Thermal Characteristics and Parametric Analysis of an Improved Solar Wall

applied sciences

Article Thermal Characteristics and Parametric Analysis of an Improved Solar Wall

Xi Zhao 1 , Jiayin Zhu 2,*, Ruixin Li 2 , Weilin Li 2 and Bin Chen 3

1 College of Architecture, Texas A&M University, College Station, TX 77843, USA; [email protected] 2 Department of Civil Engineering, Zhengzhou University, Zhengzhou 450001, China; [email protected] (R.L.); [email protected] (W.L.) 3 Department of Construction Engineering, Dalian University of Technology, Dalian 160003, China; [email protected] * Correspondence: [email protected]; Tel.: +86-135-2658-2041

Abstract: Solar air collectors installed on buildings can significantly reduce conventional energy consumption in winter and summer. However, some problems arise in the utilization process, such as overheating, inconvenient operation control and low energy efficiency, etc. This work is a parametric analysis focusing on the automatic control and thermal efficiency improvement of the solar wall. An improved color-changing solar wall integrated with automatic control components, such as a photoelectric fan and temperature-controlled damper, was proposed in this paper. Based on the experimental data, the average daily heat output of the color-changing solar wall is 1.08 MJ per unit floor area on clear days in winter and the average thermal efficiency is 56.8%. Meanwhile, a quantitative analysis was carried out based on monitoring experiments for evaluating the thermal characteristic of automatic control components. Furthermore, in order to improve the thermal performance of the solar wall, parametric analysis was performed by numerical simulation. Results from this paper can provide a theoretical basis for the application of solar air collectors in modern buildings.

Citation: Zhao, X.; Zhu, J.; Li, R.; Li, W.; Keywords: solar energy; an improved color-changing solar wall; automatic control components; Chen, B. Thermal Characteristics and field measurement; parametric analysis Parametric Analysis of an Improved Solar Wall. Appl. Sci. 2021, 11, 6325. https://doi.org/10.3390/app11146325 1. Introduction Academic Editor: Sergio Montelpare As a type of renewable energy, solar energy is widely used as an alternative to fossil energy, and has the highest potential to meet the ever-increasing energy demands. Since Received: 31 May 2021 the middle of the last century, solar air heating has aroused great interest in the community Accepted: 7 July 2021 of solar researchers because it is a relatively simple, inexpensive and low maintenance Published: 8 July 2021 application [1]. As a typical component of passive solar air heating, solar air collectors are mainly used to convert incident solar radiation into useful heat in different types of Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in buildings. These heat collectors have been adopted around the world to reduce fossil fuel published maps and institutional affil- consumption for space heating and domestic hot water production [2]. Along these years, iations. several types of solar air collectors, differentiated by the type of solar absorber element (flat plate, V-corrugated plate, cylindrical tubes, plates with fins, etc.) were designed, mathematically modelled and experimentally tested [3,4]. The thermal performance of different types of solar air collectors is studied and compared in Table1. Among them, the most common system used for absorbing solar irradiation is the flat-plate solar air Copyright: © 2021 by the authors. collectors, which are always integrated on building façades as passive heating components. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Appl. Sci. 2021, 11, 6325. https://doi.org/10.3390/app11146325 https://www.mdpi.com/journal/applsci Appl. Sci. 2021, 11, x FOR PEER REVIEW 2 of 21

Appl. Sci. 2021, 11, x FOR PEER REVIEW 2 of 21

Appl. Sci. 2021, 11, x FORTable PEER REVIEW1. Investigations on thermal performance of different types of solar air collectors. 2 of 21 Appl. Sci. 2021, 11, x FOR PEER REVIEW 2 of 21 Appl. AuthorSci. 2021, 11, x FOR PEER TypesREVIEW Diagram Inference 2 of 21 Table 1. Investigations on thermal performance of different types of solar air collectors. Appl. Sci. 2021, 11, x FOR PEER REVIEW 2 of 21 Author solarTable airTypes 1. heater Investigations duct on thermal performanceDiagram of different types of solar air collectors.Inference Appl. Sci. 2021, 11, 6325 Table 1. Investigations on thermal performance of different typesThe maximumof solar air collectors.value of the thermal perfor-2 of 18 Appl. Sci. 2021, 11, x FORhavingTable PEER multi REVIEW1. Investigations V-shaped on thermal performance of different types of solar air collectors. 2 of 21 D. JinAuthor et al. [5] solar airTypes heater duct Diagram mance parameterInference was 1.93 for the range of Author ribs onTypes the absorber Diagram The maximum valueInference of the thermal perfor- Author havingTable multi Types1. Investigations V -shaped on thermal performanceDiagram of different types of solarparameters air collectors.Inference investigated. D. Jin et al. [5] solar airplate heater duct mance parameter was 1.93 for the range of ribssolar on air the heater absorber duct The maximum value of the thermal perfor- Table 1.AuthorInvestigations havingsolarTable on airmultiTypes thermal1. heater Investigations V -shaped duct performance on thermal of performanceDiagram different typesof different of solar typesThe airmaximum of solar collectors.parameters air collectors.valueInference investigated.of the thermal perfor- D. Jin et al. [5] having multiplate V -shaped Themance maximum parameter value was of 1.93 the forthermal the range perfor- of D. Jin et al. [5] havingribs on multi the absorber V-shaped mance parameter was 1.93 for the range of D. JinAuthor et al. [5] solarribs on air Typesthe heater absorber duct Diagram mance parameterparametersInference was investigated. 1.93 for the range of Authorsolar Typesribs airon heaterplatethe absorber with jet Diagram TheThe maximum thermalparameters efficiency value Inference investigated.of ofthe proposed thermal perfor-design A. M. Abogh- plate havingimpingement multi V on-shaped corru- duct is observedparameters almost investigated. 14% more as com- D. Jin et al. [5] solar airplate heater duct manceThe parameter maximum was value 1.93 offor the the thermalrange of rarasolar et al.air [6] heatersolarribs air ducton heaterthe having absorber with jet The thermalmaximum efficiency value of of the proposed thermal designperfor- A. M. Abogh- havinggated absorbermulti V-shaped plate performanceparedparameters to parameterthe investigated. smooth duct. was 1.93 for impingement on corru- duct is observed almost 14% more as com- D. Jin et al. [5] D. Jinmulti et al. V-shaped[5] ribsplate on the mance parameter was 1.93 for the range of rara et al. [6] solarribs air on heaterthe absorber with jet The thermalthe efficiency range of of parameters proposed design A. M. Abogh-absorbersolargated air plate absorber heater with plate jet The thermalparedparameters efficiency to the smoothinvestigated. of proposed duct. design

A. M. Abogh- impingementplate on corru- duct is observed almost 14% more as com- solar air heater with jet The thermal efficiencyinvestigated. of proposed design A.rara M. et Abogh- al. [6] impingement on corru- duct is observed almost 14% more as com- rara et al. [6] impingementgated absorber on platecorru- duct is observedpared to almostthe smooth 14% duct.more as com- rara et al. [6] flatgated plate absorber solar air plate heat- TheThe annual thermalpared average to efﬁciencythe smoothof a nickel ofduct. proposed–tin selec- solar air heater with jet The thermal efficiency of proposed design A.A. Elsolar-Sebaii, air heatergated absorber with jet plate pared to the smooth duct. A. M. Abogh- design duct is observed almost 14% impingementers-double pass on flat corru- and ducttively is observedcoated absorber almost is14% higher more than as com- that

A.M. Aboghrara et al. [6] impingement on corrugated H.rara Al -etSnani al. [6] [7] flatsolar plate air heatersolar air with heat- jet TheThemore thermalannual as averageefficiency compared of ofa nickeltoproposed the– smoothtin selec-design A.A.A. M. El Abogh--Sebaii,absorber gatedv-corrugated plate absorber plate plate with a blackpared painted to the smooth absorber duct. by 29.23%. ersimpingement-double pass on flat corru- and ducttively is coated observed absorber almostduct. is 14% higher more than as thatcom- H.rara Al- Snaniet al. [6] [7] flat plate solar air heat- The annual average of a nickel–tin selec- A.A. El-Sebaii, flatgatedv -platecorrugated absorber solar air plate plate heat- withTheThe annuala black annualpared averagepainted to average the smoothofabsorber a nickel of aduct. nickel–tinby–tin 29.23%. selec- A.A. El-Sebaii, ers-double pass flat and tively coated absorber is higher than that ﬂat plateflat plate solar solar air air heat- The annual average of a nickel–tin selec- A.A. El-Sebaii, H. H.A.A. Al -ElSnani-Sebaii, [7] ers-double pass flat and Thermaltivelyselectively coated efficiency absorber coated of double absorber is higher pass than is solar higher that air H. Alheaters-double-Snani [7] ersdoublev-double-corrugated pass pass ﬂatpass solar and plateflat airand withtively a coated black painted absorber absorber is higher by than 29.23%. that

B.M. Ramani et v-corrugated plate collectorwith a black with paintedporous absorbingabsorber by material 29.23%. is Al-Snani [7] H. Al-Snani [7] collectorflat plate withsolar and air heat-with- The annualthan that average with of a a black nickel painted–tin selec- A.A. al.El -[8]Sebaii,v-corrugated v-corrugated plate plate 20Thermalwith–25% a higherblack efficiency painted than ofthat doubleabsorber of collector pass by solar29.23%. without air ersdoubleout-double porous pass pass materialsolar flat airand tively coatedabsorber absorber by is 29.23%.higher than that B.M.H. Al Ramani-Snani [7] et flat plate solar air heat- collectorThe annual with average porous absorbingof a nickel –materialtin selec- is collectorv-corrugated with and plate with- ThermalwithThermal a blackporous efficiency painted efficiency absorbing of absorberdouble of material. double pass by 29.23%.solar pass air A.A.al. El [8]-Sebaii, double pass solar air 20–25% higher than that of collector without Thermal efficiency of double pass solar air ersout-double porous pass material flat and tively coated absorber is higher than that B.M.H. doubleAl Ramani-Snani pass [7] et solardouble air pass collector solar air collectorThermalsolar withefficiency air porous collector of absorbingdouble with pass porous material solar air is B.M. Ramani et collectorv-corrugated with and plate with- collectorwith a porousblack with paintedporous absorbing absorbingabsorber material. by material 29.23%. is al. [8] collectoradouble double withpass pass andsolar solar with- air air 20–25% higher than that of collector without B.M. Ramani et al. [8] B.M. Ramaniwith and et withoutout porous porous material collectorabsorbing with materialporous absorbing is 20–25% material higher is al. 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[21 by et] rugatedal. [19] proposedor sine-wave optimal absorber structure plates, design with fins,parameters baffles orof ribsthe flat[16–-plate18]. solar collector by investigated the performanceair andTaking the absorberthe ofinstantaneous the plate solar through airefficiency collector forced of turbulence the in collector North in asdouble Eastern an evaluation channel, India, includingindex, and Zhang various V-cor- et parameters consideredal.rugated [19] proposed foror sine the-wave presentoptimal absorber structure investigation plates, design with parametersfins, were baffles collector ofor theribs flat tilt[16-–plate18 angles,]. solar singlecollector and by double glazing, massTaking flow the rate instantaneous and two differentefficiency of absorber the collector plates. as an evaluation In reference index, [Zhang22], an et al. [19] proposed optimal structure design parameters of the flat-plate solar collector by innovative solar water heater integrated with a linear parabolic reflector was proposed and experimentally tested, and the experiments showed that the device was effective during winter. Its mean daily efficiency varied between 36.4% and 51.6%. ¸Seviket al. [23] investigated the performance of two types of solar air collectors with aluminum absorbers at three different air mass flow rates. Results showed that an enhancement of 15.9–41.2% in thermal efficiency was achieved in comparison to the flat plate solar air collector. Alta [24] compared the performance of three different types of designed flat-plate solar air heaters by the energy and exergy analyses. He found that the heater with double glass covers and fins is more effective. There are different factors affecting the solar air heater efficiency, e.g., aspect ratio of collector, absorber materials, vent size, wind speed, etc. [25–28]. To improve the dis- Appl. Sci. 2021, 11, 6325 3 of 18

advantages of solar air heaters, a range of numerical simulations has been performed for thermal performance optimization [29–31]. A mathematical model based on a numerical finite-difference approach was proposed for a flat-plate solar air collector in reference [32]. Nikolićet al. [33] presented a mathematical model to determine the optimum reflector position of a double-exposure flat-plate solar collector using FORTRAN language. Based on the two-node lumped heat capacitance method, dynamic thermal performance prediction models for flat-plate solar collectors were proposed and validated using dynamic tests [34]. The thermal behavior of double parallel flow air heating collectors working by natural convection was also studied. A GTC (glazed transpired solar collector) with perforating corrugated plate was developed by Zheng et al. [35], and the simulated results showed that its thermal performance and economic characteristics were better than other transpired solar collectors. Due to the above studies, buildings integrated with passive solar heating systems are widely used because of the high heat efficiency of solar air collectors [36–42]. Pertinent literature reveals that a good number of investigations are carried out in the recent past. However, some problems also have not been solved during the application of solar air collectors, such as overheating during summer and inconvenient operation control by manual dampers. A concept of “passive heating and cooling by color-changing” was put forward in our previous research [43,44], and an experimental study of thermal responsive of the color-changing solar wall was carried out. However, there are still some problems, such as inconvenient manual control operation and low thermal efficiency. Therefore, the aim of this work is to propose the automatic control component and optimize the heat collection efficiency. To achieve this goal, the design and construction of this solar wall are detailed, photoelectric fan and temperature-controlled damper are proposed and thermal characteristics of these automatic control components are evaluated by measuring hygrothermal parameters. Meanwhile, parametric analysis was performed based on the mathematical model and the optimization results of thermal performance simulation are presented. As an outcome, the finding of this research may provide some suggestions on the energy efficiency design for newly-built rural residences in cold areas, and present the theoretical basis and technical support for renewable energy utilization.

2. Development of Automatic Control Components Integrated with Color-Changing Solar Walls Solar air collector is the core component of a passive solar house, which is mainly composed of outlet cover, absorber board, air gap, insulation plate, inlet, outlet and fans, etc. The optimum design of the solar wall is mainly to put forward the color-changing absorber board and automatic control components. Studies about the color-changing absorber board had been carried out in reference [43] and [44]. The form of the absorber board is designed as a color-changing Venetian blind that exposes its black pieces outward in winter, whereas the white pieces are exposed outward in summer. The color of the absorber board is changed manually. The operation principle of the solar wall is shown in Figure1. To analyze the thermal performance of solar walls, a full-scale experimental house integrated with solar walls was built in Dalian, China. The photo of the experimental color-changing passive solar house is shown in Figure2. The building information and envelope characteristics are presented in Tables2 and3, respectively. Color-changing solar walls were ﬁxed on the south facade, facing to the south and perpendicular to the ground to heat up the living room and bedrooms. Dimensions of the solar wall system are shown in Table4. Appl. Sci. 2021, 11, x FOR PEER REVIEW 4 of 19

Appl. Sci. 2021, 11, x FOR PEER REVIEW 4 of 21 (a) (b)

Studies about the color-changing absorber board had been carried out in reference [43] and [44]. The form of the absorber board is designed as a color-changing Venetian blind that exposes its black pieces outward in winter, whereas the white pieces are ex- Appl. Sci. 2021, 11, 6325posed outward in summer. The color of the absorber board is changed manually. The 4 of 18 operation principle of the solar wall is shown in Figure 1.

(a) (b)

Outdoor Outlet Outlet Damper Glazing Damper Figure 1. Operation principle (a) in winterGlazing (b) in summer. Reprinted with permission from ref. Insulation Plate [43]. Copyright 2021 Elsevier. Outdoor Indoor Outdoor Indoor To analyze the thermal performance Color-changing of solar walls, a full-scale experimental house absorber plate Color-changing integrated with solar walls was built（White） in Dalian, China. The photo of the experimental absorbing plate（dark） color-changing Damper passive solar house is shown in Figure 2.Damper The building information and envelope characteristics are presentedPV plate in Tables 2 and 3, respectively. Color-changing so- Inlet Solar Fan PV Plate lar walls wereSloar fix Faned on the southOutdoor facade, Inlet facing to the south and perpendicular to the ground to heat up the living room and bedrooms. Dimensions of the solar wall system are Figure 1. OperationFigure principle 1. Operationshown (a) in principle winterin Table (b () a in4.) in summer. winter Reprinted(b) in summer with. permissionReprinted with from permission ref. [43]. Copyright from ref. 2021 Elsevier. [43]. Copyright 2021 Elsevier.

To analyze the thermal performance of solar walls, a full-scale experimental house integrated with solar walls was built in Dalian, China. The photo of the experimental color-changing passive solar house is shown in Figure 2. The building information and envelope characteristics are presented in Tables 2 and 3, respectively. Color-changing solar walls were fixed on the south facade, facing to the south and perpendicular to the ground to heat up the living room and bedrooms. Dimensions of the solar wall system are shown in Table 4.

Figure 2. AA photo of the full full-scale-scale experimental house ( a) in winter ( b) in sum summer.mer.

Table 2. Building information.information.

The Ratio of Window Heat Transfer Coefficient (W/m2.·°2C)◦ Floor The Ratio of Shape Coeffi- SHGC of Heat Transfer Coefﬁcient (W/m · C) Floor to Wall in South Fa- Shape SHGC of Area/m2 2 Window to Wall in cient Windows External Area/m Coefﬁcient WindowsExternal Walls FloorFloor Roof Roof Window Window çadeSouth/% Façade/% Walls 75 21.2 0.468 0.43 0.42 0.48 0.45 2.1 75 21.2 0.468 0.43 0.42 0.48 0.45 2.1

Table 3. Building envelope construction. Figure 2. A photo of the full-scale experimental house (a) in winter (b) in summer. Table 3. Building envelope construction. Layer Construction Table 2. Building information. External wallsLayer 20 mm plaster + 370 mm solid brick Construction + 70 mm polystyrene board The RatioInternal ofExternal Window walls walls 20 mm plasterHeat +24 370Transfer0 m mmm solid solid Coefficient brick+ 70 mm(W/m polystyrene2.·°C) board Floor Shape Coeffi- SHGC of to Wall inFloor SouthInternal Fa- walls50 mm wood floor + 50 mm poured concrete 240 mm+ 10 solid0 mm brick loess + 50 mm polystyrene board Area/m2 cient Windows External Walls Floor Roof Window çadeRoof/% Floor20 mm 50 plaster mm wood + 20 ﬂoor0 m +m 50 steel mm concrete poured concrete + 50 mm + 100polystyrene mm loess +board 50 mm + polystyrene20 mm tile board Roof 20 mm plaster + 200 mm steel concrete + 50 mm polystyrene board + 20 mm tile window double glazing + aluminum alloy window frames 75 21.2 window0.468 0.43 double0.42 glazing + aluminum0.48 alloy window0.45 frames2.1

Table 3. Building envelope construction. Table 4. Dimensions of the solar wall system. Layer Construction External walls Parameter20 mm Dimensionsplaster + 370 mm solid brick + 70 m Parameterm polystyrene board Dimensions Collectors tilt angle 90 Plate thickness 3 mm Absorber surface area 1.05 m2 Glass emissivity 0.9 Thickness of air gap 300 mm Absorber plate emissivity 0.4 Thickness of insulation 3 mm Glass transmissivity 0.85 Air duct diameter 100 mm Absorber absorptivity 0.9 Glass cover thickness 1 mm Ratio between the solar wall and the ﬂoor area 0.23 Appl. Sci. 2021, 11, x FOR PEER REVIEW 5 of 19

Table 4. Dimensions of the solar wall system.

Parameter Dimensions Parameter Dimensions Collectors tilt angle 90 Plate thickness 3 mm Absorber surface area 1.05 m2 Glass emissivity 0.9 Thickness of air gap 300 mm Absorber plate emissivity 0.4 Thickness of insulation 3 mm Glass transmissivity 0.85 Appl. Sci. 2021, 11, 6325 5 of 18 Air duct diameter 100 mm Absorber absorptivity 0.9 Glass cover thickness 1 mm Ratio between the solar wall and the floor area 0.23

2.1. Application Application of of the the Photoelectric Photoelectric Fan InIn the heatheat transfertransfer mode, mode, natural natural circulation circulation is adoptedis adopted for manyfor many heat heat collectors, collectors, such suchas the as Trombe the Trombe wall, whichwall, which has the has problem the problem of low of heat low transfer heat transfer efficiency. effic Itiency. is necessary It is nec- to essaryarrange tofans. arrange However, fans. However, the problem the problem of power of supply powershould supply beshould solved be and solved multiple and mul- AC tiplepower AC supply power lines supply should lines be should arranged. be arranged. At the same At time, the same manual time, control manual is not control convenient, is not convenient,which is difficult which to is synchronize difficult to synchronize with the weather, with the and weather, easy to causeand easy problems, to cause such prob- as lems,cold air such backflow. as cold air backflow. InIn view view of the above problems, a photoelectric fan was proposed in this paper. The fanfan located located in in the the lower lower vent vent can can be be driven driven by by photovoltaic photovoltaic (PV) (PV) plates, plates, which which are are installed installed outside (as (as shown shown in in Figure Figure 33),), withwith thethe voltagevoltage ofof 1212 VV andand thethe ratedrated powerpower ofof 66 W.W. TheThe fanfan is is used to force the hot air in the airair gap.gap. In particular,particular, the problem of inconvenient manual control during the operation process can be solved. The fan speed and the mass flowflow rate are det determinedermined by solar irradiance.

Figure 3. Diagram of PV board and fan.fan.

2.2. Temperature Temperature-Controlled-Controlled Damper Insteadinstead of the Traditional WoodenWooden DamperDamper The traditional traditional damper damper is is usually usually made made of ofwood wood and and operated operated manually. manually. Due Due to the to roughthe rough production production and andmoisture moisture deformation deformation of woods, of woods, etc., etc.,the situation the situation of inflexible of inﬂexible op- erationoperation or orunusable unusable for for dampers dampers may may occur occur in in service. service. Furthermore, Furthermore, due due to to the the manual operation, dampers areare oftenoften forgotten forgotten to to close close on on cloudy cloudy days days or or at at night. night. Cold Cold air air in thein the air airlayer layer enters enters the the room room through through dampers, dampers, resulting resulting in lowering in lowering the indoor the indoor air temperature. air tempera- It ture.is difﬁcult It is difficult for users for to users accurately to accurately control the control opening the andopening closing and time closing due totime the due variability to the variabilityof the outdoor of the climate. outdoor The climate. electric The damper electric can damper solve thecan problem solve the of problem automatic of automatic operation, operbut itation, has thebut disadvantage it has the disadvantage that the upper that and the lowerupper damper and lower cannot damper be connected. cannot be connected.The temperature-controlled damper proposed in this study can solve the above problems.The It is temperature made of metal-controlled and non-deformation. damper proposed Meanwhile, in this study the dampercan solve can the be above controlled prob- automatically according to the temperature. The temperature sensing bulb is mounted on lems. It is made of metal and non-deformation. Meanwhile, the damper◦ can be controlled automaticallythe outlet, as shown according in Figure to the4 .temperature. When the outlet The temperaturetemperature issensing over 20 bulbC, is the mounted bulb starts on theand outlet, the level-arm as shown is moved in Figure from 4. a When vertical the position outlet totemperature an inclined is position. over 20 Then,°C ，the the bulb inlet startands outlet and the damper level- arearm pushed is moved by thefrom connecting a vertical rod.position Therefore, to an inclined the function position. of opening Then, and closing dampers can be achieved simultaneously. The higher the temperature is, the the inlet and outlet damper are pushed by the connecting rod. Therefore, the function of further the movement distance of the damper is. opening and closing dampers can be achieved simultaneously. The higher the temperature is, the further the movement distance of the damper is. Appl. Sci. 2021, 11, x FOR PEER REVIEW 6 of 19 Appl. Sci. 2021, 11, 6325 6 of 18

Appl. Sci. 2021, 11, x FOR PEER REVIEW 6 of 19

Figure 4. The photo and operation principle of temperature-controlled damper. Figure 4. The photoFigure and 4. The operation photo and operationprinciple principle of temperature of temperature-controlled-controlled damper. damper. 3. Thermal Characteristics Analysis of the Improved Solar Wall 3. Thermal Characteristics Analysis of the Improved Solar Wall To investigate the thermal performance of this passive house, experiments were per- To investigate the thermal performance of this passive house, experiments were 3. Thermal Characteristicsformed. As Analysisshown in Figure of the 5, the Improved measured param Solareters Wall of solar walls included surface performed. As shown in Figure5, the measured parameters of solar walls included surface To investigatetemperaturetemperature the thermal ofof plates,plates, performance velocityvelocity in in air airof gap, gap,this inlet inlet passive and and outlet. outlet. house, Indoor Indoor experiments measurement measurement parameters were parame- per- formed. As showntersare in mainly areFigure mainly indoor 5, indoor the air temperature,measured air temperature, relativeparam relative humidity,eters humidity, of heatsolar ﬂowheat walls densityflow includeddensity and black and surface globeblack globe temperature. The temperature and black globe temperature test points are located temperature of plates,temperature. velocity The in temperature air gap, inlet and black and globe outlet. temperature Indoor test measurement points are located parame- in the incenter the center of the of room. the room. All data All weredata were recorded recorded every every 10 min. 10 min The. The measuring measuring instruments instruments can ters are mainly indoorcanbe found be foundair in temperature, Table in Tab5. le 5. relative humidity, heat flow density and black globe temperature. The temperature and black globe temperature test points are located in the center of the room. All data were recorded every 10 min.outdoor The measuring instruments

can be found in Table 5. corridor outdoor rest room kitchen

indoor outdoor living room

corridorbed room bed room outdoor rest room kitchen temperature black globe temperature temperature velocity solar irradiance surface temperature heat flow density

indoor (a) layout of test points. living room

bed room bed room

temperature black globe temperature temperature velocity solar irradiance surface temperature heat flow density

(a) layout of test points.

(b) installation of sensors.

Figure 5. Schematic diagram of mea measuringsuring point arrangement in the passive solar house.house.

Table 5. Monitored data and technical specification of measuring instruments.

Monitored Parameters Instrument Name Accuracy Photos JTNT-B Surface temperature and heat ±0.1 °C Temperature flow ±0.01 W/m2 test system

(b) installation of sensors. Figure 5. Schematic diagram of measuring point arrangement in the passive solar house.

Table 5. Monitored data and technical specification of measuring instruments.

Monitored Parameters Instrument Name Accuracy Photos JTNT-B Surface temperature and heat ±0.1 °C Temperature flow ±0.01 W/m2 test system

Appl. Sci. 2021, 11, x FOR PEER REVIEW 8 of 21

Appl. Sci. 2021, 11, x FOR PEER REVIEW 8 of 21 Appl. Sci. 2021, 11, 6325 7 of 18 Appl. Sci. 2021, 11, x FOR PEER REVIEW 8 of 21 JTNT-B Appl.Surface Sci. 20 temperature21, 11, x FOR PEER and REVIEW heat ±0.1 °C 8 of 21 TemperatureJTNT-B Surface temperatureflow and heat ±0.01±0.1 W/m °C 2 Table 5. Monitored dataTemperaturetest and system technical speciﬁcation of measuring instruments. JTNT-B 2 Surface temperatureflow and heat ±0.01±0.1 W/m °C Monitored ParametersTemperature Instrumenttest system Name Accuracy Photos JTNT-B 2 Surface temperatureflow and heat ±0.01±0.1 W/m °C Temperaturetest system 2 flow JTNTJTNT-B-B ±0.01◦ W/m SurfaceAir temperature temperature and and relative heat TR-72U Temperaturetest system and humidity re- ±0.1 ±0.1C °C Surface temperature and heat ﬂow TemperatureTemperature ±0.01 W/m2 2 flow test system ±0.01 W/m AirAppl. temperature Sci. 20humidity21, 11, xand FOR relative PEER REV IEWTR -72U Temperaturetestcorder system and humidity re- ±0.1±1% °C 7 of 19

Air temperaturehumidity and relative TR-72U Temperaturecorder and humidity re- ±0.1±1% °C

humidity corder ±1% Air temperatureAir temperature and relative and relative TR-72U TemperatureTR-72U Temperature and humidity and re- ±0.1 ±0.1◦C °C

humidityhumidity humiditycorder recorder ±1%±1% Air temperatureSolar irradiance and relative TR-72U Temperature and humidity re- ±±0.11 W /m°C 2 Air temperature and relative TR-72U TemperatureE-log and humidity re- ±0.1 °C Air temperaturehumidity and relative corder ±0.0±1%1 m /s2 Solar irradiancehumidity Outdoor weathercorder station ±1 W/m±1% humidity E-log ±0.1 °C Air temperature and relative ±0.01 m/s 2 2 Solar irradianceSolar irradiance Outdoor weather station ±1 W/m±1 W/m humidity E-E-loglog ±0.1 °C Air temperatureAir temperature and relative and relative ±0.01±0.0 m/s1 m/s2 2 SolarSolar irradiance irradiance Outdoor weather station ±1 W±1/m W /m humidity Outdoor weatherE-logE- log station ±0.1 ◦C Air Airtemperature temperaturehumidity and and relative relative ±0.0±0.1±0.01 m°C/s1 m/s Solar irradiance OutdoorOutdoor weather weather station station ±1 W/m2 humidityhumidity E-log ±0.1±0.1 °C °C

Air temperature and relative KANOMAX-6004 ±0.01 m/s Air velocity Outdoor weather station ±0.01 m/s humidity HotKANOMAX-wireKANOMAX-6004 anemometer-6004 ±0.1 °C Air velocityAir velocity KANOMAX-6004 ±0.01±0.0 m/s1 m/s Hot-wire anemometer Air velocity HotKANOMAX-wire anemometer-6004 ±0.01 m/s Air velocity Hot-wire anemometer ±0.01 m/s HotKANOMAX-wire anemometer-6004 Air velocity ±0.01 m/s Hot-wire anemometer KANOMAX-6004 Air velocity FLIRFLIRFLIR T440 T440 T440 ±0.0◦ 1 m/s temperaturetemperaturetemperature field field ﬁeld Hot-wire anemometer ±1 C±1 °C±1 °C InfraredInfraredInfraredFLIR thermal thermal thermalT440 imager imager imager temperature field ±1 °C

InfraredFLIR thermal T440 imager

temperature field ±1 °C Infrared thermal imager By the uncertaintyFLIR T440 analysis, in the present study, the uncertainties in the outlet air By the uncertainty analysis, in the present study, the uncertainties in the outlet air temperature field ±1 °C temperature,By the Infrareduncertainty air massthermal analysis, flowrate imager in and the thermal present e ffistudy,ciency the are uncertainties equal ±4.8%, in±0.026 the outlet% and air±5.8% temperature,temperature, air mass airFLIR massflowrate T440 ﬂowrate and thermal and thermal efficiency efﬁciency are equal are ±4.8%, equal ±0.026±4.8%, % and±0.026 ±5.8% % and temperature field forBy forced the uncertainty convection. analysis, in the present study,±1 the °C uncertainties in the outlet air ±5.8% forInfrared forced thermal convection. imager temperature,for forced convection. air mass flowrate and thermal efficiency are equal ±4.8%, ±0.026 % and ±5.8% By the uncertainty analysis, in the present study, the uncertainties in the outlet air for forced3.1. Effect convection. of Solar Walls on the Indoor Thermal Environment and Energy Consumption temperature,3.1. Effect air of mass Solar fl Wallsowrate on theand Indoor thermal Thermal efficiency Environment are equal and ±4.8%, Energy ±0.026 Consumption % and ±5.8% 3.1. EffectBy the of uncertaintySolar Walls on analysis, the Indoor in Thermalthe present Environment study, the and uncertainties Energy Consumption in the outlet air for forcedToTo convection. analyze analyze the the heating heating and and cooling cooling effect effect of of solar solar walls walls under under extremely extremely climate climate temperature,3.1. EffectTo analyze of Solar air mass theWalls heating fl onowrate the Indoorand and cooling thermal Thermal effect e Environmentfficiency of solar are equalandwalls Energy ±4.8%, under Consumption ±0.026 extremely % and climate ±5.8% weather,weather,By the uncertainty the the monitoring monitoring analysis, data data ofin ofthreethe three present hottest hottest study, days days in the summe in uncertainties summerr (from (from 29 in Augthe 29 ustoutlet August to 31air toAu- 31 forweather, forced the convection. monitoring data of three hottest days in summer (from 29 August to 31 Au- 3.1.temperature, gEffectAugust)Toust )analyze andof Solar aircoldest and mass theWalls coldest daysheating fl onowrate thedays(from Indoorand and (from 24 cooling Janthermal Thermal 24uary January effect toe Environmentffi 27ciency Janof to uarysolar 27 are January) ) andequal inwalls winter Energy ±4.8%, under in winterwere Consumption ±0.026 extremely selected. were % and selected. Theclimate ±5.8% indoor The gust) and coldest days (from 24 January to 27 January) in winter were selected. The indoor weather,airindoor temperature the air monitoring temperature of different data of of different rooms three hottestis rooms shown days is in shown Figurein summer in 6. Figure (from6. 29 August to 31 Au- 3.1.for forcedEffectTo analyze of convection. Solar theWalls heating on the Indoorand cooling Thermal effect Environment of solar andwalls Energy under Consumption extremely climate gairust temperature) and coldest of days different (from rooms 24 Jan uaryis shown to 27 in Jan Figureuary) in6. winter were selected. The indoor weather, the monitoring data of three hottest days in summer (from 29 August to 31 Au- 20 To analyze the heating800 and cooling32 effect of solar walls under extremely climate800 3.1.air temperature Effect of Solar of Walls different on the rooms Indoor is Thermal shown Environmentin livingFigure room 6. and east Energybed room Consumption west bed room living room gust east) and bed room coldest west days bed (fromroom 24 January32 to 27 January) in winter were selected. The800 indoor 20 weather, the monitoring800 data of three hottest days corridor in summer outdoor (from 29 August to 31 Au- living outdoor room aireast corridor bedtemperatureTo room analyze soalr west irradiance of bedthe different room heating700 rooms and coolingis shown effect living in Figure room of solar 6. east bedwalls room under solar west irradiance extremelybed room climate700 15 30 corridor outdoor solar irradiance 20 outdoor corridorgust) and soalr coldest irradiance days (from800 24 Jan) uary32 to 27 January) in winter were selected. The800700 indoor

700 2 ) 15 living room weather,east bed room the monitoringwest bed room data600 of three30 hottest living days room in summer east bed room (from west 29 bed Aug roomust to 60031 Au-2

) ) air temperature of different 2 rooms is shown in Figure 6. )

) corridor outdoor outdoor corridor soalr irradiance solar irradiance 2 20 ℃ 10 800700600 32 28 800700600

( gust) and coldest days (from 24 January to 27 January) in winter were selected. The indoor ℃ )

30 ( 15 ) living room east bed room west bed room 500 living room east bed room west bed room 500) ℃ 2 28 ( ) 10 ℃ 2 outdoor corridorair temperature soalr irradiance of different700600500 rooms( is shown corridor in Figure outdoor 6. solar irradiance 700600500 ) 20 800 32 800 15 5 400 ) 30 26 living room east bed room west bed room 400 ℃ living room east bed room west bed room ) 28 ( 2 10 ℃ ) ( 5 outdoor corridor soalr irradiance 700600500400 26 corridor outdoor solar irradiance 700600500400 2 ) 32 800 20 800 ) 300

15 Temperature 300 30 Temperature ℃ ) 28 24 living room east bed room west bed room ( 2 10 0 living room east bed room west bed room ℃ ) (

Solar irradiance (W/m irradiance Solar 26 400 Solar irradiance(W/m Solar

Temperature Temperature 300 5 400300 500 2 outdoor corridor 600500 Temperature corridor outdoor solar irradiance 600 ) 0 soalr irradiance 700 200 24 700 200 Solar irradiance (W/m ) Solar irradiance(W/m

℃ 15 30

) 28 ( 10 ℃ 2

Temperature Temperature 300 300200 ( 22 200

26 400 ) 5 -5 400 Temperature 500 0 500600 24 600 1002

100Solar irradiance (W/m ) 22 Solar irradiance(W/m -5 )

℃ 28 200100

( 200

100 ℃ Temperature Temperature 10 300 26 400300 Temperature Temperature 5 400 ( 0 -10 500 0 24 20 500 0 Solar irradiance (W/m

22 Solar irradiance(W/m -5 22th 00:00 12:00 23th 00:00 12:00 24th 00:00 12:00 24:00 25th 00:00 12:00 26th 00:00 12:00 27th 00:00 12:00 24:00 -10 2001000 20 2001000 Temperature Temperature 300 300

Temperature Temperature 25th 00:00 12:00 26th 00:00 12:00 27th 00:00 12:00 24:00 05 22th 00:00 12:00 23th 00:00 12:00Time 24th 00:00 12:00 24:00 400 2426 Time 400 Solar irradiance (W/m -5 22 Solar irradiance(W/m -10 0 20 Time 0 Time 200100 25th 00:00 12:00 26th 00:00 12:00 27th 00:00 12:00 24:00 200100 Temperature Temperature 22th 00:00 12:00 23th 00:00 12:00 24th 00:00 12:00 24:00 300 300

(a) in winter Temperature (b) in summer 0 2224 -5 Solar irradiance (W/m -10 Time 1000 20 Time 1000 Solar irradiance(W/m 22th 00:00 12:00 23th 00:00 12:00FigureFigure 24th 6. 00:00 6. VariationVariation 12:00 24:00 of of indoor indoor200 air air temperature temperature25th 00:00 in in 12:00the the passive passive26th 00:00 solar solar12:00 house 27th house. 00:00. 12:00 24:00 200 -5 22 Time -10 Time 0 20 0100 22th 00:00 12:00 23th 00:00 12:00 24th 00:00 12:00 24:00 100 25th 00:00 12:00 26th 00:00 12:00 27th 00:00 12:00 24:00 As shown in Figure 6a, during the winter, the Timeindoor air temperature was above 10 -10 Time 0 20 0 22th 00:00 12:00 23th 00:00 12:00°C 24th because 00:00 12:00 of 24:00the passive heating of25th the 00:00 solar 12:00 26thwall. 00:00 While 12:00 27ththe 00:00 outdoor 12:00 24:00 temperature fluctu- Timeated between −5.9 °C and 6.6 °C , the indoor air temperatureTime of living room and bedrooms was nearly the same under the heating effect of solar walls, which fluctuated between 9.2 °C and 15.3 °C . Due to the less direct heat gain, the temperature of the corridor was much lower than the south room, in the range of 7.1–9.8 °C . During the summer, the color of the absorber board changed to white and dampers were closed to prevent heat transfer between the air channel and indoor air. As shown in Figure 6b, the outdoor air temperature fluctuated between 20.5 °C and 31.2 °C during the testing period. Under the passive cooling, the air temperature of the rooms facing south Appl. Sci. 2021, 11, 6325 8 of 18

As shown in Figure6a, during the winter, the indoor air temperature was above 10 ◦C because of the passive heating of the solar wall. While the outdoor temperature fluctuated between −5.9 ◦C and 6.6 ◦C, the indoor air temperature of living room and bedrooms was nearly the same under the heating effect of solar walls, which fluctuated between 9.2 ◦C and 15.3 ◦C. Due to the less direct heat gain, the temperature of the corridor was much lower than the south room, in the range of 7.1–9.8 ◦C. Appl. Sci. 2021, 11, x FOR PEER REVIEW 8 of 19 During the summer, the color of the absorber board changed to white and dampers were closed to prevent heat transfer between the air channel and indoor air. As shown in Figure6b, the outdoor air temperature fluctuated between 20.5 ◦C and 31.2 ◦C during the(living testing room period. and two Under bedrooms) the passive was in cooling, the range the of air 25 temperature–26.6 °C. By contrast, of the rooms the air facing tem- ◦ southperature (living of the room corrido andr two was bedrooms) lower, varying was infrom the 23.9 range to of26.9 25–26.6 °C. C. By contrast, the air ◦ temperatureThe solar of wall the corridorhas an obvious was lower, effect varying on increasing from 23.9 indoor to 26.9 temperatureC. and reducing energyThe consumption solar wall has in an winter. obvious Experiments effect on increasing were carried indoor out temperature to determine and the reducing winter energyheating consumptioneffect of the color in winter.-changing Experiments solar wall under were carriedclear weather. out to determine the winter heatingThe effect color of-changing the color-changing solar wall belongs solar wall to a under type of clear flat weather. solar air collector. The thermal efficiencyThe color-changing (η) can be obtained solar as wall the belongs ratio of tothe a useful type of energy flat solar (heat air gained) collector. by The the thermalflowing efficiencyair to the amount (η) can beof obtainedtotal solar as energy the ratio incident of the on useful the energyabsorber (heat surface gained) area by at theany flowing time as air to the amount of total solar energy incident on the absorber surface area at any time as presented as follows: presented as follows: mc푚푐p(푝T(out푇표푢푡− T−in)푇푖푛) η휂 == (1)(1) A퐴· G⋅ 퐺 The air mass flowrate m at the end of the hot air passage duct can be determined as: The air mass flowrate m ̇ at the end of the hot air passage duct can be determined as:

m푚==ρA휌f퐴u푓푢 (2)(2)

The measured outlet air temperature and air velocityvelocity of thethe collectorcollector areare shownshown inin Figure7 7a.a. BasedBased onon thethe experimentalexperimental datadata andand equations,equations, the the heat heat supplied supplied by by solar solar walls walls isis shownshown inin FigureFigure7 7b,b,the the average averagedaily dailyheat heat output outputof of the the color-changing color-changing solar solar wall wall is is 1.081.08 MJMJ perper unitunit ﬂoorfloor areaarea onon clearclear daysdays inin winter.winter. TheThe averageaverage thermalthermal efﬁciencyefficiency ofof thethe solarsolar wall is 56.8%.

500 1.2 60 400

Velocity (m/s) Outlet air temperature (℃) 300 ） 200 2 1.0 50 100 0 W/m 1 （ 0.8 40 Q 2 3 0.6 30 4 5

Velocity(m/s) 6 0.4 20 7

8 Outletair temperature (℃) 0.2 10 9 20:40 0.0 0 16:30 0:00 12:00 0:00 12:00 0:00 12:00 0:00 12:00 0:00 12:00 0:00 12:20 8:10 Time 4:00 Hour

(a) (b)

Figure 7.7. (a)) OutletOutlet airair temperaturetemperature andand airair velocityvelocity ofof thethe collectorcollector ((bb)) HeatHeat outputoutput ofof thethe solarsolar wall.wall.

The application application of of solar solar walls walls is ismainly mainly reflected reﬂected in reducing in reducing the annual the annual energy energy con- consumptionsumption of buildings. of buildings. Taking Taking the theexperimental experimental solar solar house house in Dalian in Dalian as an as example, an example, the theapplication application effect effect of solar of solar walls walls is quantitatively is quantitatively analyzed. analyzed. According to the climate data of DalianDalian and thethe thermalthermal parametersparameters ofof thethe referencereference building, the annual heating demand of the solar househouse isis 466.5466.5 MJ.MJ. AmongAmong them,them, thethe auxiliary heatheat sourcesource is is the the infrared infrared heat heat radiation radiation plate plate with with the the power power of 2100of 210 W,0 andW, and the consumptionthe consumption of the of auxiliarythe auxiliary heat heat source source during during the heating the heating period period is 129.2 is 129.2 MJ. Meanwhile, MJ. Mean- while, the internal heat gain is 44.32 MJ. According to the average sunshine hours in winter in the Dalian area, the average heating quantity of the solar wall in the whole heating period is 145.8 MJ. The attenuation effect of solar walls on the annual heating energy consumption is shown in Figure 8. Appl. Sci. 2021, 11, 6325 9 of 18

the internal heat gain is 44.32 MJ. According to the average sunshine hours in winter in the Dalian area, the average heating quantity of the solar wall in the whole heating period is Appl. Sci. 2021, 11, x FOR PEER REVIEW 9 of 19 145.8 MJ. The attenuation effect of solar walls on the annual heating energy consumption is shown in Figure8.

(a) Annual heating demand without solar walls

(b) Annual heating demand with solar walls

FigureFigure 8. 8.AnnualAnnual heating heating demand demand under under solar solar walls walls heating heating..

It Itcan can be be seen seen that that the the solar solar wall wall has has a asignificant signiﬁcant effect effect on on reducing reducing annual annual heating heating energyenergy consumpt consumption.ion. The The calculation calculation shows shows that that the the solar solar heating heating guarantee guarantee rate rate of of the the solarsolar house house is is62.8%. 62.8%. According According to tothe the annual annual energy energy consumption consumption analysis, analysis, the the energy energy-- savingsaving rate rate of of the the solar solar wall wall can can reach reach 58.8%. 58.8%.

3.2.3.2. Thermal Thermal Characteristic Characteristic of ofthe the Photoelectric Photoelectric Fa Fann TheThe mass mass flow flow rate rate of of the the air air gap gap is isan an important important factor factor to to determine determine the the thermal thermal efficiencyefficiency of of the the color color-changing-changing solar solar wall. wall. The The mass mass flow flow is isinfluenced influenced by by the the air air velocity, velocity, damperdamper area area and and the the position position of of the the control control damper. damper. In In this this case, case, the the positio positionn of of the the control control damper is ignored and the damper is in a fixed position, with the damper open area of 0.008 damper is ignored and the damper is in a fixed position, with the damper open area of m2. The influence of air temperature is also ignored. As the fan is driven by photovoltaic 0.008 m2. The influence of air temperature is also ignored. As the fan is driven by photo- panels, the wind speed is an unsteady value, which is varied with the solar irradiance. voltaic panels, the wind speed is an unsteady value, which is varied with the solar irradi- Therefore, the primary factor to characterize the thermal properties of the solar wall is to ance. Therefore, the primary factor to characterize the thermal properties of the solar wall determine the mass flow rate and velocity in the air gap. is to determine the mass flow rate and velocity in the air gap. The relationship between variables of fluid flow can be analyzed by dimensional anal- The relationship between variables of fluid flow can be analyzed by dimensional ysis. The representational correlation of the average velocity of the air layer is determined analysis. The representational correlation of the average velocity of the air layer is deter- based on the π theorem. mined based on the π theorem. The heat transfer involving motion in the air gap is caused by the photoelectric fan and the temperature difference. Factors influencing the air velocity u include thickness of the air gap 훿, height of the air gap H, the solar irradiance qi, the coefficient of thermal expansion 훽, thermal conductivity 휆, the kinematic viscosity coefficient 휈, air density휌, the thermal diffusivity a and the gravitational acceleration g (Equation (3)) [36]. Appl. Sci. 2021, 11, 6325 10 of 18

The heat transfer involving motion in the air gap is caused by the photoelectric fan and the temperature difference. Factors influencing the air velocity u include thickness of the air gap δ, height of the air gap H, the solar irradiance qi, the coefficient of thermal expansion β, thermal conductivity λ, the kinematic viscosity coefficient ν, air density ρ, the thermal diffusivity a and the gravitational acceleration g (Equation (3)) [36].

u = f (δ, H, qi, β, λ, ν, ρ, a, g) (3)

In the above 10 variables, the fundamental dimension number is 4. Four repeated variables are selected, respectively:

[ρ] = ML−3 [β] = Θ−1 [ν] = L2T−1 [H] = L (4)

The dimensionless parameter πi[ i : 1 ∼ 6] is written by the unknown exponent, and the dimension formula is as follows.

 −3 w1 −1 x1 2 −1 y1 z1 −1  [π1] = (ML ) (Θ ) (L T ) (L) (LT ) = 1  x y  −3 w2 −1 2 2 −1 2 z2  [π2] = (ML ) (Θ ) (L T ) (L) (L) = 1  w3 − x3 y3 z  [π ] = (ML−3) (Θ 1) (L2T−1) (L) 3 (MT−3) = 1 3 (5) −3 w4 −1 x4 2 −1 y4 z4 −3 −1  [π4] = (ML ) (Θ ) (L T ) (L) (MLT Θ ) = 1  w x5 y  [π ] = (ML−3) 5 (Θ−1) (L2T−1) 5 (L)z5 (L2T−1) = 1  5  −3 w6 −1 x6 2 −1 y6 z6 −2  [π6] = (ML ) (Θ ) (L T ) (L) (LT ) = 1

By the dimensional harmonious Equations, the value of each coefﬁcient is solved by:

 −1 1 1 π1 = ν H u = uH/ν = Re  −1 1  π2 = H δ = δ/H  −1 −3 3 1 3 3  π3 = ρ ν H qi = qi H /ρν −1 −1 −3 2 1 2 3 (6)  π4 = ρ β ν H λ = λH /ρβν  −1 1  π5 = ν a = a/ν = 1/Pr  −2 3 1 3 2 π6 = ν H g = gH /ν

According to Equation (6), the mathematical expression of the air velocity in the air gap is as follows,

uH δ q H3 λH2 gH3 δ gβq H4 δ Re = = f , i , , Pr, = f ( , i , Pr) = f , Ra∗ (7) ν H ρν3 ρβν3 ν2 H λν2 H

where the modiﬁed Rayleigh number Ra* is described as follows,

gβq l4 Ra∗ = i · Pr (8) λν2 Thus, the dependence of mass ﬂow rate on the solar irradiance and channel depth can be expressed by the relationship Equation (9),

δ c Re = a(Ra∗)b( ) (9) H where, Re is the Reynolds number, a, b, c is the weighted coefficient, δ is the channel depth, m; H is the channel height, m. For the experimental device, the ratio is a fixed value, δ/H = 0.133. Therefore, the mass flow rate Re can be characterized as a function of heat input, as shown in Equation (10),

Re = a(Ra∗)b (10) Appl. Sci. 2021, 11, 6325 11 of 18 Appl. Sci. 2021, 11, x FOR PEER REVIEW 11 of 19

8000Based on the experimental data, the results of a multivariate regression analysis can Experimental data Appl. Sci. 2021, 11, x FOR PEER REVIEWbe given in Fitting Figure correlation9. 11 of 19 7000 Re = 0.000129(Ra∗)0.658 (11) 6000

5000 * 0.658

8000 Re=0.000129(Ra ) Re 4000 Experimental data 7000 Fitting correlation 3000 6000 2000 5000 Re=0.000129(Ra*)0.658

Re 1000 4000 0 3000 0.0 5.0x1012 1.0x1013 1.5x1013 Ra 2000 1000 Figure 9. The relationship of Re and Ra. 0 0.0 5.0x1012 1.0x1013 1.5x1013 Ra 푅푒 = 0.000129(푅푎∗)0.658 (11)

Figure 9. The relationship of Re and Ra. FigurePhotoelectric 9. The relationship synchronization of Re and Ra .can be achieved by the photoelectric fan and the mass flow ratePhotoelectric in the air gap synchronization has a power function can be achievedrelation with by the the photoelectric solar irradiance. fan and the mass

ﬂow rate in the air gap has a power function relation∗ 0.658 with the solar irradiance. 3.3. Correlation Analysis of the Temperature푅푒 = 0 .Control000129( Damper푅푎 ) (11) 3.3.PhotoelectricThe Correlation opening Analysisdegreesynchronization of of the the damper Temperature can be is achievedrelated Control to Damperby the the outlet photoelectric air temperature. fan and Thethe masshori- flowzontal rate displacementThe in the opening air gap distance degree has a powerand of the the function damper air temperature relation is related withof tothe the outlet solar outlet damper irradiance. air temperature. were tested for The twohorizontal days, and displacement the experimental distance results and are the shown air temperature in Figure 10. of theAs shown outlet damper in Figure were 10, testedthe 3.3.horizontalfor Correlation two days,displacement Analysis and the of experimentaldistance the Temperature of the results temperature Control are shownDamper control in Figure damper 10 .is As consistent shown in withFigure the 10, outlettheThe air horizontal openingtemperature, displacementdegree and of itthe increases distancedamper with ofis therelated the temperature outlet to the temperature. outlet control air temperature. damper The distance is consistent The reaches hori- with zontalthethe longest displacement outlet when air temperature, the distance outlet temperatureand and the it air increases temperature reaches with 60 of°C the the, which outlet outlet temperature.is damper 32 cm. wereThe Thedamper teste distanced for is ◦ twoclosedreaches days, when and the the longestthe outlet experimental when temperature the outletresults is temperature lowerare shown than in reaches20 Figure °C . Therefore, 60 10.C, As which shown the istemperature 32in Figure cm. The 10,- dampercon- the ◦ horizontaltrolledis closed damper displacement when can the restrain outlet distance the temperature cold of the air temperatureinflow. is lower than control 20 damperC. Therefore, is consistent the temperature- with the outletcontrolled air temperature, damper can and restrain it increases the cold with air the inﬂow. outlet temperature. The distance reaches the longest when the outlet temperature reaches 60 °C , which is 32 cm. The damper is 70 0.014 closed when the outlet temperature is lower than 20 °C . Therefore, the temperature-con- Horizontal displacement distance

trolled 60damper Dampercan restrain open area the cold air inflow. 0.012 ) 50 0.010 2 70 0.014 40 Horizontal displacement distance 0.008 y=0.000004x1.933 60 Damper open area 0.012

30 0.006 ) 50 0.010 2

20 0.004 Damper(m area open 40 0.008 y=0.000004x1.933 10 1.933 0.002

Horizontal displacement Horizontal distance (mm) y=0.115x 30 0.006 0 0.000

2020 30 40 50 600.004 Damper(m area open Outlet air temperature (℃)

10 1.933 0.002 Figuredisplacement Horizontal distance (mm) 10. The relationship between they=0.115x outlet temperature and damper displacement distance. 0 0.000 Figure 10.The20 The comparison relationship30 between results40 ofthe the outlet heat50 temperature supplied60 and by manualdamper displacement damper and distance temperature-. controlled damperOutlet are shownair temperature in Figure (℃) 11. Figure 11 indicated that from 8:00 a.m. to 9:00 a.m.,The acomparison time lag of heatingresults of appeared the heat due supplied to the by delayed manual opening damper of and the manualtemperature damper.- controlledMeanwhile, damper between are shown 15:30 p.m.in Figure and 17:0011. Figure p.m., 11 due indicated to solar that radiation from 8:00 and a.m. other to weather 9:00 Figurea.m.,reasons, a 10. time Th theelag relationship airof heating supply between temperatureappeared the outlet due was totemperature the lower delayed than and theopening damper indoor displacementof air the temperature manual distance damper. and. the Meanwhile,artiﬁcial airbetween door did15:30 not p.m close. and in 17:00 time. p Therefore,.m., due to thesolar phenomenon radiation and of other cold weather air poured reasons,backwardThe thecomparison air and supply negative results temperature heat of the supply heat was occurred. suppliedlower than by By themanual contrast, indoor damper itair can temperature beand seen temperature that and the the heat- controlledartificial air damper door did are notshown close in inFigure time. 11. Therefore, Figure 11 the indicated phenomenon that from of cold8:00 a.m.air poured to 9:00 a.m., a time lag of heating appeared due to the delayed opening of the manual damper. Meanwhile, between 15:30 p.m. and 17:00 p.m., due to solar radiation and other weather reasons, the air supply temperature was lower than the indoor air temperature and the artificial air door did not close in time. Therefore, the phenomenon of cold air poured Appl. Sci. 2021, 11, x FOR PEER REVIEW 12 of 19 Appl. Sci. 2021, 11, x FOR PEER REVIEW 12 of 19 Appl. Sci. 2021, 11, 6325 12 of 18

backward and negative heat supply occurred. By contrast, it can be seen that the heat suppliedbackward by and the negativetemperature heat- controlledsupply occurred. damper Bywas contrast, always itpositive, can be seenwhich that solved the heatthe probsuppliedlem of by insufficient the temperature-controlledtemperature heating-controlled or reverse dampercirculation was to always some extent. positive, which solved thethe problemproblem of insufﬁcientinsufficient heatingheating oror reversereverse circulationcirculation toto somesome extent.extent.

Figure 11. The heat gain comparison of different dampers. Figure 11. The heat gain comparison of different dampers.dampers. 4.4. Thermal Thermal Performance Performance Optimization Optimization of of Solar Solar Walls Walls 4. Thermal Performance Optimization of Solar Walls ItIt is is found found that that the the thermal thermal efficiency efficiency of ofthe the current current solar solar wall wall is not is nothigh high by the by ex- the It is found that the thermal efficiency of the current solar wall is not high by the experimentalexperimental analysis. analysis. Therefore, Therefore, based based on on the the numerical numerical simulation, simulation, the the structure structure of of this this perimental analysis. Therefore, based on the numerical simulation, the structure of this solarsolar wall wall is is optimized optimized in in this this section. section. solar wall is optimized in this section. TThehe thermal thermal efficiency efficiency of of solar solar walls walls in in winter winter is is affected affected by by the the structural structural dimension dimension The thermal efficiency of solar walls in winter is affected by the structural dimension (aspect(aspect ratio, ratio, vent vent size, size, a airir channel channel thickness, thickness, etc.), etc.), absorber absorber materials materials and and curtain curtain angle, angle, (aspect ratio, vent size, air channel thickness, etc.), absorber materials and curtain angle, etc.etc. Therefore, Therefore, parametric parametric analysis analysis was was performed performed based based on on the the theoretical theoretical model. model. etc. Therefore, parametric analysis was performed based on the theoretical model. AA cover, cover, air air gap, gap, absorber absorber plate plate and and insulation insulation plate plate formed formed the the solar solar wall wall system. system. A cover, air gap, absorber plate and insulation plate formed the solar wall system. FigureFigure 12a 12a shows shows the the he heatat transfer transfer process process of of the the solar solar wall. wall. In In the the daytime, daytime, the the air air in in the the Figure 12a shows the heat transfer process of the solar wall. In the daytime, the air in the airair gap gap is is heated heated up byby thethe hothot absorberabsorber plate, plate, then then the the indoor indoor cold cold air air flows flows into into the the air gapair air gap is heated up by the hot absorber plate, then the indoor cold air flows into the air gapfrom from the the bottom bottom inlet inlet and and rises rises to theto the top top outlet outlet after after heating, heating, thus thus completing completing a cyclea cycle of ogapthef the heatfrom heat exchange the exchange bottom process. process. inlet and From From rises the the to perspective the perspective top outlet of of heatafter heat transfer, heating, transfer, the thus the heat completingheat transfer transfer process a pro-cycle cessoinf the in the solarheat solar exchange wall wall is complex, is process. complex, involving From involving the thermal perspective thermal conduction, conduction, of heat transfer, convection convection the and heat and radiation. transfer radiation. pro- The Thecessschematic schematic in the diagramsolar diagram wall of is the ofcomplex, the physical physical involving model model is thermal shown is shown inconduction, Figure in Figure 12a. convection 12a. and radiation. The schematic diagram of the physical model is shown in Figure 12a.

Figure 12. Heat transfer process (a) and thermal network model (b) of the solar wall. Figure 12. Heat transfer process (a) and thermal network model (b) of the solar wall. Figure 12. Heat transfer process (a) and thermal network model (b) of the solar wall. A thermal network for the physical model considered is shown in Figure 12b. Through A thermal network for the physical model considered is shown in Figure 12b. the above simpliﬁcations, combined with the thermal network model and assumption ThroughA thermal the above network simplifications, for the physical combined model with consideredthe thermal isnetwork shown model in Figure and 12b.as- conditions [28], heat balance equations of each component of the collector can be built. sumptionThrough conditionthe aboves simplifications,[28], heat balance combined equations with of eachthe thermalcomponent network of the model collector and can as- The heat balance equations from the thermal network at the points: besumption built. conditions [28], heat balance equations of each component of the collector can be built. The heat balancecover plate equations tg : q from= h the(t thermal− t ) + networkh (t − tat) the + hr points:t − t (12) The heat balance equationsgi fromgo theg thermala networkgi g fat the cgpoints:g s

qgi= h gog (t− t a )+ h gig ( t − t f )+ hr cgg ( t − t s ) (12) absorber platecover ts :plateqs = tg:hsu (tqs −= htf) ( +t−hsd t )+(ts h− ( tf) − + t )+hrcg hr t (s t− −t tg ))+ hrsg(ts − tso) (13) cover plate tg: gi gog a gig f cgg s (12) air gap t f : hsu As(ts − tf) + hsd As(ts − tf) + hgi Ag tg − tf)+hso Aso tso − tf) =mcp tf − tr1 (14) Appl. Sci. 2021, 11, x FOR PEER REVIEW 13 of 19

q=( ht− t )+( h t − t )+( hr t − t )+( hr t − t ) (13) absorber plate ts: s sus f sds f cgs g sgs so

Appl. Sci. 2021, 11, 6325 13 of 18 hAsuss(t− t f )+ hA sdss ( t − t f )+ hA gigg ( t − t f )+ hA sososo ( t − t f )=( mct pf − t r1 ) (14) air gap 푡푓:

NN N N hrttsg()()()()()() s− so+− htt so f − so = XjtNj so − YjtNj si − (15) insulation plate tso : hrsg(ts − tso) + hso(tf − tso) = X(j)tsojj==(00N − j) − Y(j)tsi(N − j) (15) insulation plate tso: ∑ ∑ j=0 j=0 TheThe values values of of the the parameters parameters were were obtained byby simulationsimulation using using the the MATLAB MATLAB software soft- warepackage. package. According According to the to formulae,the formulae, values values of the of parametersthe parameters were were obtained obtained by simulation by sim- ulationusing using the MATLAB the MATLAB software software package. package. Experiment Experiment data on data any givenon any day given were day selected were to selectedverify theto verify accuracy the accuracy of the model. of the The model. values The of values several of temperatureseveral temperature points were points obtained were obtainedby simulation, by simu andlation, the and comparison the comparison results areresults shown are inshown Figure in 13 Figure. 13.

12 50 Experimental data Experimental data Simulation data Simulation data

10 40

) )

℃ ℃ 8 30

6 20

Temperature( Temperature(

4 10

2 0 0:00 4:00 8:00 12:00 16:00 20:00 24:00 0:00 4:00 8:00 12:00 16:00 20:00 24:00 Time Time (a) Interface temperature of south wall (b) outlet temperature 16 Experimental data Simulation data

) ℃ 12

10 Temperature(

6 0:00 4:00 8:00 12:00 16:00 20:00 24:00 Time (c) indoor air temperature of the south room

FigureFigure 13. 13. ValidationValidation of ofsimulation simulation results results under under passive passive heating heating..

It Itcan can be beseen seen from from Figure Figure 13 that13 that there there was wasa very a verygood goodagreement agreement between between experi- ex- mentalperimental findings ﬁndings and simulation and simulation results. results. Average Average deviation deviation indices indiceswere adopted were adopted to deter- to minedetermine errors. errors. (1)(1) algebraicalgebraic average average deviation deviation::

1 훼푐 − 훼푚 휎푎푣푔 = 1∑ αc − αm (16) = 푛 훼푚 σavg ∑푛 (16) n n αm (2) average absolute deviation: (2) average absolute deviation: 1 훼푐 − 훼푚 휎푎푏푠 = ∑ | | (17) 푛1 α 훼−푚α 푛 c m σabs = ∑ (17) n n αm where αc and αm represent simulation and experimental values, respectively. Deviation analysiswhere resultsαc and areαm representsummarized simulation in Table and6. experimental values, respectively. Deviation analysis results are summarized in Table6.

Table 6. Difference between the measured value and simulated value.

Interface Temperature of The Average Deviation Outlet Temperature Indoor Air Temperature South Wall

σavg 10.5% 11.7% 5.4% σabs 12.7% 14.3% 6.4% Appl. Sci. 2021, 11, x FOR PEER REVIEW 14 of 19

Table 6. Difference between the measured value and simulated value.

Interface Temperature of The Average Deviation Outlet Temperature Indoor Air Temperature South Wall Appl. Sci. 2021, 11휎, 6325푎푣푔 10.5% 11.7% 5.4% 14 of 18

휎푎푏푠 12.7% 14.3% 6.4%

Table 5 shows the average deviation of three representative parameters. The good Table5 shows the average deviation of three representative parameters. The good agreement observed between the simulated and experimental values verified the correct- agreement observed between the simulated and experimental values veriﬁed the correct- ness and accuracy of the proposed model for further thermal design optimum studies. ness and accuracy of the proposed model for further thermal design optimum studies. Several factors that affect the thermal performance of the solar air collector mainly Several factors that affect the thermal performance of the solar air collector mainly are absorberare absorber materials, materials, structure structure size of size the of collector, the collector, such as such aspect as aspect ratio, vent ratio, size, vent etc. size, There- etc. fore,Therefore, based onbased the mathematicalon the mathematical model, parametricmodel, parametric analysis analysis about the about thermal the performancethermal per- optimizationformance optimization of the solar of wall the systemsolar wall is discussed system is asdiscussed follows. as follows.

4.1.4.1. EffectEffect ofof AbsorberAbsorber MaterialsMaterials onon thethe ThermalThermal PerformancePerformance of of Solar Solar Walls Walls TheThe commonly commonly used used materials materials for for absorber absorber boards boards are are galvanized galvanized iron iron sheet, sheet, stainless stain- steelless steel plate, plate, oxygenated oxygenate copper,d copper, aluminum, aluminum, paint paint and so and on. so The on. absorption The absorption rates arerates 0.23, are 0.82,0.23, 0.65, 0.82, 0.95, 0.65, and 0.95, 0.96 and respectively 0.96 respectively within within the temperature the temperature range ofrange 20–100 of 2◦0C.–100 Figure °C. Fig- 14 showedure 14 showed the thermal the thermal performance performance of the solarof the wall solar under wall under various various absorber absorber materials materials with anwith aspect an aspe ratioct of ratio 2. When of 2. the When material the material of the absorber of the plateabsorb waser plate galvanized was galvanized iron sheet, iron the outletsheet, temperature the outlet temperature and the heat and supply the heat were supply the minimum, were the within minimum, the range within of 15the− range23.5 ◦C of and15−2 0–803.5 °C W/m and 20.– The80 W/m absorption2. The absorption rate of paint rate andof paint aluminum and aluminum was approximately was approximately equal, asequal, was as the w thermalas the thermal efﬁciency. efficiency. The highest The highest outlet outlet air temperature air temperature reached reached 36 ◦C, 36 and °C, theand heatthe heat supply supply ranged ranged between between 0–370 0–370 W/m W/m2. Due2. Due to to a numbera number of of advantages, advantages, such such as as low low speciﬁcspecific gravity, gravity, good good thermal thermal conductivity, conductivity, less less corrosion, corrosion, easy easy processing processing and aand relatively a rela- cheaptively price,cheap aluminum price, aluminum is widely is widely used as used an absorber as an absorber plate material. plate material. Copper Copper is expensive. is ex- Stainlesspensive. steelStainless has somesteel has disadvantages, some disadvantages, such as local such corrosion, as local corrosion, low thermal low conductivity thermal con- andductivity large mass,and large etc. mass, etc.

FigureFigure 14. 14.Effect Effect of of ﬁn fin material material on on outlet outlet temperature temperature and and heat heat gain gain of of the the solar solar wall. wall.

4.2.4.2. EffectEffect ofof AspectAspect RatioRatio onon thethe ThermalThermal PerformancePerformance of of Solar Solar Walls Walls TheThe aspectaspect ratioratio isis thethe ratioratio ofof thethe height height andand width width ofof the the solar solar wall, wall, which which affects affects thethe volume volume ﬂow flow in in the the air air layer. layer. Under Under the the inﬂuence influence of of solar solar irradiance, irradiance, the the instantaneous instantaneous changechange curvescurves ofof thethe parametersparameters showshow aa cosinecosine change. change. AsAs shownshown inin FigureFigure 15 15,, asas thethe aspectaspect ratio ratio increased,increased, the theoutlet outlettemperature temperature and andheat heatsupply supplywere wereincreasing. increasing. Therefore,Therefore, thethe aspect aspect ratio ratio can can be be appropriately appropriately increased increased to improveto improve thermal thermal performance. performance. However, How- whenever, when the aspect the aspect ratio ratio was was larger larger than than 2, the 2, the variation variation range range of of the the outlet outlet temperature temperature and heat supply gradually decreased, and the increasing magnitude barely changed. Therefore, in practice, an optimal aspect ratio is between 2 and 3. In addition, under the condition of a given aspect ratio, the thermal performance can be improved by increasing ventilation quantity. Appl. Sci. 2021, 11, x FOR PEER REVIEW 15 of 19 Appl. Sci. 2021, 11, x FOR PEER REVIEW 15 of 19

and heat supply gradually decreased, and the increasing magnitude barely changed. and heat supply gradually decreased, and the increasing magnitude barely changed. Therefore, in practice, an optimal aspect ratio is between 2 and 3. In addition, under the Therefore, in practice, an optimal aspect ratio is between 2 and 3. In addition, under the Appl. Sci. 2021, 11, 6325 condition of a given aspect ratio, the thermal performance can be improved by increasing15 of 18 condition of a given aspect ratio, the thermal performance can be improved by increasing ventilation quantity. ventilation quantity.

Figure 15. Effect of shape ratio on outlet temperature and heat gain of the solar wall. FigureFigure 15.15.Effect Effect ofof shapeshape ratioratio onon outletoutlet temperaturetemperature and and heat heat gain gain of of the the solar solar wall. wall. 4.3. Effect of Vent Size on the Thermal Performance of Solar Walls 4.3.4.3. EffectEffect ofof VentVent SizeSize onon thethe ThermalThermal PerformancePerformance ofof SolarSolar WallsWalls The structure size of the vent affects the volume flow in the air gap. Figure 14 shows TheThe structurestructure sizesize ofof thethevent vent affectsaffects the the volume volume flow flow in in the the air air gap. gap. FigureFigure 14 14 shows shows the variation of volume flow and heat supply with the vent size. It can be seen that the thethe variationvariation ofof volumevolume flowflow andand heatheat supplysupply withwith thethe ventvent size.size. ItIt cancan bebe seenseen thatthat thethe volumevolume flow flow of of air air in in the the channel channel was was increased increased with with the the diameter diameter of of the the vent, vent, so so as as the the volume flow of air in the channel was increased with the diameter of the vent, so as the heatheat supply. supply. A A larger larger ventilation ventilation volume volume can can strengthen strengthen the the heat heat transfer transfer between between the the air air heat supply. A larger ventilation volume can strengthen the heat transfer between the air andand the the absorber absorber board, board, and and send send the the heated heated air air into into the the room. room. and the absorber board, and send the heated air into the room. AccordingAccording to to Figure Figure 16,16, the the inc increaserease of of vent vent diameter diameter would would contribute contribute to to improving improving According to Figure 16, the increase of vent diameter would contribute to improving thermalthermal efficiency. efficiency. However, However, the the strengthening strengthening effect effect of of heat heat supplied supplied by by the the solar solar wall wall thermal efficiency. However, the strengthening effect of heat supplied by the solar wall waswas not not obvious obvious when when the the vent vent diameter diameter was was larger larger than than 200 200 mm. mm. At At the the same same time, time, the the was not obvious when the vent diameter was larger than 200 mm. At the same time, the largerlarger size size of thethe ventvent maymay bring bring the the inconvenience inconvenience of of engineering engineering construction. construction. Therefore, There- larger size of the vent may bring the inconvenience of engineering construction. There- fore,in the in actual the actual design, design, the ideal the ideal diameter diameter of the of vent the vent should should be about be about 200 mm. 200 mm. fore, in the actual design, the ideal diameter of the vent should be about 200 mm.

FigureFigure 16. 16. EffectEffect of of vent vent size size on on volume volume flow flow and and heat heat gain gain of of the the solar solar wall wall.. Figure 16. Effect of vent size on volume flow and heat gain of the solar wall. 5.5. Conclusion Conclusionss 5. Conclusions ToTo solve solve the the proble problemm of of inconvenient inconvenient manual manual control control in the in theprocess process of operation, of operation, the To solve the problem of inconvenient manual control in the process of operation, the optimizedthe optimized color color-changing-changing solar solar wall wall with with rotatable rotatable shutters shutters and and automatic automatic control control componentsoptimized color was proposed-changing in solar this paper. wall A with quantitative rotatable study shutters was conducted and automatic for improving control the thermal performance of solar walls. Conclusions were drawn as follows. • Based on the monitoring, experimental data showed that the average daily heat output of the color-changing solar wall is 1.08 MJ per unit floor area on clear days in winter and the average thermal efficiency of the solar wall is 56.8%. Furthermore, the Appl. Sci. 2021, 11, 6325 16 of 18

thermal characteristic of the automatic control components was also carried out by ﬁeld monitoring and theoretical analysis. • Meanwhile, to improve the thermal performance of the solar walls system, thermal characteristic optimization analysis of the solar wall was also conducted based on the mathematical model. The structure dimensions and absorber materials were optimized. Optimization results showed that an optimal aspect ratio is between 2 and 3 and the ideal diameter of the vent is about 200 mm. The improved solar wall with color-changing absorber board and automatic control components proposed in this paper had a positive effect on reducing building energy consumption in cold areas, which presented the theoretical basis and technical support for renewable energy utilization.

Author Contributions: Conceptualization, X.Z. and J.Z.; methodology, X.Z. and J.Z.; software, X.Z.; formal analysis, J.Z., W.L. and R.L.; investigation, R.L. and W.L.; data curation, B.C.; writing— original draft preparation, X.Z.; writing—review and editing, J.Z.; visualization, J.Z.; supervision, X.Z.; project administration, R.L. and J.Z. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Natural Science Foundation of China (No. 51808506) and Key Specialized Research and Promotion Special Project (Science and Technology Targeted) in Henan province (No. 212102310573). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Data available on request. Conﬂicts of Interest: The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

Nomenclature

Symbols a the weighed coefficient A Absorber area, m2 2 Af Outlet area, m b the weighed coefficient c the weighed coefficient g acceleration due to gravity, =9.81(m/s2) G Solar irradiance (W/m2) h heat convection (W/m2 ◦C) H the channel height, m 2 ◦ hc heat convection between indoor air and interior surface (W/m C) 2 ◦ hrcg radiation heat transfer coefficient between cover plate and absorber plate (W/m C) 2 ◦ hrsg the radiation heat transfer coefficient between insulation plate and absorber plate (W/m C) L length unit (m) m mass flow rate, kg/s M Mass unit (kg) Pr Prandtl number q solar radiation intensity (W/m2) Ra Rayleigh number Re Reynolds number t temperature (◦C) T Unit of time(s) u air velocity, m/s Subscripts a outdoor air f air gap Appl. Sci. 2021, 11, 6325 17 of 18

fd/fu inlet/outlet g cover plate gi/go interior/exterior surface of cover plate out/in outlet/inlet r indoor air s absorber plate sd/su lower/upper surface of absorber plate si/so interior/exterior surface of south wall (insulation board) Greek symbol a the thermal diffusivity (◦C) δ thickness of the air gap β thermal expansion coefficient (K−1) ρ air density (kg/m3) η Thermal efficiency λ thermal conductivity θ tilt angle of the blind (◦) ν the kinematic viscosity coefficient πi The dimensionless parameter

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