Thermal and Surface Radiosity Analysis of an Underfloor Heating

energies

Article Thermal and Surface Radiosity Analysis of an Underﬂoor Heating System in a Bioclimatic Habitat

Abdelkader Laafer 1 , Djaffar Semmar 1, Abdelkader Hamid 1 and Mahmoud Bourouis 2,*

1 LSTM Laboratory, Department of Renewable Energy, Faculty of Technology, University of Blida 1, Soumâa Street No. 270, 09130 Blida, Algeria; [email protected] (A.L.); [email protected] (D.S.); [email protected] (A.H.) 2 Department of Mechanical Engineering, Universitat Rovira i Virgili, Av. Països Catalans No. 26, 43007 Tarragona, Spain * Correspondence: [email protected]

Abstract: This paper addresses the modeling of convective and radiative heat transfer to achieve an acceptable level of indoor temperature. The results presented were obtained in a pilot project in which an energy-efficient house was built on a site located west of Algiers. The main objective was to perform a numerical simulation to investigate how the temperature of the heat-transfer fluid circulating in the floor heating system affected the temperature of the indoor air and also how surface radiosity affected the temperature profile of the indoor air. The study employed the finite element method integrated into the Comsol Multiphysics software. The model was validated using experimental data reported in the literature for the pilothouse at the same meteorological conditions. An error of about 2.32% was apparent between the experimental and theoretical results. Results ◦ showed that the increase of the heating transfer fluid temperature from 30 to 50 C produced the same temperature of about 15.1 ◦C taken at a 50 cm height inside the room. The air temperature

Citation: Laafer, A.; Semmar, D.; remained stable, with an insignificant variation after 72 h of heating. Surface radiosity increased −2 Hamid, A.; Bourouis, M. Thermal and as a function of time and reached an almost constant value of 380 W·m after 72 h because of the Surface Radiosity Analysis of an stability of the air temperature by convection. Underfloor Heating System in a Bioclimatic Habitat. Energies 2021, 14, Keywords: underfloor heating; surface radiosity; thermal comfort; bioclimatic habitat; solar energy; 3880. https://doi.org/10.3390/ energy efficiency; Comsol Multiphysics en14133880

Academic Editor: Andrea Frazzica 1. Introduction Received: 31 May 2021 Extensive studies have been carried out to reduce energy consumption in heating and Accepted: 24 June 2021 Published: 28 June 2021 cooling systems. This reduction can be obtained through ventilation, heat sinks, insulation improvement, the use of solar panels, and the use of energy-efﬁcient appliances.

Publisher’s Note: MDPI stays neutral Energy efficiency and the integration of renewable energy to reduce energy con- with regard to jurisdictional claims in sumption in buildings have produced a new generation of buildings called zero energy published maps and institutional affil- balance (ZEB). Ferrante and Cascella [1] reported that high-performing and zero-energy- iations. balance buildings cannot be achieved by technology alone but are possible using integrated designs that combine passive tools, such as high-thermal mass brick-wall structures, high- reflective materials, solar shading devices, and ventilation strategies, with solar and wind energy microgeneration. Investigations reported in the literature showed that zero energy balance and zero Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. local CO2 emission residences are highly feasible if built in areas benefiting from the This article is an open access article Mediterranean climate [1]. They can be achieved by applying energy-efficient solutions distributed under the terms and that, at the same time, use local materials and traditional construction processes. The result conditions of the Creative Commons is high-quality performance buildings, located within recognizably urban environments. Attribution (CC BY) license (https:// Renewable energy is widely used to provide comfortable and healthy environments. creativecommons.org/licenses/by/ Experimental investigations are useful for standardized methodologies [2,3]. Floor radi- 4.0/). ation, in particular, is used for heating and cooling applications. In recent years, several

Energies 2021, 14, 3880. https://doi.org/10.3390/en14133880 https://www.mdpi.com/journal/energies Energies 2021, 14, 3880 2 of 17

researchers have investigated radiant floor heating/cooling systems. These studies have demonstrated that a lower temperature of the floor surface is sufficient to ensure thermal comfort and that the temperature limit would be the dew point in the area in question. Spaces such as atriums and lobbies often have glass facades; thus, a huge amount of sunlight is directed at the floor [4]. Zhai et al. [2] investigated the green building at the Shanghai Science Research Institute, in which 150 m2 of tubular evacuated solar collectors had been installed to generate heat for the floor heating system. The authors reported that the ratio of greenhouse gas emissions from the heating area was about 1/3 in cold weather. Temperature control feedback was then used to measure the internal load changes. The effectiveness of the proposed system, in which the indoor thermal environment was set and controlled at acceptable conditions for comfort, was demonstrated by a laboratory test and Transient Systems Simulation Program (TRNSYS) simulation [5,6]. Applying a radiant floor cooling system would help prevent condensation from occurring on the floor surface in hot and humid weather. It is necessary to assess whether a floor influences the thermal comfort of the occupants. Lim et al. [7] reported that the effect of condensation on the floor surface depends on the control or the composed control system used in the absence of a drying system. This may affect the cost of construction in the area subject to environmental assessment. In order to choose the appropriate floor surface temperature range and material, several investigations were carried out focusing on human body physiological responses, including the instance of the buttocks in contact with the flooring materials used in the ONDOL floor heating system [8]. Other researchers have investigated the radiant floor heat transfer process using analytical solutions. Yu et al. [9] presented an analytical solution using a hydronic radiant modification to enhance the thermal performance of thermally activated building systems (TABS), and it is highly recommended. Monte [10] studied the transient response of one- dimensional multilayered composite conducting slabs to a sudden temperature variation in the surrounding fluid. The author applied the method of variable separation using the partial differential equation of heat conduction to describe the thermal field of layers and set the heat exchange between the composite slab and the surrounding fluid. Lu and Tervola [11] proposed a new analytical approach of heat conduction in a composite slab subject to periodic temperature changes. Explicit solutions provided in- sights into the interaction between amplitude decay, time shifts, and signal amplitude. Beck et al. [12] carried out a research study that focused on solutions for the partial heating of rectangular solids using the time partitioning method, and it provided verification and precision features that were more than satisfactory. Tests were carried out to establish the impact of direct solar radiation and the change in the air that was brought about by the fan and rug. The cooling capacity of the test was then assessed. The findings showed that the floor cooling potential is at direct solar radiation between 32 and 110 W·m−2. The maximum surface temperature was 26 ◦C on the part of the floor that was not exposed to solar radiation. The analysis was limited because the amount of solar radiation that affected the floor was low in that season of the year [13]. To achieve more practical findings valid for an underfloor heating system for winter conditions, Acikgoz et al. [14] employed the sidewalls of an experimental chamber. As a matter of fact, radiant floor cooling systems remove heat from the system via convection and long or shortwave radiations. In doing so, these systems control the environment. Shortwave radiation heat transfer is brought about by direct sunlight-based radiation, whereas longwave radiation heat transfer is brought about by inside heat sources in buildings, particularly walls. Even though the impact of direct solar radiation on radiant floor cooling loads has been studied mathematically and experimentally, the impact of internal wall surface temperatures on cooling loads in different wall configurations has not been thoroughly covered [15]. Zhao et al. [16] reported that the interior wall surface temperatures of various nontransparent constructions would surpass 28–35 ◦C because of the solar radiation on the walls. This demonstrates how radiant floor cooling loads are affected by the impact of wall surface temperatures. Energies 2021, 14, 3880 3 of 17

Laouadi [17] developed a two-dimensional model for radiant system prediction to pre- cisely estimate the circuit tubing–concrete contact surface temperature needed to compute the thermal capacity and the ceiling/floor temperatures for moisture condensation, thermal comfort, and controls. Weber and Johannesson [18] used a simplified star network and a triangular network to describe heat transfer in thermally activated building constructions. Heat transfer within the radiant medium was solved using one-dimensional numerical modeling already integrated into the energy simulation Comsol Multiphysics® software, and a two-dimensional analytical solution was developed and integrated into the software. Other numerical and experimental investigations were focused on analyzing the characteristics of the floor temperature gradient. Holopainen et al. [19] simulated floor heating simulation using an uneven nodal network with the finite-difference heat balance method. The authors showed the benefits of placing the densest grids on the steepest curves of the temperature gradient. As far as energy consumption is concerned, thermal comfort can be obtained through radiant cooling systems rather than the traditional AC system. Top-hung windows are widely used in metropolitan structures in Australia and Indonesia. In Australia, it has been recorded that a small top-hung window can be valuable for accomplishing warm solace by diminishing the effect of outside air [20]. Sattari and Farhanieh [21] carried out a sensitivity analysis to clarify the influence of the design parameters on a floor heating system. For this purpose, a finite element model was built for a typical room equipped with the aforementioned heating system. Transient conduction, convection, and radiation mechanisms of heat transfer were taken into account in the analysis. It was observed that the design parameters had different effects on the performance of the radiant heating system. It is worth noting that the floor cover composition and thickness were the most significant parameters affecting the heating system. Zhai et al. [2] reported that the floor surface temperature is the parameter that most affects the heating/cooling capacity of radiant systems in a subtropical humid climate in Shanghai. In addition, considering comfort and air condensation, the floor surface temperature of a radiant floor system should be kept within certain temperature ranges during heating or cooling. The floor surface temperature should not be lower than 19 ◦C in summer, while it should not exceed 29 ◦C in the winter season. Therefore, floor surface temperature is the most important parameter in the design and energy assessment of radiant floor systems. Radiant heating systems provide a thermal atmosphere that is more beneficial than convective heating systems. There are several research speculations that have recognized the significance of producing better thermal comfort [22]. According to Li [23], ventilation by layers improved the quality of indoor air, thermal productivity, and thermal comfort. More importantly, Lin et al. [24] found no significant distinction in the general thermal sensation between convective and radiant heating systems, regardless of the fact that the air flow was higher in the space warmed by the convective heating system. Hu et al. [25] examined the temperature dispersion of a floor heating (FH) system, a radiator, and a fan coil unit operating continuously. The results revealed that even though the thermal environment of the FH system was the most satisfying, still, no significant variation in thermal comfort was observed between the different terminals. A pilot project by the name of “Mediterranean Energy Efficiency in the Construction Sector (Med-Enec)” was carried out by a consortium formed by the National Center for Integrated Building Studies and Research (EPST/CNERIB) and the Renewable Energy Development Centre (EPST/CDER) of Algeria. This project was carried out within the framework of the energy efficiency application in industrial construction and energy saving in buildings [26]. Imessad et al. [27] conducted a study on a pilothouse, built for the Med- Enec project, to evaluate the impact of thermal masses of eave and night ventilation to cover the energy demand for cooling. The authors concluded that the energy demand for cooling was more affected by thermal transmittance values than by the envelope thermal Energies 2021, 14, x FOR PEER REVIEW 4 of 17

buildings [26]. Imessad et al. [27] conducted a study on a pilothouse, built for the Med- Enec project, to evaluate the impact of thermal masses of eave and night ventilation to Energies 2021, 14, 3880 cover the energy demand for cooling. The authors concluded that the energy demand4 of for 17 cooling was more affected by thermal transmittance values than by the envelope thermal mass. A guideline was proposed and recommended for the optimum overhang length for mass.south-facing A guideline windows. was I proposedt was found and that recommended the combination for theof both optimum natural overhang ventilation length and forhorizontal south-facing shading windows. devices Itimproved was found thermal that the comfort combination for occupants of both and natural significantly ventilation re- andduced horizontal the energy shading demand devices for cooling. improved thermal comfort for occupants and significantly reducedThis the paper energy investigates demand the for influence cooling. that surface radiosity in underfloor heating sys- temsThis exerts paper on thermal investigates comfort the in influence buildings. that An surface analysis radiosity is made inof underfloorthe individual heating and systemscombined exerts effects on on thermal thermal comfort comfort in buildings.of surface radiosity An analysis and is the made natural of the convection individual of and air combinedflow inside effects the rooms. on thermal The behavior comfort of of surface surface radiosity radiosity and in thebuildings natural is convection analyzed ofas aira function flow inside of time. the rooms.Therefore, The a behavior theoretical of surfacestudy of radiosity a floor heating in buildings system is in analyzed a pilothouse as a functionwas carried of time.out and Therefore, validated a theoretical with experimental study of adata floor from heating a pilot system project in areported pilothouse by wasBenouali carried et al. out [2 and8] and validated Derradji with et al.experimental [29]. data from a pilot project reported by Benouali et al. [28] and Derradji et al. [29]. 2. Description of the Pilothouse 2. Description of the Pilothouse The subject of this research, presented in Figure 1, is a rural prototype house, located The subject of this research, presented in Figure1, is a rural prototype house, located west of Algiers in Souidania. The geographical coordinates are 36°707′ latitude, 2°914′ lon- west of Algiers in Souidania. The geographical coordinates are 36◦7070 latitude, 2◦9140 gitude, and 137 m altitude. The surface and volume of the pilothouse are about 80 m2 and longitude, and 137 m altitude. The surface and volume of the pilothouse are about 80 m2 240 m3, respectively. The house was designed, taking into account certain bioclimatic ar- and 240 m3, respectively. The house was designed, taking into account certain bioclimatic chitecture principles, discussed in Sections 2.1–2.6, and was considered to be highly effi- architecture principles, discussed in Sections 2.1–2.6 and was considered to be highly cient [28]. Figure 2 below shows a picture of the built-up pilothouse. efficient [28]. Figure2 below shows a picture of the built-up pilothouse.

Figure 1. Architectural plan of the pilothouse. Figure 1. Architectural plan of the pilothouse.

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Figure 2. Orientation of the pilothouse.Figure 2. Orientation of the pilothouse.

2.1. Construction2.1. Materials Construction Materials The house wallsThe were house constructed walls were using constructed stabilized using earth stabilized concrete earth (BTS). concrete BTS brick(BTS). BTS brick is is an ecologicalan building ecological material building with material excellent with moisture excellent control, moisture a long control, lifetime, a long good lifetime, good in- insulation characteristics,sulation characteristics, excellent acoustic excellent qualities, acoustic and qualities, an interesting and an interesting thermal storage thermal storage ca- capacity. To increasepacity. the To useful increase life the of theuseful BTS life bricks, of the a stabilizerBTS bricks, (cement) a stabili waszer added(cement) with was added with a quantity volumea quantity ranging volume from 3% ranging to 6%. from This 3% is an to environmentally6%. This is an environmentally sensible alternative sensible alternative to conventionalto materials. conventional materials.

2.2. Insulation 2.2. Insulation −3 The BTS wall density is about 1700 kg·m . The heat− transfer3 coefficient (K ) is The BTS wall density is about 1700 kg·m . The heat transfer coefficientwall (Kwall) is 3.6 −2 −1 −2 −1 3.6 W·m ·K Wwhen·m −2·K the−1 when wall the thickness wall thickness is 14 cm is 14 and cm 2.54 and W2.54·m W·m·K−2·K −in1 in the the case case ofof 29 cm [30]. In 29 cm [30]. In thethe case case of of the the present present study, study, additional additional insulation insulation was was required required in thein the walls. walls. This was This was carriedcarried out as out follows: as follows: • In the external walls,In the external an intermediate walls, an layer intermediate of 9 cm expanded layer of 9 polystyrenecm expanded was polystyrene used, was used, and a 1 mm thickand layer a 1 mm of polyethylene thick layer of film polyethylene was added film as awas vapor added barrier. as a vapor barrier. • The ceilingwas The well ceiling insulated was withwell 16insulated cm of expanded with 16 cm polystyrene, of expanded and polystyrene a 1 mm layer, and a 1 mm layer of polyethyleneof film polyethylene was added film for protectionwas added againstfor protection moisture against diffusion. moisture diffusion. • The floor was insulatedThe floor withwas 6insulated cm of extruded with 6 cm polystyrene of extruded (XPS). polystyrene (XPS). • The characteristics The ofcharacteristics the material of used the inmaterial each wall used of in the each pilothouse wall of the are pilothouse collected in are collected in Table1. Table 1.

Table 1. ConstitutionTable and 1. Constitution thermal properties and thermal of the properties different walls of the in different the pilothouse walls in [31 the]. pilothouse [31].

−1 −1 −2 −1 CompositionComposition Thickness (m) Thicknessλ (W (m)·m ·K λ) (W·m −1K·K wall−1) (W·m ·Kwall) (W·m −2·K −1) SEB (BTS) EPSSEB (BTS) EPS 0.14 0.14 1.3 1.3 External wall External wallXPS XPS 0.090.09 0.04 0.04 0.36 0.36 SEBSEB 0.290.29 1.3 1.3 ConcreteConcrete 0.05 0.05 1.75 1.75 XPSXPS 0.060.06 0.04 0.04 Floor Concrete 0.15 1.75 0.54 FloorMortar + sandConcrete 0.03 0.15 1.15 1.75 0.54 TilingMortar + sand 0.02 0.03 1.7 1.15 MortarTiling 0.030.02 1.6 1.7 EPSMortar 0.160.03 0.04 1.6 Ceiling 0.23 ConcreteEPS 0.080.16 1.75 0.04 Ceiling Plaster 0.04 0.35 0.23 Concrete 0.08 1.75 Plaster 0.04 0.35

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2.3. Orientation The orientation of the building was designed to take advantage of active and passive solar strategies. It also facilitated temperature moderation and the use of natural daylight. As shown in Figure2 and Table2, the house façade, which contains Zone 1 (Room 1) and Zone 2 (Room 2), was oriented to the south. The north is the coldest wall in the pilothouse; it conﬁnes a bathroom, a kitchen, and one wall in Zone 3 (living room). This conﬁguration minimizes heat losses. West and east walls prevent overheating by the absence of openings on the west side and exploit the summer winds on the north-east side for cooling.

Table 2. Composition of the different façades.

Façade Composition Dimension Room 1 Window 126 × 140 mm Room 2 Window 170 × 140 mm Living Room Patio Door 141 × 220 mm

2.4. Windows Windows and frames usually represent the “weakest point” in an energy-efficient building. Selecting appropriate windows can optimize the combination of natural lighting, ventilation, noise control, and security. Windows in the pilothouse were double-glazed with polyvinyl chloride (PVC) frames, as it has better insulating properties than aluminum. The characteristics of the windows are: −2 −1 • Heat transfer coefficient of the glazing, Kg = 1 W·m ·K ; −2 −1 • Heat transfer coefficient of the frame, Kf = 1.2 W·m ·K ; −2 −1 • Heat transfer coefficient of all window elements, Kw = 1.2 W·m ·K . The frame occupied 20% of the total window area [31].

2.5. Thermal Bridges Thermal bridges are discontinuities in any thermal barrier. They are more pronounced when the material creating the bridge is high thermal conductive. To minimize heat loss and limit the risk of condensation, Algerian DTR standards recommend choosing appropriate materials so as to guarantee that the thermal bridge is estimated lower than 20% of thermal transmittance losses [31].

2.6. Natural Cooling Because the pilothouse is located on a site with a moderate climate, the use of natural ventilation, which is a passive cooling technique, can afford signiﬁcant potential for energy savings. The natural ventilation system was ensured by openable windows to supply outdoor air at night. In addition, there are awnings on the windows, which help to block out the sun’s rays in summer.

2.7. Solar Heating System (Combisystem) Combisystems are solar heating systems that provide heat for both domestic hot water (DHW) and space heating (SH). The combisystem installed in the pilothouse was designed for a single family. The room heating was provided by radiant floor heating (RFH). This system is an efficient way to achieve thermal comfort in buildings and boasts low energy consumption. The heating system included 8 m2 of solar thermal collectors located on the house roof and oriented south at a slope of 45◦. The collector tilt angle was oriented higher than the latitude of 36◦ 7070 at Souidania as the system is mainly intended for heating in winter. The storage capacity ensuring the distribution of hot water was 300 L. The proper functioning of the combisystem was supplied by a differential bypass valve connected to the radiant floor. EnergiesEnergies 2021 2021, ,14 14, ,x x FOR FOR PEER PEER REVIEW REVIEW 77 of of 17 17 Energies 2021, 14, 3880 7 of 17

TheThe rradiantradiantadiant floorfloorfloor heatingheating (RFH)(RFH) consistedconsisted ofof aa floorfloorfloor slabslab embeddedembedded withwith serpentinesserpentineerpentine tubestubestubes supplied suppliedsupplied with withwith hot hot water water by by aa circulatingcirculating pumppump andand distributiondistributiondistribution piping.piping. The The floor floorfloor heatingheating coil coil pipes pipes were were made made of of high high-qualityhigh--qualityquality cross-linkedccrossross--linkedlinked polyethylenepolyethylene (PEX) (PEX) for: for: • Flexibility:Flexibility: they they can can bend bend into into a a wide wide radius radius turn turn if if space space permits. permits. • DirectDirect r routingroutingouting of of pipes:pipespipes: :lower lower material material cost; cost; easier easier installation. installation. • AbilityAbility to to merge merge new new PEX PEX withwith existingexisting coppercopper andand PVCPVC systems.systems. • EnvironmentalEnvironmental benefits: benefits:benefits: PEX PEX is is more more environmentallyenvironmentally friendlyfriendly thanthan copper.copper. • LongevityLongevity and and inflammability inflammabilityinflammability propertiesproperties ofof thethe installation.installation. TheThe PEX PEXPEX used used in in the the pilothouse pilothouse has has has a a athermal thermal thermal conductivity conductivity conductivity of of of λλ λ= = =0.43 0.43 0.43 W W W·m·m·−1m−1·K·K−−11−1· Kand and−1 aanda diameterdiameter a diameter ofof ΦΦ of == Φ 1616= mm.mm. 16 mm. DistributionDistribution Distribution pipingpiping piping waswas was assembledassembled assembled inin aa in looploop a loop inin each ineach each zonezone zone toto achievetoachieve achieve the the the desired desired desired thermal thermal thermal comfort. comfort. comfort. Figure Figure Figure 3 3 3 shows showsshows that that the the piping piping piping is is attached attached to to to a a a wweldedweldedelded steel steel mesh mesh with with an an insulationinsulation thicknessthickness ofof 66 cmcm ofof extrudedeextrudedxtruded polystyrene.polystyrene.

FigureFigure 3. 3. Floor FloorFloor piping pipingpiping presentation presentationpresentation in in Z ZoneZoneone 1 1 (living (living room). room).

PipesPipes were were placed placed at at a a distance distance of of 15 15 cm cm between betweenbetween each each other other near near to to the the external external walls walls andand then then increased increased up up to to 30 30 cm cm towards towards thethe ﬂoorfloorfloor centercenter toto preventprevent more more thermalthermal thermal losses.losses. losses. TheThe piping piping system system was was embedded embedded in in approximately approximately 26 26 cm cm of of concrete concrete slabslab toto setset thethe temperaturetemperaturetemperature gradientgradient up up of of the the room. room. The The 2626 cm cmcm depth depthdepth ensures ensuresensures the the RFH RFHRFH storage storagestorage and and phase phase functionsfunctionsfunctions essential essential for for hi highhighgh solar solar productivity productivity andand thermalthermal comfort.comfort. TheThe heated heatedheated zones zones are: are: ZZ Zoneoneone 1,1, ZZ Zoneoneone 2,2, 2, andand and ZZ Zoneoneone 3.3. 3. AsAs As shownshown shown inin in FigureFigure Figure 4,4,4 , therethere there isis is aa distributionadistribution distribution ofof of pipingpiping piping underunder under thethe the surfacesurface surface ofof allofall allthethe the floorfloor ﬂoor zones.zones. zones. ThisThis This arrangementarrangement arrangement waswas was de-de- signeddesignedsigned to to ensure toensure ensure a a uniform uniform a uniform distribution distribution distribution of of ofthe the the temperature temperature temperature [3 [30 [0].30]. ].

FigureFigure 4. 4. Schematic SchematicSchematic diagram diagramdiagram of ofof the the solar solar system. system.

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2.8. Operation Principle The amount of energy provided by the sun varies according to the location, the time of day, and the climatic conditions. The solar potential of Souidania (Algiers region) covers the energy requirement for heating in the winter season [32]. According to the installation diagram, presented in Figure4, solar collectors cover an area of 8 m 2 oriented towards the south with a 45◦ inclination (optimum angle for heating) [33]. These solar collectors are connected in a parallel arrangement in order to increase the flow rate, as the system is required to cover the need for space and hot water heating simultaneously. The operating principle is described as follows: Heat produced by solar collectors (1) is distributed to the tank (3) or to the serpentine tubes in the floor slab (4) through the thermal fluid. This operation is ensured by a circulating pump (2). The pump will be activated only if the solar collector hot temperature outlet reaches a certain temperature level (35 ◦C). Priority is given to DHW when the top tank temperature reaches the set point of 55 ◦C; the three-way valve (5) is switched on to supply the serpentine in the floor directly with solar-heated water. This hot water is then circulated through the tubes. The heat exchange to the room air takes place by radiation and by convection from the slab surface. Due to the high thermal capacity in the floor slab, the system response tends to be slow, but this is also an advantage for maintaining a more stable and comfortable indoor environment. Solar thermal hot water systems require an auxiliary heat source, i.e., a gas boiler (6), which provides auxiliary heat if one of the following basic conditions applies: • Insufficient solar energy to heat the water. • No solar energy to heat the water.

3. Modeling of the System Numerical simulation was carried out to analyze how conduction, natural convection, and radiosity inﬂuenced the temperature proﬁles of the air inside the chambers. Equa- tions, which describe the different processes in the system, are presented in the following subsections.

3.1. Mass Balance

The mass balance equation is expressed taking into consideration that ml is the mass fraction, and l and U are the system speed (m·s−1)[34]:

∂(ρm ) → → l + div(ρU m ) = R1 + div(τgrad(m )) (1) ∂t l l

3.2. Energy Conservation Equation The energy conservation equation is deﬁned considering S as the source term, and the conservation of the amount of motion following x is as follows [34]:

∂(ρU ) → → x + div(ρ.U U) = −div( J ) (2) ∂t x Combining both Equations (1) and (2), Equation (3) becomes:

∂(ρU ) → → x + div(ρ.U U) = −div[−µ.grad(ρ.U )] + S (3) ∂t x x These three equations may be expressed by the following generic equation: If Φ is any physical quantity, the conservation equation of Φ is written:

∂(ρ.φ) → → + div(ρ.φ.U) = div[τ.grad(φ)] + S (4) ∂t Energies 2021, 14, 3880 9 of 17

3.3. Heat Transfer Equation The heat flux density q is the energy exchanged with the surroundings through the pipes of the heating system, the floor heating, and the house air by square meter (W·m−2). The heat flux density equation q is defined by the following expression [30]:

q = K∆T (5)

where K is the overall heat transfer coefﬁcient.

3.4. Surface Radiosity Surface radiosity was used to describe the radiative ﬂux of the surface. It is assumed that the walls are diffuse and gray. For a surface element at the boundary of a cavity, the nondimensional radiosity is given by the following equation [34]:

0 J = εM1 + ρGi (6)

0 4 Considering that M1 = σ T1 and according to Kirchhoff’s law ε + ρ = 1, Equation (6) becomes: 4 (1 − ε)Gi = J − εσT1 (7) where σ = 5.675 × 10−8 W·m−2·K−4. The radiosity, J, of the low floor surface is the total flux emitted by this surface. This total flux results from: (i) the reflection of part of the incident flux, G, which falls on this surface (illumination); and (ii) the flux emitted by the surface itself due to its temperature T.

3.5. Resolution Procedure The experimental study reported by Benouali et al. [28,35] indicated that thermal loads were calculated by means of several inlet and outlet temperature measurements, which were taken at their pilothouse using thermocouples placed on the envelope as well as in certain elements of the heating system. All measurements were collected via a data logger. The numerical simulation in the present study was carried out using the Comsol Multiphysics 5.3a software [36]. The numerical model was built using a physics-controlled 2D sequential mesh with an extra-fine element size [37]. Each domain was discretized using free tetrahedral elements [38,39], forming a nonstructural mesh that was linear in the boundaries between layers [38], as shown in Figure5. The grid cell exhibits a mesh of 291,107 nodes and 24,089 internal boundaries, with different mesh sizing of the heating fluid areas, air flow, and walls, and a simulation time step of 30 min. Simulation time was about 2 h 4 min and 33 s. It was performed on a Macintosh-type computer equipped with an integrated i7 quad-core 4th-generation 2.0 GHz processor, boosted up to 3.2 GHz during the calculation with 8 GB of RAM. This was again boosted up to 64 GB during the calculation thanks to the hard disk type SSD and a 2 GHz Iris Pro graphics card. Figure6 shows the simulation results, obtained for this present work, of the air temperature variation inside the room for 132 h of floor heating. It also shows the experimental data results reported by Benouali et al. [28]. The input conditions in the simulation process were set as follows: heating system off, room temperature at 0 ◦C, water temperature in the heating circuit at 40 ◦C, and calculations taken at a 50 cm height. The volume flow rate was kept constant at 17 l·h−1·m−2. Remarkably, the temperature profile, for the simulation results, distinguishes two different periods of time. In the first period, from 0 to 72 h, there is a temperature increase from the heating starting point to the equilibrium point. This is a two-range increment of 0.58 ◦C·h−1 for the first 12 h of the day and 0.14 ◦C·h−1 for the next 60 h. This might be due to the air flow and the day–night temperature variation effect occurring at a 50 cm height inside the room. In the second period (Figure7), from 72 h to 132 h, the room temperature stabilizes at an equilibrium level of 15 ◦C, as reported in the experimental work, and this is due to a decrease in the air flow velocity at the same height of 50 cm. Energies 2021, 14, x FOR PEER REVIEW 10 of 17

Energies 2021, 14, x FOR PEER REVIEWFigure 5. Details of the nonstructured mesh. 10 of 17 Energies 2021, 14, 3880 10 of 17 Figure 6 shows the simulation results, obtained for this present work, of the air temperature variation inside the room for 132 h of floor heating. It also shows the experimental data results reported by Benouali et al. [28]. The input conditions in the simulation process were set as follows: heating system off, room temperature at 0 °C, water temperature in the heating circuit at 40 °C, and calculations taken at a 50 cm height. The volume flow rate was kept constant at 17 l·h −1·m −2. Remarkably, the temperature profile, for the simulation results, distinguishes two different periods of time. In the first period, from 0 to 72 h, there is a temperature increase from the heating starting point to the equilibrium point. This is a two-range increment of 0.58 °C ·h−1 for the first 12 h of the day and 0.14 °C ·h−1 for the next 60 h. This might be due to the air flow and the day–night temperature variation effect occurring at a 50 cm height inside the room. In the second period (Figure 7), from 72 h to 132 h, the room temperature stabilizes at an equilibrium level of 15 °C, as reported in the experimental work, and this is due to a decrease in the air flow velocity at the same height of 50 cm. Simulation results were validated with experimental values from the 72nd hour for a duration of 60 h. The experimental and theoretical temperature profiles shown in Figure 7 confirm the agreementFigure between 5. Details both sets of the of nonstructured data. The maximum mesh.mesh. and average deviations between experimental and numerical values were 0.75% and 0.35%, respectively. Figure 6 shows the simulation results, obtained for this present work, of the air temperature variation inside the room for 132 h of floor heating. It also shows the experimental data results reported by Benouali et al. [28]. The input conditions in the simulation process were set as follows: heating system off, room temperature at 0 °C, water temperature in the heating circuit at 40 °C, and calculations taken at a 50 cm height. The volume flow rate was kept constant at 17 l·h −1·m −2. Remarkably, the temperature profile, for the simulation results, distinguishes two different periods of time. In the first period, from 0 to 72 h, there is a temperature increase from the heating starting point to the equilibrium point. This is a two-range increment of 0.58 °C ·h−1 for the first 12 h of the day and 0.14 °C ·h−1 for the next 60 h. This might be due to the air flow and the day–night temperature variation effect occurring at a 50 cm height inside the room. In the second period (Figure 7), from 72 h to 132 h, the room temperature stabilizes at an equilibrium level of 15 °C, as reported in the experimental work, and this is due to a decrease in the air flow velocity at the same height of 50 cm. Simulation results were validated with experimental values from the 72nd hour for Energies 2021, 14, x FORFigure PEER REVIEW 6. ComparisonFigure 6. Comparison betweena duration between the simulationof 60 the h. simulationThe and experimental experimental and experimental and temperature theoretical temperature proﬁlestemperature profiles of ambient of profiles ambient11 air of shownair 17 during in the Figure

heating process.during the heating7 confirm process the. agreement between both sets of data. The maximum and average deviations between experimental and numerical values were 0.75% and 0.35%, respectively.

Figure 7. ComparisonFigure 7. Comparison betweenFigure the between6. theoreticalComparison the theoretical and between experimental and the experimentalsimulation temperature and temperature experimental proﬁles of profiles ambient temperature of air ambient between profiles air 72 of ambh andient air 132 h periods.between 72 h andduring 132 hthe periods heating. process.

4. Results and Discussion The following subsections present the simulation results for a full week, between 9 and 13 January, 2011. The month of January was chosen because it is one of the coldest months of the year in Algeria. These days represent the coldest week of the year. The

average outside temperature measured during this period is 10.5 °C, with a minimum value of 5.4 °C and a maximum value of 16.5 °C. A wide daily fluctuation can be observed outside, of up to 11 °C.

4.1. CFD Temperature Profiles during Floor Heating Figure 8 shows the air temperature distribution for 132 h at a floor fluid temperature of 40 °C and taken at a 50 cm height. Figure 9 shows the distribution of the average air temperature inside the living room with the floor and the pipes for 132 h (5.5 days) of heating. As shown in these figures, the simulation started with a heat transfer fluid temperature of 40 °C. The air temperature inside the house was set at 0 °C taken at a 50 cm height [40]. After 24 h of heating, the air temperature in the living room increased up to 10.5 °C. This increase continued up to 13.0 °C after 48 h of heating. After 70, 96, and 132 h of heating, the temperature reached 14.5, 14.8, and 15.2 °C, respectively. The air temperature in the living room stabilized at an average of 15.1 ± 0.35 °C, taken at a 50 cm height, after 70 h of the heating cycle.

Figure 8. Air temperature distribution over 132 h at a floor fluid temperature of 40 °C.

Energies 2021, 14, x FOR PEER REVIEW 11 of 17

Energies 2021, 14, 3880 11 of 17

Simulation results were validated with experimental values from the 72nd hour for a

duration of 60 h. The experimental and theoretical temperature proﬁles shown in Figure7 conﬁrmFigure 7. theComparison agreement between between the theoretical both sets and of data. experimental The maximum temperature and profiles average of deviations ambient air betweenbetween 7 experimental2 h and 132 h periods and numerical. values were 0.75% and 0.35%, respectively.

4.4. ResultsResults andand DiscussionDiscussion TheThe followingfollowing subsectionssubsections presentpresent thethe simulationsimulation resultsresults forfor aa fullfull week,week, betweenbetween 99 andand 1313 January,January, 2011.2011. TheThe monthmonth ofof JanuaryJanuary waswas chosenchosen becausebecause itit isis oneone ofof thethe coldestcoldest monthsmonths ofof thethe yearyear inin Algeria.Algeria. TheseThese daysdays representrepresent thethe coldestcoldest weekweek ofof thethe year.year. TheThe averageaverage outsideoutside temperaturetemperature measuredmeasured duringduring thisthis periodperiod isis 10.510.5 ◦°C,C, withwith aa minimumminimum valuevalue ofof 5.45.4 ◦°CC andand aa maximummaximum valuevalue ofof 16.516.5 ◦°C.C. AA widewide dailydaily ﬂuctuationfluctuation cancan bebe observedobserved outside,outside, ofof upup toto 1111 ◦°C.C.

4.1.4.1. CFDCFD TemperatureTemperature ProfilesProfilesduring duringFloor FloorHeating Heating FigureFigure8 8 shows shows the the air air temperature temperature distribution distribution for for 132 132 h h at at a a floor floor fluid fluid temperature temperature ◦ ofof 4040 °C and taken at at a a 50 50 cm cm height. height. Figure Figure 99 shows shows the the distribution distribution of of the the average average air airtemperature temperature inside inside the theliving living room room with with the the floor floor and and the the pipes pipes for for 132 132 h (5.5 h (5.5 days) days) of ofheating. heating. As Asshown shown in these in these figures, figures, the thesimulation simulation started started with with a heat a heattransfer transfer fluid fluid tem- ◦ ◦ temperatureperature of 40 of 40°C. C.The The air air temperature temperature inside inside the the house house was was set set at at 0 0 °CC taken at aa 5050 cmcm heightheight [[4400].]. AfterAfter 2424 hh ofof heating,heating, thethe airair temperaturetemperature inin thethe livingliving roomroom increasedincreased upup toto ◦ ◦ 10.510.5 °C.C.This This increase increase continued continued up up to 13.0to 13.0C ° afterC after 48 h48 of h heating. of heating. After After 70, 96, 70, and 96, 132and h 132 of ◦ heating,h of heating, the temperature the temperature reached reached 14.5, 14.5, 14.8, 14.8 and, 15.2and 15.2C, respectively. °C, respectively. The airThe temperature air temper- ◦ inature the in living the living room roomstabilized stabilized at an averageat an average of 15.1 of± 15.10.35 ± 0.35C, taken °C, taken at a 50 at cm a 50 height, cm height, after 70after h of 70 the h of heating the heating cycle. cycle.

FigureFigure 8.8. AirAir temperaturetemperature distributiondistribution overover 132132 hh atat aa ﬂoorfloor ﬂuidfluid temperaturetemperatureof of 4040◦ °C.C.

Figure9A–F shows the distribution of the average air temperature inside the living room with the floor and the pipes for 132 h (5.5 days) of heating. The air temperature difference, from CFD simulations, between the ambient air in the living room and the hot water in the floor heating system at different time steps is, namely: 0 h, 24 h, 48 h, 70 h, 96 h, and 132 h. In the first period, there is a low heat transfer inside the room between the underfloor heating (hot source) and the interior space (air) and surfaces. This is because the cold walls and the low floor experience thermal inertia. The walls, especially the high wall, also suffer heat losses. Afterwards, during the second period, the temperature stabilizes due to the low-velocity air flow (break flow), which already brought about a temperature increase in the air inside the room. This temperature remains stable, but the temperature difference between the underfloor heating system and the air inside the room is high due to an increased heat loss occurring at the level of the high floor. Energies 2021, 14, x FOR PEER REVIEW 12 of 17 Energies 2021, 14, 3880 12 of 17

FigureFigure 9.9. CFDCFD locallocal airair temperaturetemperature gradientgradientin inthe theliving livingroom: room: ((AA))before before heating; heating; (B(B)) after after 24 24 h h of of heating;heating; ((CC)) afterafter 48 h of heating; ( (D)) a afterfter 70 70 h h of of heating; heating; (E (E) )a afterfter 96 96 h h of of heating; heating; (F ()F a)fter after 132 132 h hof heating. of heating.

4.2. EffectFigure of Heating9A–F shows Fluid Temperaturethe distribution on the of Room the average Air Temperature air temperature inside the living roomFigure withthe 10 showsfloor and air temperaturethe pipes for variation 132 h (5.5 versus days) time of heating. in the room The atair heat temperature transfer fluid dif- temperaturesference, from rangingCFD simulations, from 30 to between 50 ◦C and the at ambient intervals air of 5in◦ C.the The living temperature room and profiles the hot showwater thein the same floor trend heating as the system heat at transfer different fluid time temperature steps is, namely: increases 0 h, 2 from4 h, 4308 h to, 7 500 h◦, C96. Theh, and effect 132 of h. the In the heat first transfer period, fluid there temperature is a low heat on transfer the air temperature inside the room inside between the room the takenunderfloor at a 50 heating cm height (hot issource) not significant and the interior as long space as the (air) initial and heating surfaces. fluid This temperature is because remainsthe cold inwalls the rangeand the of low 30–50 floor◦C, experience i.e., 10 ◦C belowthermal or inertia. over the The nominal walls, temperatureespecially the set high at 40wall◦C., also Moreover, suffer heat the airlosses. temperature Afterwards, increased during andthe second reached period, an almost the temperature constant value stabi- of 15.1lizes± due0.35 to◦ theC after low 72-velocity h regardless air flow of (break the initial flow) heating, which fluid already temperature, brought andabout the a heatingtemper- systemature increase remained in stablethe air because inside the of theroom. thermal This temp inertiaerature of the remains floor. The stable, internal but temperature the temper- showedature difference an insignificant between variation the underfloor after stabilization, heating system which and demonstrates the air inside thethe reliabilityroom is high of thisdue systemto an increased for heating heat and loss domestic occurring hot at water the level production. of the high floor. Based on other work carried out on conventional radiator systems [41], underfloor heating4.2. Effect systems of Heating exhibit Fluid a Temperature uniform distribution on the Room of Air the Temperature temperature gradient in the house comparedFigure to 10 the shows radiator air system, temperature which variation presents weakversus heating time in far the from room the at unique heat transfer source. fluid temperatures ranging from 30 to 50 °C and at intervals of 5 °C. The temperature profiles show the same trend as the heat transfer fluid temperature increases from 30 to 50 °C. The effect of the heat transfer fluid temperature on the air temperature inside the room taken at a 50 cm height is not significant as long as the initial heating fluid temperature remains in the range of 30–50 °C, i.e., 10 °C below or over the nominal temperature set at 40 °C. Moreover, the air temperature increased and reached an almost constant value of 15.1 ± 0.35 °C after 72 h regardless of the initial heating fluid temperature, and the heat-

Energies 2021, 14, x FOR PEER REVIEW 13 of 17 Energies 2021, 14, x FOR PEER REVIEW 13 of 17

ing system remained stable because of the thermal inertia of the floor. The internal tem- peratureing system showed remained an stableinsignificant because variation of the thermal after stabilization, inertia of the which floor. demonstratesThe internal tem- the reliabilityperature showed of this system an insignificant for heating variationand domestic after hot stabilization, water production. which demonstrates the reliabilityBased of on this other system work for carried heating out and on domestic conventio hotnal water radiator production. systems [41], underfloor heatingBased systems on other exhibit work a uniformcarried outdistribution on conventio of thenal temperature radiator systems gradient [41 ],in underfloor the house Energies 2021, 14, 3880 comparedheating systems to the radiatorexhibit a system uniform, which distribution presents of weak the heatingtemperature far from gradient the unique in the source. 13house of 17 compared to the radiator system, which presents weak heating far from the unique source. 20 20

C 15

r a temperature 30°C

u 10

a temperature 35°C

p 10 temperature 30°C

e temperature 40°C m temperature 35°C

p e temperature 45°C

T temperature 40°C

m e temperaturetemperature 50°C45°C T 5 temperature 50°C 5

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

6 0 4 8 2 2 6 0 4 8 2 2 6 0 4 8 2 2 6 0 4 8 2 2 6 0 4 8 2 2 6 0 4 8

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 1 1 1 2 0 0 1 1 1 2 0 0 1 1 1 2 0 0 1 1 1 2 0 0 1 1 1 2 0 0 1 1 1

: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :

6 0 4 8 2 2 6 0 4 8 2 2 6 0 4 8 Time2 (h)2 6 0 4 8 2 2 6 0 4 8 2 2 6 0 4 8 0 1 1 1 2 0 0 1 1 1 2 0 0 1 1 1 2 0 0 1 1 1 2 0 0 1 1 1 2 0 0 1 1 1 Time (h) Figure 10. Variation of air temperature as a function of time with temperature variation in the heat transferFigureFigure 10. fluid Variation. of air temperature as a functionfunction ofof timetime withwith temperaturetemperature variationvariation inin the heat transfertransfer fluid fluid.. 4.3. Effect of the Heating Fluid Temperature on the Surface Radiosity of the Floor 4.34.3.. Effect Effect of of the the Heating Heating Fluid Fluid Temperature Temperature on the Surface Radiosity of the Floor The variation of surface radiosity versus time and air temperature is presented in The variation of surface radiosity versus time and air temperature is presented in FiguresThe 11 variation and 12, respectively.of surface radiosity The data versus were timetaken and over air a weektemperature at floor isfluid presented tempera- in Figures 11 and 12, respectively. The data were taken over a week at floor fluid temperatures turesFigures ranging 11 and from 12, respectively. 30 to 50 °C at The 5 ° dataC intervals. were taken In the over first a weekperiod at from floor 0 fluid h to tempera-72 h, the ranging from 30 to 50 ◦C at 5 ◦C intervals. In the first period from 0 h to 72 h, the radiosity of radiositytures ranging of the from floor 30 surface to 50 °isC subjectat 5 °C tointervals. a variation In theof aboutfirst period 2.7% for from each 0 h5 °toC 7inc2 hrease, the the floor surface is subject to a variation of about 2.7% for each 5 ◦C increase in the heating inradiosity the heating of the fluid floor temperature. surface is subject Radiosity to a variationincreases of as about a function 2.7% offor time each and 5 °C is inc subjectrease influid the temperature.heating fluid Radiositytemperature. increases Radiosity as a increases function ofas timea function and is of subject time and to−2 day–night is subject to day–night deviations. It reaches an almost constant value of 380−2 ± 5 W·m after 72 h deviations. It reaches an almost constant value of 380 ± 5 W·m after 72 h−2 due to the dueto d ayto –thenight thermal deviations. equilibrium It reaches prevailing an almost in theconstant room. value Based of on 380 this ± 5r esultW·m and after the 7 2air h thermal equilibrium prevailing in the room. Based on this result and the air temperature temperaturedue to the thermal variations equilibrium presented prevailing on the gradient in the inroom. Figure Based 11, it on is clearthis rthatesult the and variation the air variations presented on the gradient in Figure 11, it is clear that the variation in radiosity intemperature radiosity exerts variations an insignificant presented oninfluence the gradient on the in air Figure temperature 11, it is clearduring that the the first variation period exerts an insignificant influence on the air temperature during the first period and after andin radiosity after stabilization exerts an insignificant at 72 h. influence on the air temperature during the first period andstabilization after stabilization at 72 h. at 72 h.

400

390

380

380 Temperature 30°C

2 Temperature 35°C

m 370 / TemperatureTemperature 40°C30°C

TemperatureTemperature 45°C35°C

é m 370

t / Temperature 50°C i Temperature 40°C

Temperature 45°C

d t Temperature 50°C

s 360

a 360

350

340

330

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :

8 2 2 6 0 4 8 2 2 6 0 4 8 2 2 6 0 4 8 2 2 6 0 4 8 2 2 6 0 4 8 2 2 6

330 1 2 0 0 1 1 1 2 0 0 1 1 1 2 0 0 1 1 1 2 0 0 1 1 1 2 0 0 1 1 1 2 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

: : : : : : : : : : : : : : : : Time(h): : : : : : : : : : : : : : : : : :

8 2 2 6 0 4 8 2 2 6 0 4 8 2 2 6 0 4 8 2 2 6 0 4 8 2 2 6 0 4 8 2 2 6 1 2 0 0 1 1 1 2 0 0 1 1 1 2 0 0 1 1 1 2 0 0 1 1 1 2 0 0 1 1 1 2 0 0 Time(h) FigureFigure 11. 11. RadiosityRadiosity versus versus time time at at different different temperatures temperatures of of the heating fluid ﬂuid.. Figure 11. Radiosity versus time at different temperatures of the heating fluid. The variation of radiosity surface area as a function of time and air temperature is presented in Figure 13. The 3D graph shows the variation of radiosity per unit area, inside the rooms heated by the ﬂoor heating system, as a function of time and air temperature. Radiosity shows a linear trend with increases of up to the value of 15.1 ◦C as a function of air temperature, and up to 72 h as a function of time. As previously mentioned, after 72 h of heating, radiosity per unit area remains stable as air temperature by convection remains stable. Energies 2021, 14, x FOR PEER REVIEW 14 of 17

400 floor fluide temperature (30°C) floor fluide temperature (35°C) 390 floor fluide temperature (40°C) floor fluide temperature (45°C) floor fluide temperature (50°C) 380

)

m Energies 2021, 14, x FOR PEER REVIEW / 14 of 17

Energies 2021, 14, 3880 W 370 14 of 17

(

o 360

d a 400 R 350 floor fluide temperature (30°C) floor fluide temperature (35°C) 390 floor fluide temperature (40°C) 340 floor fluide temperature (45°C) floor fluide temperature (50°C) 380

)

2 330

m 0 2 4 6 8 10 12 14 16

W 370 Air Temperature (°C)

(

i Figures 12. Surface radiosity as a function of air temperature at different floor fluid temperatures. o 360

a R 350The variation of radiosity surface area as a function of time and air temperature is presented in Figure 13. The 3D graph shows the variation of radiosity per unit area, inside 340 the rooms heated by the floor heating system, as a function of time and air temperature. Radiosity330 shows a linear trend with increases of up to the value of 15.1 °C as a function of 0 2 4 6 8 10 12 14 16 air temperature, and up to 72 h as a functionAir Temperature of time. (°C) As previously mentioned, after 72 h of heating, radiosity per unit area remains stable as air temperature by convection remains FigureFigure 12. 12. SurfaceSurface radiosity radiosity as as a a function function of of air air temperature temperature at at different different floor ﬂoor fluid ﬂuid temperatures temperatures.. stable. The variation of radiosity surface area as a function of time and air temperature is presented in Figure 13. The 3D graph shows the variation of radiosity per unit area, inside

the400 rooms heated by the floor heating system, as a function of time and air temperature. Radiosity shows a linear trend with increases of up to the value of 15.1 °C as a function of 390 air temperature, and up to 72 h as a function of time. As previously mentioned, after 72 h 380

of2 heating, radiosity per unit area remains stable as air temperature by convection remains

m / 370

stable.

o 360

R 350

340 400 330

0 390 0

0 16

2 : 14

2 380 :

4 : 12

0 10

0 : 8

2 370 : 6

0 0 4

: i 2

6 : 0

2 360 : Air Temperature (°C)

2 d Time(h)

R 350 Figure 13. Radiosity in 3D versus time and air temperature. Figure340 13. Radiosity in 3D versus time and air temperature. 330 There are no explicit investigations in the literature that explain the inﬂuence of

There8 are no explicit investigations in the literature that explain the influence of nat-

0 16

natural2 convection on surface radiosity as a function of time, especially in graphical

2 : 14

4 : 12

ural convection on 2 surface radiosity as a function of time, especially in graphical data. The

data. The present study0 is, therefore, one of the ﬁrst to develop this type of real practical 0 10

0 : 8

2 : 6

0 present study is, therefore, one of 0 the first to develop this type of real practical research

0 research on a large scale (pilothouse),: and even in room spaces. Although there is no

0 0 4

8 : 2

6 : 0

2 : Air Temperature (°C)

0 on a large scale (pilothouse), and even2 in room spaces. Although there is no representa-

0 representative equation for surface radiosity8 as a function of time, we can infer from the

Time(h) 2

1 tivegraphs equation in Figures for surface 10 and radiosity 11 that the as evolutiona function of of radiosity time, we follows can infer the from same the trend graphs as that in Figureof convection,s 10 and i.e.,11 that that the the evolution value of the of radiativeradiosity fluxfollows increases the same in the trend same as way that as of the con- air Figure 13. Radiosity in 3D versus time and air temperature. vection,temperature i.e., that increases the value as a function of the radiative of time to flux equilibrium. increases in Furthermore, the same way by lookingas the air at tem- how peratureradiosity increases behaves as a function of time room to air equilibrium. temperature Furthermore, and time, it by may looking be concluded at how There are no explicit investigations in the literature that explain the influence of nat- radiositythat natural behaves convection as a function influences of room surface air radiosity.temperature In and order time, to fullyit may understand be concluded this ural convection on surface radiosity as a function of time, especially in graphical data. The thatcoupling natural phenomenon convection betweeninfluences convection surface radiosity. and surface In order radiosity, to fully it is understand necessary to this analyze cou- present study is, therefore, one of the first to develop this type of real practical research plingthe behavior phenomenon of radiosity between as aconvection function of and air surface temperature radiosity, and time.it is necessary The phenomenon to analyze is on a large scale (pilothouse), and even in room spaces. Although there is no representa- new and has not yet been developed elsewhere before. tive equation for surface radiosity as a function of time, we can infer from the graphs in Figure5. Conclusionss 10 and 11 that the evolution of radiosity follows the same trend as that of convection,The i.e., modeling that the and value simulation of the radiative of the thermal flux increases behavior in ofthe a same solar way underfloor as the air heating tem- peraturesystem for increases residential as a buildingsfunction of were time investigated. to equilibrium. Numerical Furthermore, simulation by looking was at carried how radiosityout using behaves the Comsol as a Multiphysicsfunction of room® software, air temperature which applied and time, a finite it elementmay be concluded method to thatsolve natural physical convection problems influences governed surface by partial radiosity. differential In order equations. to fully understand The simulation this cou- tool plingdeveloped phenomenon was validated between using convection the experimental and surface data availableradiosity, in it theis necessary literature, to which analyze was obtained from a pilothouse study.

Energies 2021, 14, 3880 15 of 17

The two-dimensional study has facilitated the investigation of the different mechanisms of heat transfer in underfloor heating systems, namely: conduction, convection, and radiation. The most significant results are summarized below: • The simulation data were well in agreement with the experimental data, and the underfloor heating system maintained an average temperature of 15.1 ± 0.35 ◦C taken at a 50 cm height inside the room on stabilization after 72 h of heating. • When the heating transfer fluid temperature was increased from 30 to 50 ◦C, the result was the same temperature of 15.1 ± 0.35 ◦C taken at a 50 cm height inside the room. The air temperature remained stable with an insignificant variation after 72 h of heating. This was due to the thermal inertia exerted by the floor and confirms the reliability of this floor heating system to supply heating and domestic hot water. • During the heating process, surface radiosity increased as a function of time and reached an almost constant value of 380 ± 5 W·m−2 after 72 h because of the stability of the air temperature by convection. Radiosity variation did not significantly influence the trend in air temperature inside the room, despite the increase in heating transfer fluid temperature from 30 to 50 ◦C or that of the day–night effect.

Author Contributions: Conceptualization, D.S. and M.B.; methodology, A.L. and M.B.; software, A.L.; validation, A.L., D.S. and M.B.; formal analysis, A.L. and M.B.; investigation, A.L.; writing— original draft preparation, A.L.; writing—review and editing, M.B.; supervision, D.S., A.H. and M.B.; funding acquisition, D.S. and A.H. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Institutional Review Board Statement: Not applicable. Acknowledgments: Abdelkader Laafer gratefully acknowledges the Algerian Ministry of Higher Education and Scientific Research for funding his internship at the University Rovira i Virgili of Tarragona (Spain) under the National Exceptional Program PNE 2019-2020. The authors appreciate the suggestions put forth during the stages of writing this paper by Abir Hmida from the National Engineering School of Gabes (Tunisia), Mohamed El Amine Slimani from the University of Science and Technology Houari Boumediene (Algeria), and Nacer Eddine Settar from the University of Blida 1 (Algeria). Conflicts of Interest: The authors declare no conflict of interest.

Nomenclature

Acronyms BTS (SEB) Stabilized earth bricks CFD Computational fluid dynamics Div Divergence Grad Graduim ONDOL Conventional floor heating system in the Korean language Symbols m Mass fraction (kg) T Temperature (◦C) q Heat flux density (W) S Collector area (m2) R Thermal resistance (m2·K·W−1) K Overall heat transfer coefficient (W·m−2·K−1) t Time (s) U Velocity (m·s−1) Greek symbols λ Thermal conductivity (W·m−1·K−1) ρ Density (kg·m−3) ε Emissivity Energies 2021, 14, 3880 16 of 17

References

1. Ferrante, A.; Cascella, M.T. Zero energy balance and zero on-site CO2 emission housing development in the Mediterranean climate. Energy Build. 2011, 43, 2002–2010. [CrossRef] 2. Zhai, X.Q.; Yang, J.R.; Wang, R.Z. Design and performance of the solar-powered floor heating system in a green building. Renew. Energy 2009, 34, 1700–1708. [CrossRef] 3. Dall’O’, G.; Bruni, E.; Sarto, L. An Italian pilot project for zero energy buildings: Towards a quality-driven approach. Renew. Energy 2013, 50, 840–846. [CrossRef] 4. Olesen, B.W. Possibilities and Limitations of Radiant Floor Cooling (No. CONF-9702141); American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc.: Atlanta, GA, USA, 1997. 5. Simmonds, P. Control strategies for combined heating and cooling radiant systems. Ashrae Trans. 1994, 100, 1031–1039. 6. Song, D.; Kim, T.; Song, S.; Hwang, S.; Leigh, S.B. Performance evaluation of a radiant floor cooling system integrated with dehumidified ventilation. Appl. Therm. Eng. 2008, 28, 1299–1311. [CrossRef] 7. Lim, J.H.; Jo, J.H.; Kim, Y.Y.; Yeo, M.S.; Kim, K.W. Application of the control methods for radiant floor cooling system in residential buildings. Build. Environ. 2006, 41, 60–73. [CrossRef] 8. Song, G.S. Buttock responses to contact with finishing materials over the ONDOL floor heating system in Korea. Energy Build. 2005, 37, 65–75. [CrossRef] 9. Yu, T.; Heiselberg, P.; Lei, B.; Pomianowski, M. Validation and modification of modeling thermally activated building systems (TABS) using EnergyPlus. Build. Simul. 2014, 7, 615–627. [CrossRef] 10. De Monte, F. Transient heat conduction in one-dimensional composite slab. A natural’analytic approach. Int. J. Heat Mass Transf. 2000, 43, 3607–3619. [CrossRef] 11. Lu, X.; Tervola, P. Transient heat conduction in the composite slab-analytical method. J. Phys. A Math. Gen. 2004, 38, 81. [CrossRef] 12. Beck, J.V.; Haji-Sheikh, A.; Amos, D.E.; Yen, D. Verification solution for partial heating of rectangular solids. Int. J. Heat Mass Transf. 2004, 47, 4243–4255. [CrossRef] 13. Pantelic, J.; Schiavon, S.; Ning, B.; Burdakis, E.; Raftery, P.; Bauman, F. Full scale laboratory experiment on the cooling capacity of a radiant floor system. Energy Build. 2018, 170, 134–144. [CrossRef] 14. Acikgoz, O.; Karakoyun, Y.; Yumurtacı, Z.; Dukhan, N.; Dalkılıç, A.S. Realistic experimental heat transfer characteristics of radiant floor heating using sidewalls as heat sinks. Energy Build. 2019, 183, 515–526. [CrossRef] 15. Feng, J.; Schiavon, S.; Bauman, F. New method for the design of radiant floor cooling systems with solar radiation. Energy Build. 2016, 125, 9–18. [CrossRef] 16. Zhao, K.; Liu, X.H.; Jiang, Y. Application of radiant floor cooling in large space buildings—A review. Renew. Sustain. Energy Rev. 2016, 55, 1083–1096. [CrossRef] 17. Laouadi, A. Development of a radiant heating and cooling model for building energy simulation software. Build. Environ. 2004, 39, 421–431. [CrossRef] 18. Weber, T.; Jóhannesson, G. An optimized RC-network for thermally activated building components. Build. Environ. 2005, 40, 1–14. [CrossRef] 19. Holopainen, R.; Tuomaala, P.; Piippo, J. Uneven gridding of thermal nodal networks in floor heating simulations. Energy Build. 2007, 39, 1107–1114. [CrossRef] 20. Kitagawa, H.; Asawa, T.; Kubota, T.; Trihamdani, A.R.; Sakurada, K.; Mori, H. Optimization of window design for ventilative cooling with radiant floor cooling systems in the hot and humid climate of Indonesia. Build. Environ. 2021, 188, 107483. [CrossRef] 21. Sattari, S.; Farhanieh, B. A parametric study on radiant floor heating system performance. Renew. Energy 2006, 31, 1617–1626. [CrossRef] 22. Wang, Y.; Zhang, X.; Ji, J.; Tian, Z.; Li, Y. Numerical simulation of thermal performance of indoor airflow in heating room. Energy Procedia 2019, 158, 3277–3283. [CrossRef] 23. Li, H.; Xi, C.; Kong, X.; Lin, Z.; Wang, L. A comparative experimental investigation on radiant floor heating system and stratum ventilation. Sustain. Cities Soc. 2020, 52, 101823. [CrossRef] 24. Lin, B.; Wang, Z.; Sun, H.; Zhu, Y.; Ouyang, Q. Evaluation and comparison of thermal comfort of convective and radiant heating terminals in office buildings. Build. Environ. 2016, 106, 91–102. [CrossRef] 25. Hu, B.; Wang, R.Z.; Xiao, B.; He, L.; Zhang, W.; Zhang, S. Performance evaluation of different heating terminals used in air source heat pump system. Int. J. Refrig. 2019, 98, 274–282. [CrossRef] 26. Report of the Cooperation Project CDER/CNERIB with Med-Enec. Energy Efficiency in the Construction Sector in the Mediterranean. June 2007. Available online: https://www.africapresse.paris/L-Algerie-experimente-l-habitat (accessed on 13 March 2020). 27. Imessad, K.; Derradji, L.; Messaoudene, N.A.; Mokhtari, F.; Chenak, A.; Kharchi, R. Impact of passive cooling techniques on energy demand for residential buildings in a Mediterranean climate. Renew. Energy 2014, 71, 589–597. [CrossRef] 28. Benouali, H.; Brara, A.; Mahdad, M.; Mokhtari, F. Caractérisation Thermophysique et Suivi Thermique de Deux Bâtisses Réalisées en Blocs de Terre Comprimée; XXIXe Rencontres Universitaires de Génie Civil: Tlemcen, Algeria, 2011; pp. 254–264. 29. Derradji, L.; Imessad, K.; Amara, M.; Boudali Errebai, F. A study on residential energy requirement and the effect of the glazing on the optimum insulation thickness. Appl. Therm. Eng. 2017, 112, 975–985. [CrossRef] Energies 2021, 14, 3880 17 of 17

30. DTR C3-2. Thermal Regulation of Residential Buildings e Calculating Methods for Determining Building Heat Losses; CRIB: Algiers, Algeria, 2019. Available online: https://www.academia.edu/11791860/DTR_C3_2_Reglement_thermique_des_batiments_ dhabitation_regle_de_calcul_des_peperdition_calorifique_FACICULE1 (accessed on 28 February 2020). 31. Semache, A.; Hamidat, A.; Benchatti, A. Impact study of the solar energy on the energy performances of the rural housing in Algeria. Int. J. Heat Technol. 2015, 33, 229–236. [CrossRef] 32. Yaiche, M.R.; Bouhanik, A.; Bekkouche, S.M.A.; Malek, A.; Benouaz, T. Revised solar maps of Algeria based on sunshine duration. Energy Convers. Manag. 2014, 82, 114–123. [CrossRef] 33. Martinez, P.J.; Velázquez, A.; Viedma, A. Performance analysis of a solar energy driven heating system. Energy Build. 2005, 37, 1028–1034. [CrossRef] 34. Sacadura, J.F. Initiation Aux Transferts Thermiques. 1978. Available online: https://www.worldcat.org/title/initiation-aux- transferts-thermiques/oclc/957575746?referer=di&ht=edition (accessed on 28 February 2020). 35. Mokhtari, F. Thermal Study and Dimensioning of the Solar Heating System of a Detached House Design of a Numerical Simulation Model; University of Sciences and Technology Mohamed Boudiaf: Oran, Algeria, 2017. 36. Wang, H.; Yu, Y.; Yu, J.; Wang, Z.; Li, H. Development of erosion equation and numerical simulation methods with the consideration of applied stress. Tribol. Int. 2019, 137, 387–404. [CrossRef] 37. Helaly, H.O.; Awad, M.M.; El-Sharkawy, I.I.; Hamed, A.M. Theoretical and experimental investigation of the performance of adsorption heat storage system. Appl. Therm. Eng. 2019, 147, 10–28. [CrossRef] 38. Gothäll, H. How to Inspect Your Mesh in COMSOL Multiphysics. COMSOL Multiphysics 2017. Available online: https: //www.comsol.com/blogs/how-to-inspect-your-mesh-in-comsol-multiphysics (accessed on 12 May 2017). 39. Calbureanu, M.; Talu, M.; Travieso-González, C.M.; Talu, S.; Lungu, M.; Malciu, R. The finite element analysis of water vapor diffusion in a brick with vertical holes. In Proceedings of the International Conference on Mathematical Models for Engineering Science-Proceedings, Puerto De La Cruz, Esp, Spain, 30 November–2 December 2010. Available online: http: //hdl.handle.net/10553/48823 (accessed on 2 March 2020). 40. Hernández, F.F.; López, J.M.C.; Gutiérrez, A.F.; Muñoz, F.D. A new terminal unit combining a radiant floor with an underfloor air system: Experimentation and numerical model. Energy Build. 2016, 133, 70–78. [CrossRef] 41. Errebai, F.B.; Derradji, L.; Amara, M. Thermal Behaviour of a Dwelling Heated by Different Heating Systems. Energy Procedia 2017, 107, 144–149. [CrossRef]