1. Introduction
Worldwide, the construction and building sector is responsible for more than 40% of total energy consumption (see
Figure 1a) and contributes one third of CO
2 emissions [
1]. In Morocco, consumption represents about 25%, from which 18% concerns residential buildings while the rest is devoted to the tertiary sector [
2].
This expenditure will escalate even more in the coming years given an increasing rate of population increase, as well as the still-improving standards of living [
3]. This will not only lead to an increase in the construction rate and in the use of household equipment (e.g., HVAC), which increase electricity consumption, but also to the increase of harmful gas emissions. In order to face the climate change facing the world, reducing energy consumption is becoming an obligation more than a luxurious choice of living. Different countries have adopted laws and construction regulations in order to rationalize construction behavior and register the building sector through energetic sobriety while emphasizing on the comfort of occupants. Indeed, seventy-three countries have their own codes while eight are in the development process. Among these seventy-three, we can find four with voluntary residential codes, twelve with voluntary tertiary codes, fifty-one with imperative tertiary codes and forty-one with obligatory residential codes [
4].
Thermal regulation represents a basic document for energy optimization in a building’s envelope at the design and conception phases. The appropriate approaches have been then developed to fit each zone according to its corresponding meteorological data [
5]. In fact, one of the most efficient approaches to ensure energy efficiency in buildings is to analyze and study interfaces between all involved aggregated components (see
Figure 1b) [
6]: (i) much attention should be paid to the building’s construction materials (envelope and internal partitions) and its properties (orientation, landscape, design, internal distribution of the components, etc.), (ii) integration of active/passive systems in order to boost audible, visual and thermal comfort by integrating ICT technologies and concepts (e.g., Internet of Things, Big Data, forecast and prediction analytics) for data acquisition and control [
7], and (iii) efficient incorporation of renewable energy technologies (e.g., solar panels, wind turbines) [
8] and energy storage [
9,
10] devises (e.g., batteries, hydrogen).
The main idea behind this work is to focus on the building’s envelope by investigating the impact of thermo-mechanical aspects on its behavior. In literature, many researchers have carried out lots of work on thermal analyses of building as a means of ensuring thermal comfort. Candau and Piar [
11] tracked indoor temperature of a building in response to externally imposed excitations. A comparative study between simulation and experimentation has been held, basing their analysis on, respectively, model identification and spectral analysis. Gargari et al. [
12] presented in their work a ‘public housing’ building type simulation to evaluate energy savings generated by the change of insulation materials for external walls while adopting a green roof solution. Results showed that for a building with insulation that responds to restrictive energy regulation, moderate benefits are received from a green roof’s integration. Houda et al. [
13] worked on improving the evaluation method of thermal comfort in office buildings through the arid zones with dry and hot climates, by the analysis of the external intervening parameters. It was shown that predictive comfort and perceived comfort are different, since the first can be calculated based on bioclimatic parameters; as for the second, it varies according to occupants.
Not only that, but other researchers have also investigated cavities with various geometries and a variety of construction materials. For instance, Markatos and Perideous [
14] refined a calculation method essentially intended to procure solutions of heat transfer, turbulent flow and buoyancy-driven laminar flow in a square cavity with differentially heated side walls. They also took into consideration a refined mesh for fairly high Rayleigh numbers. The outcomes of their research mainly concern rectangular cavities with Rayleigh numbers going up to 10
6, a Prandtl number of 0.71 and an aspect ratio of 1. Nonetheless, the method is considered to be more general and can be applied to any kind of geometry. Another interesting work has been performed by Cordoba et al. [
15]. In this, the authors conducted a numerical study on a laminar, steady, incompressible, free convection with surface radiation in a two-dimensional open cavity. A heating source was imposed on the wall in parallel to the opening, while the rest of the walls were considered adiabatic. The governing equations of, respectively, energy, mass and momentum were resolved based on the usage of a finite volume approach, which was implemented in FORTRAN. Their study revolved around heat transfer characteristics, the orientation of the structure, and the influence of surface radiation on the fluid flow. Reported results showed that the heat transfer decreases when decreasing the cavity tilt angle for all used values of Rayleigh number and emissivity. They also mentioned that, at a certain tilt angle value, thermal radiation exchange between walls is much more significant. De Vahl [
16] investigated the bi-dimensional circulation of air in an enclosed square cavity. Desirable movement was generated using a gradient of temperature imposed at both left and right walls as boundary conditions. Accordingly, De Vahl was able to prove that, in terms of vorticity transport and energy equations for Rayleigh numbers, up to 2 × 10
−5, can converge. Additionally, he also reported the impact of the Prandtl number, which can play the role of a stabilizing factor, especially if it ranges from 10
−1 to 10
3. Karatas and Derbently [
17], in their study, have considered conjugated radiation and natural convection in a rectangular-shaped closed cavity with only one active vertical wall. The cooled surface is made of aluminum and plastic for the rest of the structure. However, since all walls are painted in white, the emissivity is considered to be constant.
Other research work focused on the influence of the aspect ratio on the Nusselt number and hence on the heat transfer with respect to the height of the cavity. For example, Yousaf and Usman [
18] presented, in their work, an algorithmic study on a natural convection in two-dimensional square cavity with the presence of sinusoidal roughness elements, which are located simultaneously on hot and cold walls. To solve momentum and energy equations, various Rayleigh numbers, varying between 10
3 and 10
6, were used for a Newtonian fluid with a Prandtl number of 1. Results showed that the presence of these elements has an impact on the hydrodynamic and thermal behavior of the fluid in the cavity. Khatamifar et al. [
19] presented numerical simulation results related to combined heat transfer and natural convection flow in a gradually heated square cavity for a large scope of the Rayleigh number (10
5–10
9). In fact, simulations were carried out using the finite volume method following three dimensionless partition thicknesses and positions. Results showed that the Nusselt number increases with the Rayleigh number but decreases with the thickness. Pandey et al., in their paper [
20], presented a review of numerical and experimental research works linked to natural convection in enclosures with/out the presence of internal bodies. These latter were taken under different shapes in order to figure out their impact on buoyancy driven-flow among enclosures. The used methods mainly cover spectral element method, finite element approaches, Latice Boltzmann method (LBM), finite volume method and so on. Their paper also discussed the effect of multiple parameters, such as Rayleigh, Grashof, and Prandtl numbers, in order to make the optimal choice of design parameters according to the desired system requirements. Ouakarrouch et al. [
21] presented a simulation englobing the conduction heat transfer and natural convection as well as radiative heat through two kinds of alveolar walls used in a recent building’s construction (3- and 6-hole numbers). Results showed that heat transfer is increased once radiative transfer is considered into calculations. Further, it was proved that conductive transfer accounts for almost the half of the heat flux in the block of 20 incorporating a thermally conducting vertical partition.
In most of the research work, and to the best of our knowledge, researchers mainly emphasize characterizing the thermal behaviors of cavities with different shapes. These latter are either heated using sun rays or a simple heating source so that an active wall is always present. They almost never take into account the co-existence of all thermal phenomena (natural convection, conduction, internal/external radiation) to study the thermal behavior of regular cavities. In the work presented in this paper, we shed more light on the thermal characterization of the envelope of a chosen structure using a combination between radiation, conduction among the different materials, and natural convection in a rectangular cavity clogged with air. Not only that, but we also conduct a mechanical study to evaluate stress distribution on the walls of a structure subjected to its own weight.
The main objective is to carry out a transient thermo-mechanical characterization of buildings’ envelopes. In fact, we are aiming to evaluate heat losses through the walls and especially through potential thermal bridge areas, by means of calculating transmittance coefficients. Once the behavior is known and the simulation models are fitted by means of experimentations in real sitting scenarios, we will be able to introduce (as perspective to this work) new functional materials in order to decrease heat losses and to contribute to energy harvesting.
A small-scale building, called EEBLAB (Touax Maroc, Mohammedia, Morocco) (energy efficient building laboratory), is used as a testbed in order to conduct experimental and simulation evaluations. Its structure is essentially made of galvanized steel for the external walls, roof and flooring base. Expanded polyurethane is injected into the external walls as a means of insulation. Two types of internal insulation are used: chipboard for the floor and an air gap and plaster boards for the roof. Thermal sensors are placed in different areas on the surfaces of the walls in order to obtain real-time temperature values, which are used to evaluate thermal transmittance coefficients. It is also worth to note that some sensors are placed in areas where thermal bridges are expected to appear. These areas were distinguished using a thermal camera [
22] (thermography analysis). Based on experimental results, a finite-element-based numerical model was developed. Simulations were directed and the main outputs are presented to show the accuracy and the performance of the developed mechanical and thermal models.
The leading grants of this work compared to our previous published paper [
23] are threefold:
Extensive experiments have been conducted using thermography analysis to detect thermal bridge placement among the EEBLAB.
A transient numerical model is proposed for buildings’ thermal characterization, taking into account its dynamic behavior.
A mechanical numerical model is presented to evaluate the distribution of mechanical stress towards buildings’ envelopes in response to the effect of their own weights.
The remainder of this paper is structured as follows.
Section 2 presents an overview of the theoretical backgrounds allowing the creation of both thermal and mechanical models. In
Section 3, we introduce the materials and methods, including numerical and experimental set-ups, used to develop and validate the numerical models. Results and discussion are presented in
Section 4, where a mesh sensibility study is also presented.
Section 5 concludes the paper and provides some perspectives on this work.