal behaviour perspective, these lightweight buildings exhibit several possible drawbacks, such as reduced thermal inertia and high thermal bridges effects (e.g., due to the steel frame), when not correctly designed and executed [15, 17]. Additionally, the accurate computation of thermal transmitances (\(U\)-values) or thermal resistances (\(R\)-values) of LSF components is more challenging,since the simplified analytical methods prescribed in the ISO 6946 standard [9] are not applicable whenever the steel frame goes through the thermal insulation. [PERSON] et al. [18] performed a review of the calculation procedures for analytical methods to estimate the thermal transmittance of LSF walls, and made a comparison of accuracy between six analytical methods previously identified in the literature, which were applied to 80 different LSF wall configurations. They found good precision in all the studied analytical methods, the worst accuracy being offered by cold frame walls, wherein all the thermal insulation is located within the air cavity. Unexpectedly, it was found that two analytical methods, namely, the ASHRAE Zone Method (7.7%) and Gorgolewski Method 2 (9.9%), developed explicitly for LSF elements showed worse average precision (root mean square _U_-values errors) than the ISO 6946 Combined Method (7.1%). It is common sense that the surface-to-surface or conductive thermal resistance (_Rcond_) is a unique value for a specific building component (e.g., wall), regardless of the boundary conditions, i.e., ambient temperature difference and surface thermal resistances. This approach is much more versatile, since the total thermal resistance (_Rtot_) could be easily computed by adding the corresponding surface thermal resistances (_R_si and _R_se) to the provided _Rcond_ value. This why some technical _R_-value catalogues [19], as well as some research works (e.g., experimental [20] or parametric studies [21]), provide the _Rcond_ values as results, instead of the _Rtot_ value. The previous approach is suitable and accurate for building components with homogeneous layers, i.e., having a unidirectional heat flow. However, the previous methodology may encounter some inaccuracy whenever the thermal bridge effect is relevant, such as in cold frame LSF walls [22; 23]. We did not find in the literature any systematic research study assessing the influence of the surface resistances on the conductive thermal resistance of walls, such as LSF walls. In this article, the relevance of surface resistances to the conductive _R_-values of lightweight steel-framed walls is assessed by performing a numerical simulation study. To this end, four LSF walls were computed, with different levels of thermal conductivity inhomogeneity, making use of four finite elements' numerical simulation tools. Moreover, six external thermal surface resistances (_R_se) were modeled, ranging from 0.00 up to 0.20 m\({}^{2}\).K/W, giving rise to 96 different evaluated models.