Microsoft Word - 1969.docx Adv Syst Sci Appl 2025; 3; 52-73 Published online at https://ijassa.ipu.ru. Analysis of the Thermal Behavior of a Workspace in the Adrar Region Oudrane Abdellatif1*, Aour Benaoumeur2, Bada Abdelmalek1,3, Kheiri Abdelhamid4 1) Ahmed Draïa University of Adrar, Adrar, Algeria 2) National Polytechnic School of Oran, Oran, Algeria 3) University of Science and Technology of Oran, Bir El Djir, Algeria 4) University of Lorraine, Lorraine, France Abstract: This study presents an experimental and numerical investigation of the thermal behavior of a workplace located in the Adrar region. Temperature variations within the building were analyzed through a detailed modeling approach and validated using data collected during a 20-day experimental campaign conducted in May 2024. All modes of heat transfer were considered, and energy balance equations were formulated for each structural material. The resulting system of equations was solved using an implicit finite-difference scheme combined with the Gauss algorithm and an iterative procedure, accounting for the dependence of convective and radiative heat-transfer coefficients on the surrounding temperatures. Numerical results indicate that the thermal conductivity of the heavy concrete bricks, together with the local climatic conditions, significantly contributes to indoor temperature increases. Comparison of numerical predictions with experimental measurements for two representative days (May 10 and May 18, 2024) demonstrated excellent agreement, with errors not exceeding 4%. The findings provide insights into the thermal performance of public buildings in the Adrar region and offer a reliable numerical tool for engineers to select appropriate construction materials. The study also highlights that modern building materials, when used without adequate thermal insulation, can lead to excessive indoor temperatures and uncontrolled energy consumption in this desert environment. Keywords: Habitable construction, Thermal behavior, Workplace, Heat convection, Thermal conductivity, Building materials, Desert areas, Internal temperature. Nomenclatures Cp Specific heat -1-1 .KJ.Kg e Material thickness m Fi Geometric form factor - I Electric current intensity mA hr Radiation heat exchange coefficient -1-2 .kW.m hconv Convection heat exchange coefficient -1 . -2 kW.m hcext External heat exchange coefficient for convection -1 . -2 kW.m L Length m mps Mass of the South wall Kg QCCv Amount of heat exchanged by convection W Qdoor Amount of heat exchanged by the door W Qwall Amount of heat exchanged by the wall W Qabsor Amount of heat absorbed W Qsource Amount of heat from the source W qr Amount of radiative flux W.m-2 φ Heat flux density W.m-2 R Electrical resistance Ω SPS South wall surface m2 Tamb Room temperature °C Tground Soil temperature °C Tair Air temperature °C Text External temperature °C Tint Internal space temperature °C * Corresponding author: abdellatif.habadat@gmail.com, +213662830459 OUDRANE A., AOUR B., BADA A. AND KHEIRI A. 53 Copyright ©2025 ASSA. Adv. in Systems Science and Appl. (2025) ΔT Temperature deviation °C TVC Temperature of the celestial vault °C TPSI Internal south wall temperature °C TPNI Temperature of the internal north wall °C TPFPI Internal temperature of the wall ceiling °C glas U Surface thermal transmittance coefficient of glass W.m-2. K-1.J-1 Vair Air volume m3 Vwind Average wind speed m. s-1 Lettres Grecques  Absorption coefficient -  Emissivity coefficient -  Thermal conductivity -1-1 .KW.m  Density Kg.m-3 σ Stefan-Boltzmann constant W. m-2. K-4 Nombres Adimensionnels Gr Grashof number - Pr Prandtl number - Ra Rayleigh number - Abreviation PS South wall - PN North wall - PE East wall - PO West wall - PFP Ceiling wall - PSI Internal south wall - PNI Internal north wall - PEI Internal east wall - POI Internal west wall - PFPI Internal ceiling wall - PSE External south wall - PNE External north wall - PEE External eat wall - POE External west wall - PFPE External ceiling wall - HTC Building heat transfer coefficient - DPS Date palm spikelet - DPF Recycled date palm fiber - DPP Petiole of the date palm - XPS Panneau de polystyrène extrudé - PCM Phase change materials - HTR Hourly temperature reduction - HHGR Hourly reduction in heat gain - ECA Evaporative air conditioning - NV Natural ventilation - 1. INTRODUCTION Quantifying thermal exchanges between buildings and their surrounding environment at the urban scale requires a detailed understanding of local energy balances across multiple levels, from districts and building clusters down to individual structures and specific building components. The multiscale nature of this problem makes optical sensor technologies particularly relevant, as they enable non-contact spatial measurements that remain effective at various scales. Recent advances in sensor technology have enhanced the resolution of detection matrices and improved associated optical systems, allowing for more precise analysis of observed scenes. The luminance measured by these sensors originates from multiple elements within the field of view, from which surface temperatures of the urban environment can be inferred [1,2]. Establishing the relationship between measured luminance, the temperature of individual components, and heat transfer through building envelopes requires comprehensive modeling of the underlying physical phenomena [1,3,4]. These mechanisms are highly interdependent, as surface energy balances are strongly influenced by local climatic conditions. A review of existing methods for quantifying thermal exchanges in buildings indicates that their development has been largely shaped by methodological choices, attracting growing interest from the scientific community concerned with energy storage and conservation. Several representative studies are highlighted below for illustrative purposes. 54 OUDRANE A., AOUR B., BADA A. AND KHEIRI A. Copyright ©2025 ASSA Adv. in Systems Science and Appl. (2025) Kumaraswamy et al. [5] investigated thermal storage in building materials and long-term energy conservation using phase-change materials (PCM). Due to their latent heat capacity, PCMs can store significant amounts of heat or cold within limited volumes, reducing fluctuations in indoor air temperature and maintaining thermal comfort over extended periods. Selecting an appropriate PCM, however, requires careful consideration of local climatic constraints. Kaoutari et al. [6] conducted numerical and experimental analyses of coupled heat and moisture transfer in a biobased double-layer wall system, integrating measured material properties into a dynamic model based on the approaches of Künzel and Mendes. Finite- difference methods were employed to solve the coupled transfer processes, with transient simulations representing real winter and summer conditions. Comparisons demonstrated that experimental data provided highly accurate solutions. Virginia et al. [7] examined uncertainties associated with co-heating tests to evaluate the impact on estimated building Heat Transfer Coefficients (HTC), showing that weather conditions, complex building designs, and experimental practices can significantly influence HTC estimates. Belatrache et al. [8] explored the use of date palm waste as insulating material in arid climates, demonstrating reductions in cooling electricity consumption of up to 64.7% compared to traditional constructions. Laidi et al. [9] assessed energy performance of a single- family house with a mansard roof in Algeria, showing that attics, insulated or not, contribute to reduced cooling demand across various climatic zones. Jiang et al. [10] modified clay walls with cement, gravel, sand, and polypropylene fibres, highlighting the strong heat and moisture buffering capacity of the modified walls, reducing indoor temperature and humidity fluctuations. Chaoping et al. [11] studied thermal optimization of traditional rural dwellings in northeastern Sichuan, comparing four wall renovation strategies through numerical simulations. Central insulation combined with extruded polystyrene (XPS) panels significantly improved indoor thermal comfort. Qudama et al. [12] investigated compacted PCMs integrated into building envelopes under warm climates, achieving hourly temperature and heat gain reductions of up to 15.1% and 34.9%, respectively, and lowering indoor temperatures by up to 4 °C. Yadeta et al. [13] conducted a field survey of thermal comfort in 104 dwellings, producing adaptive comfort models essential for designing sustainable dwellings in regions with limited energy access. Guo et al. [14] performed on-site studies of office buildings in Turpan, China, under evaporative cooling and natural ventilation, revealing discrepancies with current adaptive comfort standards and providing guidance for updating design parameters and passive strategies. Building on these insights, the present study investigates the thermal behaviour of a workplace in the Adrar region of southern Algeria. An experimental campaign conducted in May 2024 over 20 days was implemented to validate the numerical results obtained from a thermal model developed for this work. Temperature and humidity measurements (Testo 175T2, Testo 175T3, and Testo 174H) included interior surface temperatures of south and north walls, interior roof surface temperature, indoor air temperature, indoor relative humidity, and outdoor air temperature. To achieve the stated objectives, this work is structured as follows. A description of the studied workplace, serving as an office for a university lecturer, is provided in Section 1, followed by the climatic characteristics of the Adrar region in Section 2. Section 3 details the measurement instruments and the simplifying assumptions adopted in the experimental protocol. The mathematical modeling of the energy balance is introduced in Section 4, and finally, Section 5 presents a comprehensive analysis of the results along with a comparison between experimental observations and numerical predictions based on a typical day. OUDRANE A., AOUR B., BADA A. AND KHEIRI A. 55 Copyright ©2025 ASSA. Adv. in Systems Science and Appl. (2025) 2. EXPERIMENTAL STUDY ELEMENT The workspace under study corresponds to the office of a university professor. In the numerical model, the room is idealised as a rectangular control volume, as shown in Figure 2.1. The enclosure comprises one external door and one glazed opening. All façades of the office are unobstructed and directly exposed to solar radiation throughout the day, implying that both shortwave and longwave radiative exchanges occur without shading effects. Fig. 2.1 View and geometric dimensions of the workplace 2.1. Geometrical and Physical Properties of the Workplace The experimental workspace was designed considering both its geometric configuration and physical properties, which serve as input parameters for the thermal model. These characteristics were defined in accordance with civil engineering practices appropriate for desert climates. The external walls are composed of a double-layer masonry construction with a total thickness of 49 cm, incorporating a 5 cm air cavity that functions as thermal insulation. All surfaces are assumed to be homogeneous and isotropic for thermal calculations. Table 2.1.1 provides a detailed overview of the geometric dimensions of the experimental element. Table 2.1.1. Geometric dimensions of the workplace Width (m) Length (m) Height (m) Thickness (m) Surface (m2) South wall 3.60 3.60 3.20 0.49 12.96 North Wall 3.60 3.60 3.20 0.49 12.96 East Wall 3.90 3.90 3.20 0.49 15.21 West Wall 3.90 3.90 3.20 0.49 15.21 Ceiling tile 3.60 3.90 - 0.20 14.04 Floor Slab 3.60 3.90 - 0.22 14.04 Table 2.1.2 summarizes the construction materials assigned to each wall of the experimental workspace, along with their relevant thermophysical properties, which are used as input parameters in the numerical thermal model. Table 2.1.2 Construction materials of the workplace South wall North Wall East Wall West Wall Ceiling tile Floor Slab Materials Double wall in red brick + exterior coating + air blade + Interior coating Red brick + Exterior coating+ Interior coating Red brick + exterior coating+ Interior coating Red brick + exterior coating+ Interior coating Concrete Brick (Hourdis) + reinforced concrete + Interior coating+ exterior coating Granite tiles + Heavy concrete Building materials with appropriate physical and thermal properties are essential for accurately simulating heat transfer. Accordingly, these properties have been carefully determined to enable precise modelling of the various thermal exchanges. Table 2.1.3 presents the physical and thermal properties of all materials used in the study: Table 2.1.3. Physical and thermal properties of building materials [15-18] ρ (Kg. m-3) Cp (J.Kg-1.K-1) λ (W.m-1.K-1) ɛ α Red brick 300 800 0.08 0.93 0.60 56 OUDRANE A., AOUR B., BADA A. AND KHEIRI A. Copyright ©2025 ASSA Adv. in Systems Science and Appl. (2025) Hourdis brick 1800 1000 1.15 0.97 0.60 Reinforced concrete 2400 1000 2 0.97 0.60 Heavy concrete 2300 1000 2.71 0.97 0.60 Cement + Earth + Red paint 1959 1.492 0.671 0.95 0.75 Plaster 850 936 0.35 0.97 0.21 Granite tiles 2200 936 2.1 0.97 0.58 Air gap 1.200 1000 0.04 0.40 0.40 Glazing 130 720 2.50 0.89 0.08 Figure 2.1.1 illustrates the detailed geometric configuration of the external wall section considered in the experimental study. Fig. 2.1.1. Engineering of the structure of a wall with two walls separated by an air gap 3. DESCRIPTION CLIMATIC OF THE ADRAR REGION The present study was conducted in Adrar, located in the southwest of Algeria, covering an area of 424.948 km² with a population of 402,197 inhabitants according to the 2008 census (see Figure 3.1). The region possesses significant potential for renewable energy exploitation, particularly solar and wind resources [19-22]. Adrar’s climate is classified as hot desert (BWh) according to the Köppen system [23,24], characterized by extreme aridity, low and irregular precipitation (annual average <50 mm), and prolonged periods of high ambient temperatures, often exceeding 45 °C during summer months. Relative humidity remains very low, typically below 20%, while annual global solar irradiation is exceptionally high, exceeding 2,800 kWh/m²/year. These climatic conditions result in substantial solar and convective heat loads on building envelopes, which are critical parameters for thermal modeling and the assessment of passive cooling strategies in buildings [23,24]. Fig. 3.1. Geographical location of the study area [22] OUDRANE A., AOUR B., BADA A. AND KHEIRI A. 57 Copyright ©2025 ASSA. Adv. in Systems Science and Appl. (2025) As shown in Figure 3.2, Adrar exhibits very mild winters and extremely hot, sunny summers. The city experiences a maximum average temperature of 46 °C in July, making it one of the hottest cities in the world. In July 2023, temperatures peaked at 49.9 °C, while in August 2023, a day was recorded with a minimum of 35.5 °C and a maximum of 49.8 °C [25]. Fig. 3.2. Evolution of the average seasonal temperature range at the Adrar region in 2023 [25] 4. TEMPERATURE MEASUREMENT DEVICES Temperatures were measured and recorded continuously every 24 hours over a period of 20 consecutive days in the workplace using Testo devices, as shown in Figure 4.1. Measurements were performed on the interior surfaces of the south and north walls, the roof, as well as in the indoor air volume, with additional recordings of the outdoor air temperature. The instrumentation provided high-resolution data with a precision of ±0.1 °C for temperature and ±2 % for relative humidity, ensuring accurate input for thermal modeling. Fig. 4.1. Measuring and recording devices for different temperatures of the workplace 4.1. Simplifying Assumptions of the Experimental Process To ensure the proper execution of the experiment, several simplifying assumptions were adopted, which can be summarized as follows:  The outdoor air temperature is assumed to be equivalent to the ground temperature. 58 OUDRANE A., AOUR B., BADA A. AND KHEIRI A. Copyright ©2025 ASSA Adv. in Systems Science and Appl. (2025)  Humidity effects are neglected due to the region’s persistent arid conditions.  Heat transfer is considered to be unidirectional. Figure 4.1.1 illustrates the locations of the measuring devices both inside and outside the workplace. Fig. 4.1.1. Position of measuring devices inside and outside the workplace 5. MATHEMATICAL MODELLING OF THERMAL BEHAVIOUR 5.1. Loads Due to the Room Glazing Glass walls are characterized by their absorption and transmission coefficients. Accordingly, the heat flux absorbed by a windowpane can be expressed by the following relation [26]: )( intglasglas TTSUQ extccv  (5.1.1) In this context, the physical and thermal properties of the glass are considered, as summarized in Table 5.1.1. Table 5.1.1. Physical and thermal properties of the glass of the workplace [27,28]. ) 11 glas ..(  KmW ).( 3 glas  mKg )..( 11 glas  KKgJCp )..( 12 glas  KmWU )( glas Cme Single Glass Window 1.05 2300 837 5.6 1 5.2. Loads due from the Workplace Door The door in this workplace influences the internal heat exchange. The approximate amount of heat transferred through the door can be expressed by the following relation [29]:  intdoordoor TTShQ extconv  (5.2.1) 5.3. Thermal Convection Loads  Convection Outside the Workplace In this case, the modeling focuses exclusively on heat transfer due to thermal convection through the five walls of the workplace, as described by the following relation [30-32]:  iextiextconviwall TTShQ  )()( (5.3.1) The convective heat transfer coefficient on the exterior surfaces of the element is calculated using the following relation [33,34]: wind)( )8,3(7,5 Vh extconv  (5.3.2) It was noted that the exterior façade of the south wall is the only surface directly exposed to solar radiation. Opaque materials are characterized by an absorption coefficient specific to visible radiation, and the net absorbed flux represents the corresponding heat source. By OUDRANE A., AOUR B., BADA A. AND KHEIRI A. 59 Copyright ©2025 ASSA. Adv. in Systems Science and Appl. (2025) neglecting the portion of flux reflected back to the environment, the heat generated by these radiative exchanges is expressed by the following relation [33]:   n i sourceabsor tFSG i S i QQ )( (5.3.3)  Convection in the workplace The thermal energy resulting from the heat exchange between the indoor air and the interior surfaces of the workplace walls is calculated using the following relation (Equation 5.3.4) [35,36]:   n i amb i walliconvwallconv TTShQ ).(. (int))( (5.3.4) Natural convection occurs when a temperature gradient induces motion in the air, producing what are referred to as convective flows. Heat transfer within a fluid layer is governed both by thermal conduction and by the movement of the fluid. When a thermal gradient is applied across the surface layers, a corresponding density gradient develops [35]. Experimentally, it is observed that after a certain period, the fluid begins to move spontaneously, marking the onset of convection. This onset is characterized in Table 5.23.1 by a dimensionless parameter known as the Rayleigh (Ra) number [36]. Table 5.3.1. Expression of convective transfer coefficients [35,36]. Surface description Flow regime Scope of validity Pr.GrRa  Expression Vertical wall Laminar regime 9 10Pr. 4 10 Gr   4/1 .42,1 L T vhcon  Turbulent regime 9 10Pr. Gr   3/1 .31,1 L T vhcon  Upper surface of a horizontal hot plate or lower surface of a cold plate Turbulent regime 9 10Pr. 4 10 Gr   4/1 .32,1 L T vhcon  Laminar regime 9 10Pr. Gr   3/1 .52,1 L T vhcon  Lower surface of a hot plate or upper surface of a cold plate Turbulent regime 9 10Pr. 4 10 Gr   4/1 .59,0 L T vhcon  Laminar regime 9 10Pr. Gr 5.4. Thermal Conduction Loads Figure 5.4.1 presents a geometric schematic of the exterior south wall of the study element. It also illustrates the directions of heat transfer and thermal processes occurring within the wall materials. For a linear temperature profile, the heat flux through the wall is calculated using the following relation [37,38]: dx dT SQ .. (5.4.1) In steady-state conditions, the heat flux through the wall is conserved and can be expressed using the following relation [39]:      1 int 1 . . . . . . n i i i i i i ext i i i i i S T T Q h S T T h S T T e          (5.4.2) 60 OUDRANE A., AOUR B., BADA A. AND KHEIRI A. Copyright ©2025 ASSA Adv. in Systems Science and Appl. (2025) Fig. 5.4.1. Equivalent electrical diagram of a multilayer wall 5.5. Solar Radiation Loads To consider the optical and geometric properties of the considered surfaces, the form factor F’i+1 can be defined using the following expression [40]: 1 11 1 1 ' 1 111                 i i i i iii i ii S S F F     (5.5.1) The net radiative flux ‘'qr,i i+1’’ between the surfaces at temperatures ‘'Ti’' and ‘'Ti+1 ’’, is expressed by the following relation [41]:  4 1 4' 11,   iiiiiiir TTFSq  (5.5.2) In linearized form, qr,i+1 is written in expression 5.5.3 as follows:  11,1,   iiiiriir TTh (5.5.3) The general expression for the radiative heat transfer coefficient between surfaces i and i+1 is given by the following relation [38-40]:     11 1 1 1 2 1 2 1, 111            i i i i iii i iiii iir S S F TTTT h      (5.5.4) 5.6. Principle of Thermal Analysis by the Nodal Method The nodal method is particularly well suited for simulating the thermal behavior of buildings. It enables a global representation of the entire structure, including fluid circuits, and allows problems of different physical nature to be solved within a unified framework [42,43]. Moreover, its computational cost and memory requirements are significantly lower compared to finite element analyses. This approach offers sufficient flexibility to refine the mesh locally when necessary. Based on the thermal–electrical analogy, the nodal method consists in discretizing the physical system into a finite number of isothermal elementary volumes (nodes). The thermal response of the system is obtained by solving the set of energy conservation equations, with one governing equation associated to each node. The thermal balance of node i which exchanges heat by conduction with node j, by convection with node k, by radiation with node l, by fluid transport with node m, and interacts OUDRANE A., AOUR B., BADA A. AND KHEIRI A. 61 Copyright ©2025 ASSA. Adv. in Systems Science and Appl. (2025) with heat sources or sinks n, leads to the nonlinear differential equation expressed in relation 5.6.1 [43-45].            4 4 Source *. . . . . . . . . . . . . iji j i ik k i i il i i m i ni l n j Convection TransportRayonnement Conduction SdT V Cp T T h S T T S F T T m Cp T T Q dt li                 (5.6.1) The solution of each governing equation yields the temperature of the corresponding node as well as the associated heat fluxes. In the nodal framework, the residential thermal system is represented analogously to an electrical network: the thermal inertia of each node is modeled by a thermal capacitance, conductive and convective exchanges are represented by thermal conductances, imposed temperatures correspond to potential (voltage) nodes, and imposed heat flows are treated as current sources. Under this analogy, the global set of coupled nonlinear equations describing the system can be written in the compact matrix form expressed in relation 5.6.2 [45-47].        ( ) ( ) ( ) ( ). . . . .i i cond j j i conv j k i Ray l l i fluid m m i source dT C Q T T Q T T Q T T Q T T Q dt          (5.6.2) 5.7. Thermal Balance of Study Element The thermal balance represents an evaluation of all energy inputs and outputs associated with the studied element over a defined time interval [33, 34]. The mathematical model developed for the thermal analysis was validated using experimental measurements, as detailed in the section dedicated to physical results and interpretation. In accordance with the nodal modelling approach, each wall of the structure is treated as an individual node, and a specific thermal balance is established to describe all heat transfer mechanisms acting within that wall. Given that the studied enclosure comprises five walls, the resulting system of equations includes ten coupled thermal balance equations, to which an additional equation describing the natural convection of the confined indoor air must be added. Relations 5.7.1 and 5.7.2 illustrate representative equations of the global system obtained through numerical modelling in this study [45].  Thermal balances of exterior facades of the workplace In this configuration, the global energy balance comprises five independent equations, each associated with one of the external façades of the workplace, which exchange heat with the outdoor environment. Each equation explicitly accounts for the local climatic boundary conditions, as well as the thermal and physical properties of the construction materials constituting the corresponding façade. ( ) ( ) ( , ) ( , ) ( ) ( ) ( , ) ( , ) ( ) ( ) . . . . . . . . . . . . . . . . . PS P PS PSE PS C ext r VC PSE r SOL PSE PS PSE PS PS PN P PN PNE PN C ext r VC PNE r SOL PNE PN PNE PN PN PO P PO POE PO C ext PO PO m C T h T T h T h T S t S m C T h T T h T h T S t e m C T h T S t e                                    ( , ) ( , ) ( ) ( ) ( , ) ( , ) ( ) ( ) ( , ) ( , ) . . . . . . . . . . . . . . . . . r VC POE r SOL POE PO POE PFP P PFP PFPE PFP C ext r VC PFPE r SOL PFPE PFP PFPE PFP PFP PE P PE PEE PE C ext r VC PEE r SOL PEE PE PE T h T h T m C T h T T h T h T S t e m C T h T T h T h S t e                                 .PE PEET                                (5.7.1)  Thermal balance of interior facades of the workplace Similarly, the internal energy balance of the workplace considered in this study was established. It consists of six governing equations, each describing the heat transfer mechanisms acting on the internal façades of the enclosure. These equations account for 62 OUDRANE A., AOUR B., BADA A. AND KHEIRI A. Copyright ©2025 ASSA Adv. in Systems Science and Appl. (2025) convective, conductive, and radiative exchanges occurring between the indoor air and the corresponding internal surfaces. ( ) ( ) ( , ) ( , ) ( , ) ( , ) ( , ) ( ) ( ) ( , ) ( , ) ( , . . . . . . . . . . . . . . . PS P PS PSI PS C int r PSI PNI r PSI POI r PSI PEI r PSI PFPI r PSI PP PS PS PN P PN PNI PN C int r PNI PSI r PNI PEI r PNI POI PN PN m C T h T T h T h T h T h T h T S t e m C T h T T h T h T h S t e                              ) ( , ) ( , ) ( ) ( ) ( , ) ( , ) ( , ) ( , ) ( , ) ( ) ( ) . . . . . . . . . . . . . . . . r PNI PFPI r PNI PP PO P PO POI PO C int r POI PSI r POI PNI r POI PEI r POI PFPI r POI PP PO PO PFP P PFP PFPI PFP C int PFP PFP T h T h T m C T h T T h T h T h T h T h T S t e m C T h T T S t e                               ( , ) ( , ) ( , ) ( , ) ( , ) ( ) ( ) ( , ) ( , ) ( , ) ( , ) ( , ) . . . . . . . . . . . . . . . r PFPI PSI r PFPI PNI r PFPI POI r PFPI PEI r PFPI PP PE P PE PEI PE C int r PEI PSI r PEI POI r PEI PNI r PEI PFPI r PEI PP PE PE air h T h T h T h T h T m C T h T T h T h T h T h T h T S t e m                           ( ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ). . . . . . . . . . . . .P air air PS PN PO PE PFP PP C PSI air C PNI air C POI air C PEI air C PFPI air C PP air air air air air air air air C T S S S S S S h T h T h T h T h T h T S t S S S S S S                           (5.7.2) Processing of Input and Output Data Figure 5.8.1 illustrates the detailed computational flowchart employed for the numerical simulation. The diagram details the sequential operations implemented to evaluate the heat transfer mechanisms occurring within and around the workplace over a 24-hour representative cycle. The resulting system of linearized equations obtained from the numerical model was solved using the Gauss elimination algorithm. The flowchart also clearly specifies the input parameters required at the initialization stage of the simulation, as well as the output variables produced at each iteration. It is important to highlight that the computation relies on time-averaged boundary and operating conditions, defined over discrete intervals throughout the day. OUDRANE A., AOUR B., BADA A. AND KHEIRI A. 63 Copyright ©2025 ASSA. Adv. in Systems Science and Appl. (2025) Fig. 5.8.1. Computational flowchart of the numerical heat transfer modeling 6. RESULTS AND DISCUSSION 6.1. Validation of the Developed Numerical Model The validation of the numerical model developed in this study, based on data from two representative days, May 10th and May 18th, is presented in Figure 6.1.1. The results show a good agreement between the measured and simulated temperatures. Validation was performed for the following temperature types: TPN (Figure 6.1.1a, May 18th, 2024), Tin (Figure 6.1.1b, May 18th, 2024; Figure 6.1.1c, May 10th, 2024), and Text (Figure 6.1.1d, May 10th, 2024), with all comparisons yielding satisfactory results. These findings confirm that the developed numerical model is valid and can be reliably used to simulate other thermal quantities, such as the temperature of wall façades and the solar flux incident on both the exterior and interior surfaces of the workplace. The maximum discrepancy between measured and calculated temperatures over the two selected days did not exceed 4%, further demonstrating the model’s accuracy. (a) (b) (c) (d) Fig. 6.1.1. Comparison between the measured temperature variations and the calculated temperature. 6.2. Analysis of Experimental Data Figure 6.2.1 illustrates the temporal evolution of the external Text and internal Tint temperatures as a function of local time over the course of the experimental period. Figure 6.2.1(a) presents the variation of the external temperature Text at the study site over seven selected days. It can be observed that the daily external temperature profiles exhibit a similar pattern throughout 64 OUDRANE A., AOUR B., BADA A. AND KHEIRI A. Copyright ©2025 ASSA Adv. in Systems Science and Appl. (2025) the week. During the night, from the early hours until sunrise at around 8:00 a.m., Text ranges from 16.3°C (May 1st, 2024) to 31.8°C (May 20th, 2024). Following sunrise, the temperature gradually increases, reaching a peak in the late afternoon, approximately 5:00 p.m., with maximum values ranging from 40.31°C on May 1st, 2024, to 49.25°C on May 13th, 2024. Thereafter, the temperature gradually decreases and stabilizes within a limited range between 22.9°C (May 1st, 2024) and 31.0°C (May 13th, 2024). The average external temperature over the seven selected days is approximately Text (average) = 45.7°C. Figure 6.2.1(b) shows the internal temperature Tint evolution at the study location as a function of local time. The results indicate that the internal temperature profiles for the seven days follow a similar daily trend. Notably, on May 1st and May 2nd, 2024, Tint exhibits slightly lower values compared to the other selected days. The maximum internal temperature reached Tint = 30.1°C at 6:00 p.m. on May 1st and 2nd, whereas for the remaining days, the peak internal temperature was Tint = 33.5°C at approximately 1:00 p.m. These observations indicate that the average internal temperature during early May in this desert region is relatively moderate but shows a gradual increase over the course of the month. (a) (b) Fig. 6.2.1. Evolution of external and internal temperature as a function of local time for different days of the experiment. 6.3. Analysis of Typical Day May 1st, 2024 Figure 6.3.1 illustrates the temporal evolution of the thermal behavior of the study site over a typical day, May 1st, 2024, as a function of local time. Figure 6.3.1(a) presents the variations of the internal air temperature Tint and relative humidity (RH) throughout the day. It is observed that Tint and RH follow a similar trend until approximately 10:00 a.m. From 1:00 p.m. onward, the relative humidity begins to evolve inversely with respect to the internal temperature: as Tint increases, RH decreases, reaching a maximum temperature of Tint = 30°C at 6:00 p.m. and a minimum relative humidity of RH = 15.5%. Figure 6.3.1(b) shows the comparison between the indoor Tint and outdoor Text air temperatures. Both quantities exhibit similar diurnal patterns, with a maximum of T = 41°C at 6:00 p.m. and a minimum of T = 15°C at 8:00 a.m. Figure 6.3.1(c) presents the evolution of the internal air temperature Tint along with the temperatures of the selected internal wall façades measured during the experiment. The temperature profiles of the walls follow the same general trend as Tint, with a minimum of TPFPI = 27.3°C recorded at the lower inner ceiling façade at 6:00 p.m. and a maximum of TPSI = 29.8°C at 10:00 p.m. on the inner south wall façade. A noticeable time lag of approximately Δt = 5 h is observed between the peak of the south wall inner façade temperature and the other temperatures TPNI, Tint and TPFPI. This lag is attributed to the thermal inertia of the building materials, their heat storage capacity, and delayed heat release. Figure 6.3.1(d) compares the external temperature Text with the temperatures of the internal wall façades selected for measurement. The peak temperature of the inner south wall façade OUDRANE A., AOUR B., BADA A. AND KHEIRI A. 65 Copyright ©2025 ASSA. Adv. in Systems Science and Appl. (2025) TPSI = 29.65°C occurs at 2:00 a.m., showing a time difference of Δt = 4 h relative to the other measured temperatures TPNI, Text and TPFPI. The minimum external temperature of Text = 16.3°C is recorded at 7:00 a.m. These observations highlight the significant role of material properties in inducing a time lag (Δt) between the internal south wall surface and other measured temperatures, reflecting the impact of thermal inertia and heat storage on the dynamic thermal response of the building. (a) (b) (c) (d) Fig. 6.3.1. Evolution of the thermal behavior of the element studied as a function of local time during the typical day May 1st, 2024. 6.4. Analysis of the Typical Day May 10th, 2024 Figure 6.4.1 illustrates the temporal evolution of the thermal behavior of the study site during a typical day, May 10th, 2024. Figure 6.4.1(a) presents the comparison between internal air temperature Tint and internal relative humidity (RH) as a function of local time. The results indicate an inverse relationship between Tint and RH throughout the day. Before noon, the minimum internal temperature of Tint = 30.6°C is observed at 8:00 a.m., while the relative humidity reaches a maximum of RH = 16.5%. In the afternoon, this trend reverses: Tint peaks at 32.9°C and RH reaches a minimum of 14.9% at 4:00 p.m., confirming the expected inverse correlation between internal temperature and relative humidity. Figure 6.4.1(b) compares the internal Tint and external Text air temperatures throughout the day. Both temperatures follow a similar diurnal trend, with a maximum of T = 46.5°C recorded at 4:00 p.m. and a minimum of T = 22°C at 8:00 a.m. A temperature difference of ΔT = 4°C 66 OUDRANE A., AOUR B., BADA A. AND KHEIRI A. Copyright ©2025 ASSA Adv. in Systems Science and Appl. (2025) is observed between Tint and Text between 11:00 p.m. and midnight, explaining the higher internal temperature relative to the external environment during this period. Figure 6.4.1(c) shows the comparison between the internal temperature Tint and the temperatures of the selected internal wall façades TPSI, TPFPI and TPNI over the day. A temperature difference of ΔT = 1.6°C is observed between the north wall inner façade TPNI, the roof inner façade TPFPI, and the internal air temperature Tint, indicating that the roof inner surface is hotter than the other façades in the afternoon. Additionally, the inner south wall façade reaches its peak temperature of TPSI = 33.6°C at 10:00 p.m., exhibiting a time lag of Δt = 6 h relative to the internal air temperature Tint, due to the thermal inertia of the southern wall. Figure 6.4.1(d) presents the comparison between external temperature Text and the selected internal wall temperatures TPSI, TPFPI and TPNI. The south wall inner façade shows higher temperatures with a clear time lag of Δt = 6 h relative to Text, TPNI and TFPI. The outdoor temperature peaks at Text = 45.7°C at 4:00 p.m., while the south wall inner surface reaches its maximum of TPSI = 33.6°C at 10:00 p.m. These observations highlight the influence of construction material properties, as the north wall and roof slab exhibit distinct thermal behavior compared to the south wall, due to differences in thermal inertia and heat storage capacity. (a) (b) (c) (d) Fig. 6.4. Evolution of the thermal behavior of the element studied as a function of local time during the typical day May 10th, 2024. 6.5. Examination of a Week During the Experience Period Figure 6.5.1 illustrates the evolution of the thermal behavior at the study site over a 7-day period, from May 1st to May 7th, 2024. Figure 6.5.1(a) presents the temporal variations of the OUDRANE A., AOUR B., BADA A. AND KHEIRI A. 67 Copyright ©2025 ASSA. Adv. in Systems Science and Appl. (2025) internal air temperature Tint, external air temperature Text, and internal relative humidity (RH) as a function of local time. During this period, the maximum external temperature gradually increased, starting from Text = 42.7°C on May 1st and reaching Text = 50°C on May 7th. In contrast, the internal air temperature remained relatively stable, ranging between Tint = 29°C and 33°C over the seven days. Meanwhile, the internal relative humidity exhibited a decreasing trend, from a maximum of RH = 16% on May 1st to RH = 13% by May 7th, reflecting the gradual increase in internal temperature. Figure 6.5.1(b) shows the comparison between the temperatures of the selected internal wall façades TPSI, TPFPI, TPNI and the external air temperature Text as a function of local time. The external temperature remains higher than the internal wall temperatures throughout the seven-day period. The north wall inner façade temperature remained relatively stable, between 23°C and 30°C, while the inner south wall and roof inner façade temperatures follow a similar trend, with a mean deviation of ΔT = 6°C. These observations highlight the influence of wall orientation and material thermal properties on the thermal response of the building envelope. (a) (b) Fig. 6.5.1. Evolution of temperature and relative humidity of the studied element during 7-days of experiment as a function of local time. 7. ANALYSIS AND INTERPRETATION OF COMPUTED THERMAL DATA 7.1. Effect of wall thickness on internal temperature variations Figure 6.6.1 presents the temporal evolution of the internal air temperature Tint of the workplace as a function of wall thickness over a full diurnal cycle, corresponding to the sun’s trajectory. The results demonstrate a clear inverse correlation between wall thickness and internal temperature, highlighting the thermal damping effect of increased wall mass. For a wall thickness of 0.15 m, the peak internal temperature reaches Tint, max = 41°C, whereas for 0.30 m, the peak decreases to Tint, max = 36°C. The observed temperature difference (ΔT = 5°C) is associated with an estimated temporal phase shift of Δt ≈ 1 h, indicating a delay in the thermal response of the internal environment due to the walls’ heat storage capacity and thermal inertia. This behavior is consistent with nodal modeling predictions, where each wall is represented as a discrete thermal node with capacitance proportional to its mass and conductance defined by its thermal properties. The phase shift and amplitude attenuation of internal temperature underscore the critical role of wall thickness in modulating diurnal thermal fluctuations and controlling indoor thermal comfort under high solar loading conditions. 68 OUDRANE A., AOUR B., BADA A. AND KHEIRI A. Copyright ©2025 ASSA Adv. in Systems Science and Appl. (2025) Fig. 6.6.1. Evolution in the temperature of the internal medium is a function of the evolution of the walls thickness. 7.2. Seasonal variation of the average external temperature in the year 2024 Figure 6.6.2 illustrates the annual evolution of the average outdoor temperature Text, avg in the Adrar region during 2024. The temperature profile exhibits a distinct pyramidal seasonal pattern, with extreme values observed during summer and winter. Peak summer temperatures reach or exceed 50°C, whereas winter minima range between 20°C and 22°C. Transitional seasons, spring and autumn, display intermediate average temperatures between 35°C and 40°C. Fig. 6.6.2. Seasonal variation in the average outdoor temperature on 2024 depending on the year months. These results confirm that the Adrar region is among the hottest regions globally, as evidenced by the extreme summer temperatures relative to other seasons. In nodal modeling of building envelopes, these external temperature variations serve as the primary driving forces for conduction, convection, and radiative exchanges, influencing both internal air temperatures and wall surface thermal responses. The extreme summer conditions further underscore the importance of accounting for thermal inertia, phase lag, and material-specific heat capacity in predicting internal thermal comfort and evaluating envelope performance. OUDRANE A., AOUR B., BADA A. AND KHEIRI A. 69 Copyright ©2025 ASSA. Adv. in Systems Science and Appl. (2025) 7.3. Seasonal variation in the average global solar flux during the year 2024 Figure 6.6.3 shows the seasonal evolution of average solar irradiance for the year 2024. The irradiance exhibits consistent peak values across all seasons, ranging from 1000 W·m⁻² to 11000 W·m⁻², with the maximum occurring in spring (11000 W·m⁻²). These observations highlight the significant seasonal influence of solar radiation on the thermal loading of building envelopes, which is a critical boundary condition for heat transfer simulations and nodal thermal modeling. The high solar loading during peak periods underscores the importance of accounting for material thermal inertia and facade orientation in predicting indoor thermal behavior. Fig. 6.6.3. Seasonal variation of the average solar flux in 2024 based on the year months. 8. CONCLUSION This study combined experimental measurements and numerical simulations to analyze the thermal behavior of a workplace in Adrar. Wall temperatures and indoor relative humidity were recorded in May 2024 using Testo devices. The developed mathematical model accurately reproduced the experimental results, with an average error below 4%, validating its reliability for predictive thermal simulations. Numerical analyses were extended to evaluate the influence of seasonal variations and material properties on internal temperatures over the entire year 2024. The main conclusions from this combined experimental and numerical study are as follows:  The average outdoor temperature at the workplace in May 2024 ranged between 40°C and 45°C.  The average internal temperature was maintained between 30°C and 35°C.  The average internal relative humidity during the same period was approximately 13%.  The temperature difference between the external environment and the interior surfaces of the workplace walls reached ≈6°C. These results indicate that the internal thermal conditions are significantly higher than the ideal thermal comfort range. This can be attributed to extreme solar loading, low ambient humidity, and the thermal properties of the envelope. As a future perspective, practical interventions are proposed to mitigate internal heat gains. Notably, the replacement of the existing air-gap insulation with locally available palm residue- based insulation is under investigation, aiming to enhance thermal damping and reduce peak internal temperatures under extreme climatic conditions. 70 OUDRANE A., AOUR B., BADA A. AND KHEIRI A. Copyright ©2025 ASSA Adv. in Systems Science and Appl. (2025) ACKNOWLEDGMENT We sincerely thank Professor Benaoumeur Aour, Head of the Laboratory of Applied Biomechanics and Biomaterials at the National Polytechnic School of Oran, for his guidance and thorough review of this project. Our gratitude also extends to Professor Hamouda Messaoud, Head of the Laboratory for Sustainable Development and Informatics (LDDI) at Adrar University, for his support in providing climate data for the Adrar region. We are furthermore grateful to the Algerian Directorate-General for Research and Technological Development (DGRST) for their encouragement and support throughout this research. REFERENCES 1. Lalanne, N., Krapez, J., Niliot, C. & Briottet, X. (2013) Modeling of thermal behavior and high-resolution infrared rendering of external surfaces of an urban fragment and thermal bridges of buildings, Proc. of French Thermal Congress (Gérardmer, France). 2. Leschok, M., et al. (2024) Thermal and manufacturing properties of hollow-core 3D-printed elements for lightweight facades, Developments in the Built Environment, 19, 100485. doi: 10.1016/j.dibe.2024.100485. 3. Zhou, H., Puttige, A. R., Nair, G. & Olofsson, T. (2024) Thermal behaviour of a gypsum board incorporated with phase change materials, Journal of Building Engineering, 94, 109928. doi: 10.1016/j.jobe.2024.109928. 4. Oudrane, A. & Aour, B. (2017) Numerical Simulation of Heat Exchanges for a Desert House Type Adrar, AEF, 24, 63–75. doi: 10.4028/www.scientific.net/aef.24.63. 5. Kumaraswamy, J., Vijay Praveen, P.M., Hassan A.H., Alzahrani, S., Sharma, V., et al. (2024) Experimental investigation of heat transfer rate for building roof with corrugated sheets using phase change material (PCM), Case Studies in Thermal Engineering, 59, 104508. doi: 10.1016/j.csite.2024.104508. 6. Kaoutari, T. & Louahlia, H. (2024) Experimental and numerical investigations on the thermal and moisture transfer in green dual layer wall for building, Case Studies in Thermal Engineering, 53, 103946. doi: 10.1016/j.csite.2023.103946. 7. Gori, V., Johnston, D., Bouchié, R. & Stamp, S. (2023) Characterisation and analysis of uncertainties in building heat transfer estimates from co-heating tests, Energy & Buildings, 295, 113265. doi: 10.1016/j.enbuild.2023.113265. 8. Belatrache, D., Bentouba, S., Zioui, N. & Bourouis, M. (2023) Energy efficiency and thermal comfort of buildings in arid climates employing insulating material produced from date palm waste matter, Energy, 283, 128453. doi: 10.1016/j.energy.2023.128453. 9. Laidi, S., El Hassar, S. M. K., Mahrane, A. & Sellami, R. (2024) Study and modeling of the thermal behavior of buildings with attic roof in the Algerian climate context, International Journal of Sustainable Building Technology and Urban Development, 3–22. doi: 10.22712/susb.20240002. 10. Jiang, B., Lua, R., Jiang, M., Wang, L., Chun, L., et al. (2024) Experimental study on thermal and humidity properties of modified rammed earth buildings in winter, Building and Environment, 258, 111583. doi: 10.1016/j.buildenv.2024.111583. 11. Hou, C., Hu, W., Jiang, Y. F. & Gao, W. (2024) Optimization and Renovation Design of Indoor Thermal Environment in Traditional Houses in Northeast Sichuan (China) —A Case Study of a Three-Section Courtyard House, Sustainability, 16, 2921, doi: 10.3390/su16072921. OUDRANE A., AOUR B., BADA A. AND KHEIRI A. 71 Copyright ©2025 ASSA. Adv. in Systems Science and Appl. (2025) 12. Al-Yasiri, Q. & Szabob, M. (2023) Hourly analysis of temperature and heat gain reduction for building envelope-compacted phase change material in extremely hot conditions, Journal of Energy Storage, 68, 107838, doi: 10.1016/j.est.2023.107838. 13. Yadeta, C., Indraganti, M., Tucho, G. T. & Alemayehu, E. (2023) Study on adaptive thermal comfort model and behavioral adaptation in naturally ventilated residential buildings, Jimma Town, Ethiopia, Energy & Buildings, 298, 113483. doi: 10.1016/j.enbuild.2023.113483. 14. Guo, Y., Tang, H., Gao, Y., Wang, Y., Meng, X., et al. (2023) Thermal comfort and adaptive behaviors in office buildings: A pilot study in Turpan (China) during summer, Heliyon 9, e20646. doi: 10.1016/j.heliyon.2023.e20646. 15. Energie Plus (2024), [Online]. Available: https://energieplus- lesite.be/donnees/enveloppe44/enveloppe2/conductivite-thermique-des- materiaux/#Les_metaux 16. Cerezo, V. (2005). Mechanical, thermal and acoustic properties of a material based on plant particles: experimental approach and theoretical modeling. Ph.D. Thesis, National Institute of Applied Sciences of Lyon. 17. Bendahir, F. & Elfodda, K. (2017). Master's thesis, University of Adrar. 18. TAHITI Polynésie (2023) Application sheet for energy regulations for buildings in French Polynesia, [Online]. Available: https://www.developmentaid.org/donors/view/190456/energy-and-mining-service-french- polynesia-service-de-lenergie-et-des-mines-tahiti. 19. Loumani, A., Tahri, A., Mediani, A., Larbi, A., Braham, C. W., et al. (2022) Assessment Biodiversity of Medicinal Plants Used in Treatments for Native People in Adrar, Algeria, International Journal of Design & Nature and Eco-dynamics, 17(3), 469–473. doi: 10.18280/ijdne.170319. 20. Mediani, A., Moungar, H., Larbi, A., Loumani, A., Chaouch, W.B., et al. (2019) The isothermal sorption measurement and the isosteric heats determinations for the South Algerian date varieties, Instrumentation Mesure Métrologie, 18(4), 389–396. doi: 10.18280/i2m.180408. 21. Semmani, I., Elaloui, F. & Loumani, A. (2021) Microbiological and physicochemical assessment of mentha pulegium before and after solar drying, [Online]. Available: https://dspace.univadrar.edu.dz/jspui/handle/123456789/6127. 22. Danoune, M. B., Djafour, A., Hamouda, M., Degla, A., Gougui, A., et al. (2023) A Technical and Economical Assessment of Hydrogen Production Potential from Solar Energy in Adrar, Algeria, Proc. of the second International Conference on Energy Transition and Security (Adrar, Algeria). doi: 10.1109/ICETS60996.2023.10410685. 23. Benmedjahed, M., Dahbi, A., Hadidi, A. & Mouhadjer, S. (2021) Temperature and Wind Distribution Effects on Wind Energy Production in Adrar Region (Southern Algeria), International Journal of Sustainable Development and Planning, 16(8), 1473–1477. doi: 10.18280/ijsdp.160808. 24. Peel, M. C., Finlayson, B. L. & McMahon, T. A. (2007). Updated world map of the Köppen-Geiger climate classification, Hydrology and Earth System Sciences Discussions, 4(2), 439–473. doi: 10.5194/hess11-1633-2007. 25. Climates for traveling. Global Climate Guide, [Online]. Available: https://www.climatestotravel.com/info/contact 72 OUDRANE A., AOUR B., BADA A. AND KHEIRI A. Copyright ©2025 ASSA Adv. in Systems Science and Appl. (2025) 26. Bouitna, M. (2014). Study of the contribution of phase change materials for passive air conditioning. Master's Thesis, University of Blida in Algeria. 27. Morel N. & Gnansounou, E. (2007). Building energy. New edition of the course previously given by Claude-Alain Roulet and Arnaud Dauriat. Lausanne, France: Federal Institute of Technology in Lausanne. 28. Penu, G. (2013) Building thermal. Dunod. Paris, France: Dunod. 29. Boukli, M. A. H., Amara, S. & Chabane, N. E. S. (2011) Thermal requirements and temperatures evolution in an ecological house, Energy Procedia, 6, 1–5. doi: 10.1016/j.egypro.2011.05.013. 30. Katunsky, D., Katunskà, J., Dolnikovà, E., et al. (2024) Preserving the historical value and thermal properties of renovated. buildings: The case of reconstructed town houses in Kosice, Slovakia, Frontiers of Architectural Research, 13(1). doi: 10.1016/j.foar.2024.04.007. 31. Lin, Y. J., et al. (2013) Design of a sustainable planting module for extensive green roofs in tropical climate, Advanced Materials Research, 650, 677–680. doi: 10.4028/www.scientific.net/amr.650.677. 32. Saikrishnan, V., Jagadeesh, P. & Jayasuriyaa, K. (2015) Experimental investigation of solar paraffin wax melting unit integrated with phase change heat energy storage by using phase change material, AMM, 766–767, 451–456. doi: 10.4028/www.scientific.net/amm.766- 767.451. 33. Oudrane, A. & Aour., B. (2019) Study and characterization of thermal comfort in a desert climate, Adv. Syst. Sci. Appl., 19(2), 63–79. 34. Ding, K., Calautit, J. K. & Jimenez-Bescos, C. (2024) Significance of external wind conditions on the convective heat transfer coefficients (CHTC) and energy performance in multi-zone high-rise buildings, Energy & Buildings, 320, 114570. doi: 10.1016/j.enbuild.2024.114570. 35. Oudrane, A., Aour, B., Hamouda, M., Mokretar, S. El & Benhamou, M. (2018) Thermal exchanges of the walls of a habitable environment: study and analysis, Renewable Energy Review, 21(2), 231–245. doi: 10.54966/jreen. v21i2.685. 36. Oudrane, A. (2018) Contribution to modeling and development of heating systems solar for individual use. Ph.D. Thesis, Oran Polytechnic School (ENPO-MA). 37. Ravello, B., Rajaoarisoab, L. & Maurice, O. (2020) Thermal modelling of multilayer walls for building retrofitting applications, Journal of Building Engineering, 29, 101126. doi: 10.1016/j.jobe.2019.101126. 38. Zhakatayev, T., Kakimovab, K., Taukenovaa, L. & Serikovc, T. (2022) Simulation and calculation of heat transfer in multilayer wall structures based on iterative models, Journal of Siberian Federal University. Engineering & Technologies, 15(5), 622–633. doi: 10.17516/1999-494X-0410. 39. Tamene, B. Y., Abboudi, S. & Bougriou, C. (2014) Numerical and economical study of thermal insulation in multi-layer wall exposed to real climatic conditions, Athens Journal of Technology Engineering, 1(2). 40. Herrando, M., Markides, C. N. & Hellgardt, K. (2014) A UK-based assessment of hybrid PV and solar-thermal systems for domestic heating and power: System performance, Applied Energy, 122, 288–309. doi: 10.1016/j.apenergy.2014.01.061. 41. Rahiminejad, M. & Khovalyg, D. (2022) Numerical and experimental study of the dynamic thermal resistance of ventilated air spaces behind passive and active facades, Building and Environment, 225, 109616. doi: 10.1016/j.buildenv.2022.109616. OUDRANE A., AOUR B., BADA A. AND KHEIRI A. 73 Copyright ©2025 ASSA. Adv. in Systems Science and Appl. (2025) 42. Charmantray, C. (2020) Transversalization of a nodal model of thermal behavior of a Diesel at low temperature in transient regime. MEGA Doctoral School Thesis, Central School of Lyon. 43. Kim, S., Joo, H. G. & Lee, H. C. (2024) Nodal method for handling irregularly deformed geometries in hexagonal lattice cores, Nuclear Engineering and Technology, 56, 772–784. doi: 10.1016/j.net.2023.07.021. 44. Derakhtenjani, A. S., Candanedo, J. A., Chen, Y., Dehkordi, V. R. & Athienitis, A. K. (2015) Modeling approaches for the characterization of building thermal dynamics and model- based control: A case study, Science and Technology for the Built Environment, 21, 824–836. doi: 10.1080/23744731.2015.1057060. 45. Oudrane, A., Aour, B. & Hmouda, M. (2022) The implementation of numerical codes for the analysis of solar flux inputs and the optimization of thermal comfort for a Monobloc habitat, European Journal of Computational Mechanics, 31(2), 155–196. doi: 10.13052/ejcm2642- 2085.3121. 46. Liu, W., Liu, X., Chow, T., Hao, Y., Lau, W., et al. (2024) Thermal characteristics of heat- pipe-ring embedded building facades as both building-integrated and building-attached solar collectors, Case Studies in Thermal Engineering, 60, 104621. doi: 10.1016/j.csite.2024.104621. 47. Kaoutari, T. & Louahlia, H. (2024) Experimental and numerical investigations on the thermal and moisture transfer in green dual layer wall for building, Case Studies in Thermal Engineering, 53, 103946. doi: 10.1016/j.csite.2023.103946.