A novel ANN-based approach to estimate heat transfer coefficients in radiant wall heating systems

Accepted Manuscript Title: A Novel ANN-Based Approach to Estimate Heat Transfer Coefficients in Radiant Wall Heating Systems Authors: Ozgen Acikgoz, Alican C ¸ ebi, Ahmet Selim Dalkilic, Aliihsan Koca, Gursel ¨ C ¸ etin, Zafer Gemici, Somchai Wongwises PII: DOI: Reference:

S0378-7788(16)31013-1 http://dx.doi.org/doi:10.1016/j.enbuild.2017.03.043 ENB 7468

To appear in:

ENB

Received date: Revised date: Accepted date:

29-9-2016 16-2-2017 13-3-2017

Please cite this article as: Ozgen Acikgoz, Alican C ¸ ebi, Ahmet Selim Dalkilic, Aliihsan Koca, Gursel ¨ C ¸ etin, Zafer Gemici, Somchai Wongwises, A Novel ANN-Based Approach to Estimate Heat Transfer Coefficients in Radiant Wall Heating Systems, Energy and Buildingshttp://dx.doi.org/10.1016/j.enbuild.2017.03.043 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

A Novel ANN-Based Approach to Estimate Heat Transfer Coefficients in Radiant Wall Heating Systems Ozgen Acikgoza,*, Alican Çebia, Ahmet Selim Dalkilica,*, Aliihsan Kocab, Gürsel Çetinb, Zafer Gemicib, Somchai Wongwises3 a

Heat and Thermodynamics Division, Department of Mechanical Engineering, Yildiz Technical University, Yildiz, Istanbul 34349, Turkey b

Mir Arastirma ve Gelistirme A.S., 34220 Istanbul, Turkey

c

Fluid Mechanics, Thermal Engineering and Multiphase Flow Research Lab. (FUTURE), Department of

Mechanical Engineering, Faculty of Engineering, King Mongkut’s University of Technology Thonburi, Bangmod, Bangkok 10140, Thailand

* Corresponding authors. Tel.: +90 212 3832821; fax: +90 212 3832914; E-mail address: [email protected] (O. Acikgoz). Tel.: +90 212 3832821; fax: +90 212 3833034; E-mail address: [email protected] (A.S. Dalkilic).

Highlights     

Experiments are conducted in an experimental chamber with a constant dimensions. ANN techniques are employed to study the radiant heating thermal behaviors. It is found that the Levenberg-Marquardt network gives the most successful data. The effect of supply water temperature on heat transfer coefficients is revealed. Through the ANN data correlations for heat transfer coefficients are derived.

Abstract This paper includes the validation of ANN solutions by reliable experiments to research the heat transfer characteristics in an actual size room in a laboratory. Experimental tests have been done in an experimental chamber at a constant height and a floor area. Heating through three different wall configurations is implemented during experiments. Furthermore, various ANN techniques in Matlab are employed to study the thermal behaviors of the problem with regard to the alterations of heat transfer coefficients. Backpropagation learning methods of Levenberg-Marquardt, Bayesian regularization, resilient backpropagation and scaled conjugate gradient with multilayer perceptron

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network are used in order to show the artificial intelligence’s predictability area. Reference temperatures for corresponding heat transfer coefficients, heated wall temperatures and supply water temperatures are assigned as input variables, while convective, radiative and total heat transfer coefficients are defined as outputs. In conclusion, developed and detailed ANN model predicted heat transfer coefficients very successfully in tolerable deviation proportions from experimental findings. Also, the influence of supply water temperature on these coefficients was revealed. Moreover, the estimations of the ANN approach have been compared with the radiant heating and cooling data in the literature and a strong consistency has been noticed. Keywords: Radiant heating; Heat transfer coefficients; convection; radiation; ANN; Enclosures. Nomenclature A

: area (m2)

AUST

: average unheated surface temperature (oC)

Ebi

: blackbody emissive power of examined surface (W/m2)

Fi-j

: view factor between the examined and j surfaces

Fs-j

: view factor between the radiant surface and j surfaces

F1-n

: view factor between the examined surface and the surroundings

H

: height of the enclosure (m)

hc

: convective heat transfer coefficient (W/m2K)

hr

: radiative heat transfer coefficient (W/m2K)

ht

: total heat transfer coefficient (W/m2K)

Ji

: thermal radiosity of examined surface (W/m2)

Jj

: thermal radiosity of j surface (W/m2)

L

: length of both dimensions of floor (m)

Qhr

: radiant heat transfer of heated wall (W)

Qr

: total radiative heat transfer (W)

qc

: convective heat flux (W/m2)

2

Ts, Ta, Tc, Tf, Top : temperature of heated wall surface, air, ceiling, floor, and operative temperature (oC) ΔT

: temperature difference between radiant heated wall and reference temperature at

corresponding heat transfer coefficients 1. Introduction In these days, radiant heating systems are prevalently being used in recently built buildings as well as in buildings of which their conventional heating and cooling systems have been improved. Because, these systems are capable of coming up with more desirable temperature distribution in buildings and also lowering air movements compared to conventional heating techniques via low temperature heating techniques. From this point of view, it is obvious that as well as lower amounts of exergy destruction, higher levels of energy efficiency due to the low temperature supply water temperatures are yielded. These benefits primarily result from the fact that radiant heating and cooling systems are generally performed regarding with renewable energy sources such as heat pumps and solar collectors. In radiant heating systems, the heating panels emit heat by both radiative and convective phenomena. Furthermore, decreasing temperature differences among surface and air temperatures, compared to the conventional heating choices, will make possible to improvement in thermal comfort due to decreased air movements in the enclosure. In addition, thermal emissivity of the panel surfaces, dimensions of the enclosure and also the thermal boundary conditions of the walls affect the heat transfer occurring among the enclosure’s surfaces. Because accurate execution of heat transfer coefficients in living places has had great effect on the determination of heating and cooling loads, thermal comfort and energy economics, it is an easily noticeable fact that radiative and convective phenomena that refer to radiative and convective heat transfer coefficients carry extreme significance in the procedure and sizing steps of radiant heating and cooling systems. In a great number of papers in the literature, the radiative heat transfer coefficient was ascertained approximately constant in these systems. From this point of view, it is clear that the parameter that has had the most importance in the sizing process and thermal comfort calculations of radiant systems is the convective heat transfer coefficient. Thus, the existing work has been performed so as to validate the heat transfer coefficient results of an experimental work, through Artificial Neural Networks (ANN)s. (ANN)s are computational data operation systems which are composed through the way of a biological brain's learning ability and processing approach. They are capable of learning through not

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only experimental but also numerical data that involve the effect of many parameters [1-4]. Therefore, (ANN)s have been utilized in many engineering areas thus far, and their application range is progressively expanding. In this study's context, it should be expressed that (ANN)s have been performed in many heat and mass transfer analysis. They suggest a novel path to investigate these systems which are affected by numerous parameters. Hence, the estimation of Nusselt numbers and also the convective heat transfer coefficients for a radiant wall heating system was performed by an ANN approach in this current work. Some of the studies over the heat transfer applications in the relevant studies were given in the next passages. Beausoleil-Morrison [5] has shown the influence of convective heat transfer coefficient correlations on the heating load estimates of buildings, by performing experiments in an insulated sample structures that contain radiant heating systems. Among numerical works employing different convective heat transfer coefficient equations, measurements through the test buildings have determined 8% difference. Furthermore, they concluded that building load was more sensitive to employed convective heat transfer coefficient correlations and the arranged set point of the room than building fabric thermal material goods and air infiltration. ASHRAE [6] have considered the convective modeling of surfaces in building energy simulation software as a noteworthy research subject. Moreover, Beausoleil-Morrison [7] pointed out that energy request and consumption would noticeably be influenced by the selection of convective heat transfer coefficient algorithm, and hence suggested a new technique for enhancing the surface convection. Besides, Le Dreau and Heiselberg [8] noticed that the convective heat transfer coefficient influenced on the peak cooling load in rooms too. Nonetheless, at the starting, convective heat transfer in buildings was considered by means of the correlations which were found with the statement that convective heat transfer indicated an inclination to indicate parallel behavior to free-edge insulated plates. Whereas the amount of experimental works carried out in real-size rooms were growing, it was perceived that air flow over surrounding surfaces, in spite of the fact that they were not heated or cooled, influenced the flow pattern on adjacent walls. Besides, since air flows over all surfaces, it influences the flow pattern in the entire enclosure. From this point of view, equations produced for free plates may not be properly used for natural convection complications in enclosures [9]. The latest significant experimental and numerical works implemented in enclosures that encompass the radiant wall issue are as follows: Min et al. [10] searched Rayleigh numbers between 109 to 1011 and with enclosure sizes 3.60 by 7.35 by 2.40 m, 3.60 by 7.35 by 3.60 m, and 3.60 by 3.60 by 2.40 m, proposed correlations for convective heat transfer coefficients. They were developed for non-ventilated environments. Unheated surfaces

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were preserved at constant temperature. Surfaces’ temperatures and heat fluxes given in the enclosure were determined. Radiation influences were taken into account too. While the surfaces’ temperatures which were unheated varied between 4.4oC and 21.1oC, temperatures of the floor surfaces varied between 24oC and 43.3oC and the temperature of the ceiling surface varied between 32.2oC and 65.6oC. Awbi and Hatton [11] studied free convection in two dissimilar enclosures. The enclosures' dimensions were 2.78 by 2.30 by 2.78 m and 1.05 by 1.01 by 1.05 m. One wall of the enclosures were evaluated as a "heat sink" by means of an air conditioner positioned in a small room beside the large enclosure. Opposite and adjacent walls to the "heat sink" wall were heated with impregnated flexible sheets that had a 200 W/m2 output. Thermoelements were located at inner and outer sides of the surfaces. Reference air temperature for wall heating system were found to be 100 mm from the heated surface and stated to it as the "undisturbed air temperature”, the temperature outside the thermal boundary layer, altenatively. Finally, temperature difference variant in the convective heat transfer coefficient and Nusselt number correlations were determined as the temperature difference between the surface and the undisturbed air temperature. Miriel et al. [12] have scrutinized the thermal efficiency of radiant ceiling panels having copper tubes with aluminum fins experimentally. It was determined that 1/3 of the cooling at the ceiling was by means of convection, and 2/3 of it via radiation. Furthermore, Strand and Petersen [13, 14] studied radiant heating and cooling systems using numerical methods. Rahimi and Sabernaeemi [15] experimentally examined radiative and convective phenomena in an enclosure with an under-floor heating system. In order to obtain a thermal map of both the internal and external surfaces, 104 thermocouples were positioned on the surfaces. Moreover, for calculating the radiation occurred between surfaces, a model was proposed and it was decided that 75-80% of the heat was conveyed by means of radiation from the floor to the surrounding surfaces. Awbi [16] depicted the outputs of a CFD work on the convective heat transfer coefficients at a heated wall, a heated floor and a heated ceiling. The researcher benefitted from some turbulence models: a standard k-ε model by wall functions and a low Reynolds k-ε model. The outputs were compared with the data calculated through two experimental chambers. Causone et al. [17] estimated the heat transfer coefficients, radiative, convective and total- within an experimental chamber that benefitted from a radiant ceiling under characteristic occupation situations in addition to a residential building condition. The outputs of them are in good agreement with those in open sources. Mhyren and Holmberg [18] focused on various heating systems via CFD softwares, related with the technique performed in the current study. Authors used a surface to surface radiation model and a k-ε turbulence model as well. As a result, radiant heating systems have been determined as the best suitable heating selection 5

regarding with comfort. Jeong and Mumma [19] investigated the capacity of cooling enhanced by way of mixed convection in mechanically aired spaces. The outputs of them have shown that the cooling capacity of the panel might be increased within the ratio range of 5-35%. Koca et al. [20] did an experimental work to calculate radiative, convective and total heat transfer coefficients in a chamber. The aim was to estimate the coefficients at various place configurations. Three different wall panel preparations and seven water flow temperatures within the range of 30-42oC were done. Cholewa et al. [21] indicated to calculate the heat transfer coefficients at the surfaces of cooled and heated radiant floors within a test room. Finally, authors declared that heat transfer coefficients of this area were larger than actual values by 10-30%. Chicote et al. [22] presented a study about the cooling capacity and the heat transfer coefficients for a cooled radiant ceiling, considering the sufficient thermal comfort deal in the experimental setup. They also concluded that heat transfer estimations in relation to the operative temperature as the unique temperature and using total coefficient are unsuitable, but evaluating radiation and convection distinctly is appropriate. Rahimi and Sabernaeemi [23] examined the percentage of radiative and convective heat transfer in the heat conveyed from the ceiling of a room to other surfaces, through an experimental enclosure which is included with a radiant ceiling heating circuit. Researchers calculated the both sides of the surfaces of the enclosure with 108 elements. Using the measured temperatures, first they calculated conductive heat transfer. Then, by the use of net-radiation method, the authors determined the radiation exchange between internal surfaces. Briefly, researchers reported that more than 90% of heat was conveyed via radiation from the heated surface. Karadağ [24] investigated the radiative, convective and total heat transfer coefficient in an enclosure cooled from its ceiling, with both theoretical and numerical approaches as well. The author calculated the radiative heat transfer at various surface emissivity, room dimensions and thermal boundary conditions. In conclusion, the author proposed new equations concerning with convective and total heat transfer in a room cooled from its ceiling. Khalifa [25] performed an intensive overview of two- and three-dimensional free convection, concentrating primarily on heat transfer in buildings. He indicated that the differences were around up to a factor of 5 for vertical surfaces, 4 for horizontal surfaces facing upward and 8 for horizontal-facing downward surfaces. Li et al. [26] considered free convection in a working office room under typical occupied conditions equivalent to a temperature difference of 1.5°C. In that investigation, Karadağ and Teke [27] calculated the amount of radiative and convective heat transfer coefficients in a room that was heated from its floor, in relation to room sizes and thermal situations of the room. Consequently, the authors determined that the proportion of heat transfer coefficients varied between 0.8 to 1.6 and this proportion increased with decreased temperature difference at the floor and increased at the walls and ceiling as well. Additionally, Karadağ and Teke [28] investigated the alteration of the Nusselt number with the Rayleigh number under the condition of 6

heating from the floor and insulated ceiling. The authors have also derived correlations that incorporate aspect ratio (H/W≤0.5 and H/W>0.5) into them. Though significant amount of experimental and numerical analysis exist over the heat transfer phenomena in radiant heated and cooled rooms in the relevant literature, an ANN-based detailed prediction method given in this study has not been developed so far. In this current work, initially, experimental investigations were carried out on radiant wall heating system in an experimental chamber built in a laboratory to obtain data in a stable environment. To acquire a sufficient number of data for an ANN study and to encompass the effects of different wall heating configurations to obtain a general behavior of the radiant wall heating, the tests were conducted at three different configurations and supply water temperatures. Afterward, validation of the experimental results with ANN case studies, conducted at the boundary conditions measured through the chamber, were performed. As a result, we progressed and performed various ANN models to predict the experimental and numerical validated results properly and also determine the most appropriate ANN model to predict heat transfer characteristics in real-size rooms heated by radiant wall heating systems. 2. Experimental Setup 2.1. The preparation of the test space The climatic test space was prepared to pretend several heating applications under many climatic situations. The climatic space used for the experiments was constructed to act out the probable structure and physical appearance of a actual size room (given in Fig.1a) as precisely as possible. The space, composing of 5 volumes enclosing the test chamber: ceiling (volume-1), floor (volume-4), exterior (volume-2), inner volume (volume-3) and studied volume (volume-5), is described by a floor area of 24 m2 (6.00 m × 4.00 m) and an internal height of 3.00 m. The wall sorts are determined as the sandwich type with polyurethane insulation between two layers that are made of sheet steel to increase the strength with its engagement and locking mechanism. The isolation thicknesses and the coefficient of thermal transmittance of walls for each zone were calculated in relation to Turkish Standard (TS) item 825 (thermal insulation requirements for buildings), shown in Table 1a [29]. The window, (115 cm × 160 cm) which overlooks the zone-2, is double-glazed and the door (82 cm × 204 cm) is single glazed with U-value of 2.20 W m-2 K-1 and 2.60 W m-2 K-1, correspondingly. Temperature, humidity and air velocity variety of the stated 4 volumes are given in Table 1b. 2.2. The radiant panel The radiant panel (Fig. 1b) that was arranged for current work contains four layers, that are drywall, aluminum foil, heating pipe serpentine and isolation; from inner to outer layers. The serpentine is 7

installed in the drywall. The thickness of the drywall layer is 15 mm whereas the panel insulation thickness is 30 mm. In addition, there is a 0.3 mm thick aluminum foil layer between the drywall and the insulation layer covering the slot that the serpentine is installed. The serpentine has cross-linked polyethylene (PEX) pipes with a 10.1 mm diameter and 150 mm pipe spacing. Expanded polystyrene (EPS) is evaluated as an insulation material that has a coefficient of thermal transmittance value of 0.035 W m-1 K-1 (at 10˚C). Main characteristics of tested radiant panels were given in Table 1c. The test room was built with the installation of 7 radiant wall panels (The sizes of the wall panel are 2.2 m x 1 m) that were fixed on the entire northward and westward walls. Two of them were placed on the northward wall at both sides of the window and five of them were placed on the westward wall (Fig. 2a). Figs. 2b, 2c and 2d show the dissimilar preparations of the heated panels: In case 1, two panels were mounted on the northward wall; in case 2, five panels were mounted on the westward wall and in case 3, seven panels were mounted on both northward and westward walls. 2.3. The hydraulic system of the experimental chamber The temperature of the water pumped to the panels can differ in relation to the heating season for dissimilar climatic conditions. A water preparing system was evaluated in the experiment space. By means of this system, water is circulated to the panels for all the 3 conditions so as to get more dependable outputs at the end of the investigation. As presented in Fig. 3a, the inlet water, that has access to the system through the tank (the water temperature is obtained using a chiller for the cooling case and using electric resistances for the heating case), initially reaches to a four-way valve. At this point, the four-way valve makes available a blend through a return pipeline. The mixed water temperature exits the four-way valve in order to be identical to the water inlet temperature and comes the pump to provide the necessary pressure. After the pump, the water reaches to a three-way valve. The aim of the three-way valve is to return excess of the fluid back in order to remain equal to the flow rate of the water in case the water that approaches from the pump has a higher flow rate than essential. Now, the fluid passes through the flow meter, where the volumetric flow rate is measured. After completing the cycle in the panels, the water comes to the four-way valve once more through the return line, and it is mixed with the water coming from the tank if required. 2.4. The measurement equipment The indoor air temperatures of the experiment space were measured by using K-type thermocouples (chromel-alumel) that are positioned vertically 10 cm, 110 cm, 170 cm and 250 cm above the floor and positioned in two dissimilar locations symmetrically in regard to the center of the chamber. In this manner, a more uniform and precise temperature distribution was obtained with the

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measurements taken. The relative humidity was measured at two points that are at the same place with thermocouples. The indoor humidity was measured via a sensor with a sensitivity of ±3.5%. The temperature of each unheated surfaces were measured from the middle point of the walls by type K thermocouples. Four thermocouples were positioned on the west facade wall on the same line at 1.5 m. Moreover, a thermocouple was mounted on the window surface. Three flow meters measured the water flow rate at the inlet of each panel group. The working temperature was measured by thermal comfort measurement device that was placed at the center of the chamber as presented in Fig. 3b. The data from the sensors were conveyed to the related signal conversion panels on PXI and saved in a computer. The data was recorded at intervals of 1 minute. The LabVIEW program, that permitted the diagrams of the data values to be observed instantaneously, was evaluated to use the data. The program makes available the occasion to arrange factors and automation as well. 2.5. The experimental technique The best dependable evaluates are those depend on measurements done in full scale experiment chambers. In current study, three cases were considered practically. For all the cases, the water flow rate and the environmental situations were fixed at specific values. The aim of existing work was to determine the heat transfer coefficients between the radiant wall panels and the chamber air. In relation to the EN 14240 standard [30], the measurements were performed under stabile conditions for at least three different temperature variations between the room air temperature and the average heating water temperature. Within the aim of the experimental works, seven different water supply temperatures were experienced for each case. The emissivity of the chamber surfaces and radiant floor surfaces was determined using an infrared thermal imaging camera and calibrated thermocouples. The surface temperature was determined via temperature sensors. At that point, the surface emissivity was changed in the pyrometer setup so as to get the equal temperature of the examined surface as achieved before by means of the temperature sensors [31]. All the air temperature sensors and the surface temperature sensors (K-type thermocouples) were calibrated and their accuracy was equal to 0.1 K. All the measured values by the use of the calibrated sensors were archived with 1 minute intervals. But the values of the heat transfer coefficients were calculated after the studied system obtained a stable state. It means that the investigated system in a stable state was described by physical properties which were fixed in time. 3. Theoretical Calculations In this section, the calculation steps followed in the determination of heat transfer coefficients have been presented. According to the measurements, in the first step, the total heat transfer is found by Eq. (1). 9

Q t = mh cp ΔT (1) Determination of the radiative heat transfer is a requirement for calculating the convective heat transfer. It should be stated that in the current work to calculate the radiative heat transfer, the net radiosity method has been performed. In current situation, the radiative heat transfer emitted from the heated wall to the surrounding surfaces is found by Eq. (2). Q r = Q11 + Q12 + Q13 + Q14 + Q15 + Q16

(2)

The total of view factors necessary for calculating the radiation is shown in Eq. (3). F11 + F12 + F13 + F14 + F15 + F16 = 1

(3)

According to Eq. (4) six dissimilar formulas which characterize the radiative heat transfer at each surface of the enclosure are obtained and solved by the program, Engineering Equation Solver (EES). Ebi −Ji 1−ε εAi

= ∑6j=1

Ji −Jj 1 Fij Ai

(4) Afterward, through J1, for the radiosity of heated wall is used in Eq. (5) and net radiation from this wall is determined. Qr =

Eb1− J1 1−ε εA1

(5) Furthermore, the reference temperature used for calculating the radiative heat transfer coefficient is the mean unheated surface temperature (AUST) and it is obtained by Eq. (6). 4

AUST = √∑nj=1(Fs−j TJ4 )

(6)

The radiative heat transfer coefficient is determined by Eq. (7). hr =

Qr A(Th − AUST)

(7)

Finally, the net radiative heat transfer through the radiant wall is calculated by Eq. (8). Qc = Qt − Qr (8)

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The convective heat transfer coefficient is determined by Eq. (9), while the reference temperature is the air temperature at the center of the chamber. Qc 𝑠 −Ta )

h𝑐 = A(T (9)

Similarly, the total heat transfer coefficient that is encompasses both radiative and convective phenomena in the enclosure is calculated by Eq. (10). ht = A

Qt h (T𝑠 −T𝑜𝑝 )

(10) 4. ANN Development Artificial neural networks showed their remarkable capability in various prediction applications. Their ability to learn new data and adaptive performance make them ideal for numerous practices. Physical problems with time consuming solution procedures or even problems without solutions can be solved swiftly and with high accuracy by using neural networks as long as the necessary data is available. Incomplete data can also be predicted by neural network due to its high generalization capability. Selection of correct methods and parameters, necessity of high number of data and lack of any exact procedure to define the neural network structure are the most pronounced drawbacks of this artificial intelligence technique. Especially, proper construction of neural network and selection of parameters are of great importance for an applicable network in real cases otherwise, developed network may over fit the existing training data which leads to the loss of the generalization ability. Seven input and three output parameters were selected to define the numerical results in neural network system. Inputs and outputs were Tw, Ts, Tfloor, Tceiling., Ta, Top, AUST and hr, hc, ht respectively. Since it was proven as a confident structure for prediction purposes, multi-layer perceptron (MLP) was selected in this study. Data according to the selected parameters were implemented into the network structure after going through a normalization process. In order to find the best neural network system that defines the numerical results, 120 network structures having one hidden layers were trained by different learning algorithms. Four different training algorithms namely LevenbergMarquardt, Bayesian regulation, resilient backpropagation and scaled conjugate gradient were used with purelin transfer function since dependence between input and outputs were strongly linear as observed from experimental results. It should also be noted that different neural network models

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were generated for different heating configurations. This approach was adopted in order to develop satisfying correlations for each case. One hidden layered MLP network structures were used in the analysis. It is inconvenient to use more than two hidden layers due to the high amount of computations. It is also found by researchers that using more than two hidden layers do not show better performance than the neural networks with lower hidden layers [32]. Neuron numbers in hidden layer varied between 1 and 20 for all training functions. Schematic representation of one hidden-layered neural network can be seen in Fig. 4. Initial values of weights and biases were determined by the method proposed by Nguyen and Widrow [33] each time for a new neural network. This method is found to decrease computation time especially when the hidden neuron numbers are high. Data division percentages for training, testing and validation sets were 75%, 15% and 15% respectively. Two different performance parameters were used in order to describe the success of the neural network. These were mean square error (MSE) and correlation coefficient (R) defined as follows: 1

MSE = n ∑i=1(fi − yi )2 (11) R=

∑i(fi −f̅)(yi −y ̅)

2 ∑i(fi −f̅) ∑i(yi −y ̅) 2

(12) where 𝑓𝑖 , 𝑦𝑖 , 𝑛 and 𝑦̅ represent predicted value, real value, pattern number and the mean value of real values respectively. 5. Results and Discussion 5.1. General interpretations In order to determine the heat transfer characteristics in an actual size room, experimental and ANN studies were performed. The results of the measurements acquired by applying three discrete wall heating configurations and different supply water temperatures, and thus the heat-transfer coefficients that were calculated via these parameters, are presented in Table 2. These results are an expanded version of the work of Koca et al. [20] with an individual case study number of 84 different measurements, which is substantially reasonable to be performed in an ANN approach. In addition to the 84 presented measurements and their results, as abovementioned, an ANN approach has also been implemented to ascertain a novel method to estimate the heat transfer characteristics of radiant wall heating systems. To achieve this purpose, among all learning 12

algorithms and 80 networks, Levenberg-Marquardt network with 17 neurons, 5 neurons and 19 neurons had the best performance values for configuration 1, 2 and 3 respectively. Neural networks with resilient backpropagation training algorithm have least performance values within all learning algorithms. Performance results of the corresponding networks and obtained linear correlations were presented in Table 3a and 3b respectively. 5.2. Heat transfer coefficients In the present study, the radiative, convective and total heat-transfer coefficient values for the heated radiant walls were determined by using an experimental chamber as well as a novel ANN approach. The results are detailed in Table 4. In Fig. 5, the ANN results of radiative heat transfer coefficients are compared with the experimental data. From the figures, it is evident that the radiative ANN results remain within 5% deviation interval, which can be seen as a very credible range. As extensively explained the study of Acikgoz [34], it can also be deduced from Figs. 8-10 that different radiant wall heating configurations in a room can slightly change radiative heat transfer coefficients owing to the change on view factor values and thus AUST. Nonetheless, an average radiative heat transfer coefficient value of 5.0 W/m2K is acquired through the ANN approach, which represents both three wall heating configurations. Fig. 6 demonstrate the convective heat transfer coefficient data obtained from the ANN approach. It is noticeable that the convective heat transfer coefficient estimations of the ANN work have had the maximum deviations of 5%, 5% and 30% from experimentally gained data, at wall configuration 1, 2 and 3, respectively. Slightly higher proportion of deviation that was only seen on particular and limited number of points in Fig. 13 could be attributed to possibly experimental errors which can be naturally faced in experimental studies. Hence, it is presumable that these errors may deviate estimations performed by ANN method as well. Furthermore, if the maximum deviation ratios from experimental data found in radiative and convective are compared, it is obvious that far less proportion of deviations exist not only due to the reasons explained in previous lines, but also because the radiative heat transfer coefficient is acquired by theoretical methods, in other words, via net-radiosity method. Fig. 7 reveal the comparison between the total heat transfer coefficient values determined by both methods. In radiant wall heating configurations 1, 2 and 3, maximum deviation proportions of 5%, 30% and 10% were noticed, respectively. It should be noted that, the ANN deviations in Fig. 15, which correspond to wall configuration 2, are at the highest ratio and may be accounted for completely different wall configurations in experimental case studies, and thus this may lead to deviations in ANN predictions. 13

Also, in Figs. 8 the influence of supply water temperature on heat transfer characteristics are examined. As seen in Fig. 17, the radiative heat transfer coefficient illustrates a very slight tendency to increase with increasing supply water temperature at all three wall heating configurations. It is clear that in Fig 18-19, the convective heat transfer coefficient shows an unchanging trend with ascending values of supply water temperature for wall configuration 1 and 2, whereas it demonstrates a diminishing inclination for wall configuration 3. Moreover, in Figs. 9 the variations of radiative, convective and total heat transfer coefficients with corresponding temperature difference values are illustrated. As seen in Fig. 20, the radiative heat transfer coefficient draws a slightly increasing trend line with increasing values of temperature difference (Ts-AUST). Fig. 9 indicates the change in convective heat transfer coefficient with temperature difference (Ts-Ta). It is obvious that at wall heating configurations 1 and 2, this coefficient draws an unchanging trend, although it shows a more scattered and a slightly decreasing tendency at wall configuration 3. This state may be accounted for unavoidable experimental errors in experimental measurements, which may result in a deviating influence on data obtained through ANN, as well. 5.3. Validation of the results From the data presented in the previous sub-section, it is clear that the ANN method progressed for radiant heating applications and explained in Section 4 has validated the experimental data. However, supporting the acquired data with recently published experimental and numerical data in the literature has always become a favorable criteria for comparison. To this end, recent radiant heating and cooling data have been gathered in Table 4. In terms of radiative heat transfer coefficients, it is obvious that there have been differences of 12%, 10%, 12%, and 8% between the average results of the present study and Causone et al. [17], Acikgoz [34], Cholewa et al. [21], and Chicote et al. [22], respectively. This shows that the radiative heat transfer phenomenon in an enclosure heated from its walls which is calculated by net-radiosity method in experimental and numerical works in the literature is also able to be estimated within a credible range through the ANN approach developed in the present paper. Also, for the convective heat transfer coefficient the results of the current paper were compared with the average data from Acikgoz [34] and Awbi and Hatton [11], and thus, average deviations of 29% and 11% were found between the relevant works and the ANN results of the present study, respectively. The deviations may be accounted for differences in wall heating arrangements in rooms and possibly confronted unavoidable experimental errors, as well. Though, as stated by Causone et al. [17] and Chicote et al. [22], the calculation method of the reference temperature for the total heat transfer coefficient has still been

14

a controversial task for researchers in this field, the data obtained from the present work were compared with relevant radiant heating and cooling applications. In this context, it was seen that difference ratios of 16%, 12%, and 6% existed between the results of this study and studies of Acikgoz [34], Cholewa et al. [21], and Chicote et al. [22], respectively. The deviations can be evaluated to be in a credible range and these differences between these works may be attributed to differences on the determination of reference temperature for this coefficient, and also even the differences on the calculation method for operative temperature which has been widely selected as the proper reference temperature. 6. Conclusion In this study, the heat transfer characteristics in an actual size room were investigated by comparing experimentally acquired data with ANN results. Experiments were conducted for a room which was heated through three different wall configurations for a constant height and a floor area. Furthermore, ANN studies were performed for tested room dimensions and heating configurations by selecting 7 input parameters and 3 outputs as radiative, convective, and total heat transfer coefficients. The conclusions reached from the present study are summed up with the following statements. 

Among various learning algorithms and networks, it was found that the Levenberg-Marquardt network with 17 neurons, 5 neurons, and 19 neurons provided the most successful results compared to the experimental data of the present work for wall heating configurations 1, 2 and 3, respectively.



From the ANN work, average heat transfer coefficient values of 5.0 W/m2K, 2.7 W/m2K, and 9.00 W/m2K were recommended for radiative, convective and total heat transfer coefficients, respectively.



Through the ANN investigation, 3 novel linear correlations for radiative, convective, and total heat transfer coefficients were derived and contributed to the literature.



Additionally, a great amount of experimental wall radiant wall heating data have been gained for the relevant literature.



It is also thought that the correlations derived under the abovementioned wall heating conditions can be beneficial for building energy simulation (BES) programs of which were proved by many researchers that substantially sensitive to convective heat transfer modeling.

Acknowledgement This study has been financially supported by Yildiz Technical University Scientific Research Projects Coordination Department, Project Number: 2015-06-01-KAP02. 15

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18

a)

b) Fig. 1. General view of the test room (a), and radiant panel (b)

19

a)

b)

c)

d)

Fig. 2. View of the radiant panels mounted to the test room (a), different arrangements of the wall panels Case 1 (b), Case 2 (c), and Case 3 (d)

20

a)

b) Fig. 3. Hydraulic circuit of the test system (a), and the measurement equipment (b)

21

Fig. 4. Schematic representation of one hidden-layered neural network 5,1

4,9

2

hr, ANN [W/m K]

5,0

4,8

4,7

4,6

4,5 4,5

4,6

4,7

4,8

4,9 2

hr, exp [W/m K]

22

5,0

5,1

a)

5,6

2

hr, ANN [W/m K]

5,4

5,2

5,0

4,8

4,8

5,0

5,2

5,4

5,6

2

hr, exp [W/m K]

b)

5,30

5,20

2

hr, ANN [W/m K]

5,25

5,15

5,10

5,05

5,00 5,00

5,05

5,10

5,15

5,20

5,25

2

hr, exp [W/m K]

5,30

c)

Fig. 5. Comparison between experimental and ANN results of radiative heat transfer coefficients for wall configuration 1 (a), 2 (b), and 3 (c)

3,2

2

hc, ANN [W/m K]

3,4

3,0

2,8

2,8

3,0

3,2 2

hc, exp [W/m K]

23

3,4

a)

3,2

2

hc, ANN [W/m K]

3,4

3,0

2,8

2,8

3,0

3,2

3,4

hc, exp [W/m2 K]

b)

2,4 2,2

1,8

2

hc, ANN [W/m K]

2,0

1,6 1,4 1,2 1,0 0,8 0,8

1,0

1,2

1,4

1,6

1,8

2,0

2,2

2,4

2

hc, exp [W/m K]

c)

Fig. 6. Comparison between experimental and ANN results of convective heat transfer coefficients for wall configuration 1 (a), 2 (b), and 3 (c) 8,8

2

ht , ANN [W/m K]

8,6

8,4

8,2

8,2

8,4

8,6 2

ht , exp [W/m K]

24

8,8

a)

10

2

ht , ANN [W/m K]

12

8

6

6

8

10

12

2

ht, exp [W/m K]

b)

8,2 8,0

7,6

2

ht , ANN [W/m K]

7,8

7,4 7,2 7,0 6,8 6,6 6,6

6,8

7,0

7,2

7,4

7,6

7,8

8,0

8,2

2

ht , exp [W/m K]

c)

Fig. 7. Comparison between experimental and ANN results of total heat transfer coefficients for wall configuration 1 (a), 2 (b) and 3 (c) 6,0 Configuration 1 Configuration 2 Configuration 3

2

hr, ANN [W/m K]

5,5

5,0

4,5

4,0 28

30

32

34

36

38

40

o

Tw [ C]

25

a)

4,0

3,5

2

hc, ANN [W/m K]

3,0

2,5

2,0

1,5 Configuration 1 Configuration 2 Configuration 3

1,0

0,5 28

30

32

34

36

38

40

o

Tw [ C]

(b)

12

10

2

ht , ANN [W/m K]

11

9

8

Configuration 1 Configuration 2 Configuration 3

7

6 28

30

32

34

36

38

40

o

Tw [ C]

c)

Fig. 8. The variation of ANN results of the radiative (a), convective (b) and total (c) heat transfer coefficient with supply water temperature 7 Configuration 1 Configuration 2 Configuration 3

2

hr, ANN [W/m K]

6

5

4

3 3

4

5

6

7 o

T [ C]

26

8

9

10

a)

6

4

2

hc, ANN [W/m K]

5

3

2 Configuration 1 Configuration 2 Configuration 3

1

0 3

4

5

6

7

8

9

10

o

b)

T [ C]

12

Configuration 1 Configuration 2 Configuration 3

10

2

ht, ANN [W/m K]

11

9

8

7

6 2

3

4

5

6

7

8

o

T [ C]

9

10

c)

Fig. 9. The change of the ANN radiative heat transfer coefficient results with temperature difference (Ts-AUST) (a), (Ts-Ta) (b), and (Ts-Top) (c)

27

Table 1 General assumptions on the model a) Controlled parameters in zones Ceiling

Floor

Facade Room

Interior Room

Temperature Range

-10˚C / +40˚C

+0˚C / +30˚C

-10˚C / +40˚C

+0˚C / +30˚C

Temperature Tolerance

± 0.5 ˚C

± 0.5 ˚C

± 0.5 ˚C

± 0.5 ˚C

Humidity Range

n/a

n/a

%35 / %85 RH

n/a

Humidity Control Steps

n/a

n/a

%1

n/a

Humidity Tolerance

n/a

n/a

± % 0.5 RH

n/a

Air Velocity

n/a

n/a

0.5 – 5 m/s

n/a

b) Coefficient of thermal transmittance of surfaces U (W/m2K)

Surfaces Ceiling

0.3

Floor

0.4

North Wall

0.4

West Wall

0.4

East Wall

0.8

South Wall

0.8 c) Main characteristics of tested radiant panel Characteristic

(1)

Ø10.1x1.1 mm pex-b (crosslinked polyethylene) pipe

(2)

15 mm drywall

(3)

0.3 mm aluminum foil

(4)

30 mm EPS (expanded polystyrene)

28

Table 2 Experimental measurements and heat transfer coefficient results obtained by both experimental and ANN methods Test descript or 1 2 3 4 5

Wall Configuration 1

6 7 8 9 10 11 12 13 14 15

Tw 29,6 5 31,3 9 32,9 6 34,6 4 36,2 0 37,8 9 39,3 5 29,6 0 31,3 5 32,9 7 34,7 0 36,1 9 37,8 4 39,3 7 29,7 0

Ts 23,2 2 24,2 6 25,2 4 26,3 6 27,1 1 28,1 0 29,0 6 23,1 5 24,1 6 25,2 9 26,3 4 27,1 4 28,1 2 29,1 7 23,3 1

Tf 16,9 9 17,5 4 18,0 1 18,4 6 18,8 6 19,4 4 19,9 2 16,9 8 17,5 2 17,9 9 18,4 2 18,8 2 19,4 1 19,8 9 17,0 0

Tc 16,1 6 16,7 5 17,2 4 17,7 4 18,1 7 18,7 9 19,3 5 16,1 3 16,7 3 17,2 3 17,7 1 18,1 4 18,7 6 19,3 2 16,1 7

Ta 17,0 5 17,6 5 18,1 5 18,6 7 19,1 3 19,7 6 20,3 4 17,0 0 17,6 2 18,1 3 18,6 3 19,0 9 19,7 3 20,3 0 17,0 3

Top 17,0 8 17,7 0 18,2 0 18,7 3 19,1 8 19,8 0 20,3 9 17,0 5 17,7 0 18,2 0 18,6 9 19,1 5 19,8 0 20,3 6 17,1 0

AUST

qr(W/m 2 )

qc(W/m 2 )

qt (W/m2 )

16,85

30,77

19,88

50,65

4,84

4,70

3,22

3,24

8,26

8,25

17,44

33,20

21,70

54,90

4,87

4,73

3,29

3,31

8,37

8,36

17,92

35,86

23,36

59,22

4,90

4,77

3,29

3,32

8,41

8,41

18,41

39,33

25,02

64,34

4,95

4,81

3,25

3,27

8,43

8,41

18,84

41,18

26,85

68,03

4,98

4,84

3,37

3,37

8,58

8,55

19,42

43,55

28,20

71,75

5,02

4,88

3,38

3,37

8,65

8,61

19,96

45,99

29,44

75,43

5,06

4,91

3,38

3,38

8,70

8,66

16,83

30,52

20,23

50,76

4,83

4,69

3,29

3,26

8,32

8,27

17,42

32,54

22,07

54,61

4,83

4,73

3,37

3,31

8,45

8,37

17,91

36,22

23,16

59,38

4,91

4,77

3,23

3,27

8,38

8,37

18,38

39,39

25,49

64,88

4,95

4,80

3,31

3,29

8,48

8,44

18,80

41,50

26,64

68,14

4,98

4,84

3,31

3,35

8,53

8,53

19,39

43,78

26,35

70,13

5,01

4,88

3,14

3,31

8,43

8,55

19,93

46,70

29,08

75,78

5,06

4,92

3,28

3,32

8,60

8,61

16,86

31,20

19,29

50,49

4,83

4,69

3,07

3,19

8,13

8,21

29

hr(W/m K)

hr,ANN (W/m2K )

hc (W/m2K )

hc,ANN (W/m2K )

ht (W/m2K )

ht,ANN (W/m2K )

2

16 17 18 19 20 21 22 23 24 25 26 27 28

31,3 8 32,9 6 34,5 5 36,2 2 37,9 2 39,3 3 29,6 5 31,4 4 32,9 6 34,6 6 36,2 0 37,9 2 39,3 5

24,2 8 25,2 2 26,1 9 27,1 5 28,2 7 29,1 3 23,1 8 24,3 6 25,2 9 26,3 2 27,1 5 28,1 7 29,0 2

17,5 4 18,0 1 18,4 7 18,8 7 19,4 4 19,9 3 17,0 0 17,5 5 18,0 2 18,5 0 18,9 0 19,4 7 19,9 5

16,7 5 17,2 4 17,7 4 18,1 7 18,7 9 19,3 5 16,1 8 16,7 6 17,2 5 17,7 7 18,2 1 18,8 1 19,3 7

17,6 4 18,1 4 18,6 7 19,1 2 19,7 5 20,3 4 17,0 4 17,6 5 18,1 5 18,6 9 19,1 5 19,7 7 20,3 5

17,7 0 18,2 0 18,7 2 19,2 0 19,8 0 20,4 0 17,1 0 17,7 0 18,2 0 18,7 8 19,2 0 19,8 0 20,4 0

17,44

33,30

21,77

55,07

4,87

4,73

3,28

3,30

8,37

8,35

17,93

35,79

23,18

58,97

4,91

4,77

3,27

3,33

8,40

8,42

18,42

38,42

25,25

63,67

4,94

4,80

3,36

3,35

8,53

8,48

18,84

41,37

26,76

68,13

4,98

4,84

3,33

3,33

8,57

8,52

19,42

44,43

28,09

72,53

5,02

4,88

3,30

3,30

8,56

8,55

19,97

46,32

28,67

74,99

5,05

4,91

3,26

3,33

8,59

8,62

16,87

30,48

20,22

50,70

4,83

4,69

3,29

3,27

8,34

8,28

17,46

33,65

21,48

55,13

4,87

4,73

3,20

3,30

8,28

8,34

17,93

36,12

23,18

59,30

4,91

4,77

3,25

3,31

8,36

8,40

18,44

38,98

25,49

64,47

4,95

4,80

3,34

3,27

8,55

8,42

18,88

41,20

26,62

67,81

4,98

4,84

3,33

3,39

8,53

8,57

19,44

43,79

28,82

72,61

5,02

4,88

3,43

3,39

8,67

8,62

19,98

45,66

28,99

74,64

5,05

4,91

3,34

3,41

8,66

8,69

30

Table 2 Experimental measurements and heat transfer coefficient results obtained by both experimental and ANN methods (cont.) Test descript or 1 2 3 4 5

Wall Configuration 2

6 7 8 9 10 11 12 13 14 15

Tw 29,4 8 30,9 9 32,3 0 33,8 3 35,2 5 36,7 8 38,2 1 29,4 5 31,0 2 32,2 9 33,8 0 35,2 6 36,7 4 38,2 5 29,4 8

Ts 23,6 8 24,9 0 25,6 7 26,7 3 27,7 3 28,5 6 29,5 9 23,6 2 24,9 1 25,6 3 26,7 1 27,7 2 28,5 2 29,5 9 23,6 8

Tf 18,8 6 19,7 3 20,0 3 20,6 2 21,1 7 21,5 6 22,1 4 18,7 5 19,7 1 19,9 9 20,5 9 21,1 5 21,5 4 22,1 0 18,8 7

Tc 18,4 9 19,3 9 19,7 8 20,4 5 21,0 7 21,5 5 22,2 6 18,4 1 19,3 9 19,7 5 20,4 2 21,0 6 21,5 4 22,2 2 18,5 0

Ta 19,1 5 20,0 6 20,4 2 21,1 0 21,7 2 22,1 3 22,8 0 18,9 1 19,8 9 20,1 9 20,8 7 21,4 9 21,9 0 22,5 4 19,0 0

Top 19,2 2 20,1 5 20,5 9 21,3 6 21,9 5 22,3 9 23,0 5 19,0 6 20,0 3 20,3 1 21,0 2 21,6 5 22,4 0 23,1 0 19,1 8

AUST

qr(W/m 2 )

qc(W/m 2 )

qt (W/m2 )

hr(W/m2 K)

hr,ANN (W/m2K )

hc (W/m2K )

hc,ANN (W/m2K )

ht (W/m2K )

ht,ANN (W/m2K )

19,04

23,75

15,54

39,29

5,12

5,05

3,43

3,38

8,81

10,62

19,93

25,72

15,59

41,30

5,18

5,10

3,22

3,20

8,70

10,61

20,30

27,95

16,58

44,52

5,21

5,14

3,16

3,17

8,77

10,74

20,95

30,31

16,97

47,28

5,24

5,20

3,01

3,05

8,80

10,87

21,55

32,61

17,68

50,29

5,28

5,24

2,94

2,92

8,71

10,80

22,00

34,90

19,37

54,26

5,32

5,28

3,01

3,01

8,80

10,95

22,65

37,18

20,08

57,26

5,36

5,33

2,96

2,96

8,76

10,97

18,68

23,89

15,51

39,40

4,83

4,81

3,29

3,31

8,64

10,49

19,63

25,82

15,46

41,27

4,89

4,86

3,08

3,11

8,46

10,43

19,95

27,92

17,27

45,19

4,92

4,86

3,18

3,07

8,50

10,36

20,59

30,34

16,03

46,37

4,96

4,89

2,75

2,90

8,15

10,35

21,18

32,64

17,90

50,54

4,99

4,93

2,88

2,79

8,33

10,34

21,60

34,77

19,28

54,05

5,02

4,96

2,91

2,93

8,83

10,99

22,21

37,38

20,33

57,71

5,07

5,00

2,89

2,85

8,90

11,07

18,78

23,71

15,30

39,01

4,83

4,82

3,26

3,30

8,66

10,54

31

16 17 18 19 20 21 22 23 24 25 26 27 28

31,0 0 32,3 0 33,8 2 35,2 7 36,7 9 38,2 1 29,5 0 30,9 5 32,3 1 33,8 6 35,2 2 36,8 2 38,1 6

24,9 0 25,6 8 26,7 2 27,7 3 28,5 6 29,6 1 23,7 3 24,8 9 25,6 9 26,7 6 27,7 3 28,5 9 29,5 8

19,7 4 20,0 3 20,6 2 21,1 7 21,5 6 22,1 4 18,9 6 19,7 5 20,0 6 20,6 5 21,1 8 21,5 7 22,1 8

19,4 0 19,7 9 20,4 5 21,0 7 21,5 5 22,2 5 18,5 6 19,3 9 19,8 2 20,4 8 21,0 8 21,5 6 22,2 9

19,8 9 20,2 3 20,9 0 21,5 1 21,9 3 22,5 8 19,0 6 19,8 9 20,2 6 20,9 2 21,5 3 21,9 4 22,6 2

20,0 9 20,4 5 21,1 6 21,8 9 22,4 4 23,1 0 19,2 0 20,0 4 20,4 3 21,2 6 21,8 1 22,5 0 23,1 9

19,65

25,69

15,67

41,36

4,89

4,85

3,13

3,12

8,60

10,51

19,99

27,98

16,57

44,55

4,92

4,86

3,04

3,05

8,52

10,49

20,61

30,26

17,48

47,74

4,96

4,91

3,00

2,94

8,59

10,56

21,20

32,60

17,46

50,06

4,99

4,95

2,81

2,82

8,57

10,69

21,62

34,90

19,69

54,60

5,03

4,97

2,97

2,91

8,93

11,01

22,25

37,30

19,98

57,29

5,07

5,00

2,85

2,81

8,81

10,99

18,85

23,62

15,83

39,45

4,84

4,81

3,39

3,28

8,71

10,46

19,64

25,64

15,65

41,28

4,89

4,85

3,13

3,09

8,52

10,41

20,02

27,89

15,95

43,84

4,91

4,86

2,94

3,05

8,33

10,42

20,64

30,33

17,40

47,73

4,95

4,91

2,98

2,93

8,67

10,65

21,21

32,55

17,72

50,26

5,00

4,94

2,86

2,79

8,50

10,53

21,63

35,00

19,15

54,15

5,03

4,97

2,88

2,89

8,89

11,05

22,29

36,97

19,83

56,80

5,07

5,01

2,85

2,89

8,89

11,15

32

Table 2 Experimental measurements and heat transfer coefficient results obtained by both experimental and ANN methods (cont.) Test descript or 1 2 3 4 5

Wall Configuration 3

6 7 8 9 10 11 12 13 14 15

Tw 29,3 7 31,1 7 32,9 4 34,5 4 36,3 8 38,0 2 39,8 4 29,3 8 31,0 4 32,7 9 34,2 5 36,1 9 37,8 3 39,5 9 29,3 6

Ts 24,8 8 26,0 7 27,3 2 28,1 8 29,7 8 30,6 2 32,0 8 24,9 1 26,0 5 27,2 9 28,1 3 29,7 6 30,5 9 32,0 6 24,8 8

Tf 21,1 4 21,7 8 22,5 7 22,8 6 24,0 6 24,1 7 25,3 9 21,1 9 21,7 6 22,5 2 22,7 9 24,0 4 24,0 6 25,3 7 21,1 3

Tc 20,6 3 21,4 2 22,3 3 22,7 2 23,9 7 24,3 4 25,4 8 20,6 7 21,4 0 22,2 8 22,6 6 23,9 6 24,3 0 25,4 6 20,6 2

Ta 21,5 0 22,2 8 23,1 8 23,5 3 24,8 2 25,2 1 26,3 7 21,5 4 22,2 6 23,1 4 23,4 7 24,8 1 25,1 7 26,3 5 21,4 9

Top 21,7 4 22,5 8 23,4 8 23,8 6 25,2 0 25,5 7 26,7 5 21,7 4 22,5 5 23,4 4 23,8 0 25,2 0 25,5 4 26,7 1 21,8 0

AUST

qr(W/m 2 )

qc(W/m 2 )

qt (W/m2 )

hr(W/m2 K)

hr,ANN (W/m2K )

hc (W/m2K )

hc,ANN (W/m2K )

ht (W/m2K )

ht,ANN (W/m2K )

21,33

17,85

6,73

24,58

5,03

5,03

1,99

1,86

7,83

7,71

22,07

20,24

4,95

25,18

5,06

5,06

1,31

1,66

7,21

7,56

22,93

22,38

5,11

27,48

5,10

5,10

1,23

1,47

7,16

7,39

23,30

24,98

4,86

29,84

5,11

5,12

1,05

1,34

6,90

7,18

24,54

27,13

5,26

32,40

5,18

5,18

1,06

1,42

7,07

7,43

24,87

29,88

4,31

34,19

5,20

5,20

0,80

1,15

6,77

7,11

26,01

31,92

5,32

37,24

5,26

5,26

0,93

0,96

6,99

6,99

21,38

17,79

6,63

24,41

5,03

5,04

1,97

1,88

7,70

7,67

22,05

20,23

6,87

27,11

5,06

5,06

1,82

1,93

7,76

7,84

22,89

22,44

7,51

29,96

5,10

5,10

1,81

1,81

7,80

7,74

23,24

25,03

8,47

33,51

5,11

5,11

1,82

1,99

7,72

7,87

24,53

27,11

8,35

35,46

5,18

5,18

1,69

1,82

7,77

7,89

24,82

29,99

10,79

40,78

5,19

5,19

1,99

1,66

8,06

7,67

25,99

31,91

10,26

42,17

5,26

5,26

1,80

1,55

7,88

7,57

21,32

17,90

6,59

24,49

5,04

5,03

1,95

1,81

7,96

7,74

33

16 17 18 19 20 21 22 23 24 25 26 27 28

31,0 9 32,8 1 34,3 3 36,2 1 37,6 4 39,5 9 29,3 7 31,0 7 32,8 2 34,3 8 36,2 4 37,4 6 39,7 0

26,0 7 27,3 1 28,1 6 29,7 8 30,6 5 32,1 1 24,8 6 26,0 9 27,3 6 28,2 5 29,8 0 30,5 1 32,2 1

21,7 9 22,5 8 22,8 6 24,0 6 24,2 7 25,4 2 21,0 9 21,8 0 22,6 1 22,9 2 24,0 7 24,1 8 25,5 6

21,4 2 22,3 3 22,7 2 23,9 7 24,3 8 25,5 0 20,6 0 21,4 4 22,3 6 22,7 8 23,9 9 24,1 6 25,6 8

22,6 0 23,1 9 23,5 3 24,8 2 25,2 4 26,3 9 21,4 6 22,3 1 23,2 2 23,6 0 24,8 4 25,1 8 26,3 9

22,5 5 23,5 0 23,8 5 25,2 0 25,6 0 26,8 0 21,7 1 22,6 1 23,5 0 23,9 3 25,2 0 25,7 0 26,8 4

22,07

20,22

7,06

27,28

5,06

5,05

2,03

2,14

7,75

7,83

22,94

22,33

7,54

29,87

5,10

5,10

1,83

1,72

7,83

7,67

23,30

24,88

9,11

34,00

5,11

5,12

1,97

1,72

7,89

7,59

24,54

27,14

8,39

35,54

5,18

5,18

1,69

1,84

7,76

7,89

24,92

29,80

8,31

38,12

5,21

5,20

1,54

2,06

7,55

8,07

26,04

31,96

9,53

41,49

5,26

5,26

1,67

1,59

7,82

7,69

21,29

17,94

6,90

24,84

5,04

5,03

2,03

1,87

7,88

7,71

22,09

20,24

6,82

27,06

5,06

5,06

1,80

1,94

7,78

7,88

22,97

22,39

7,45

29,84

5,11

5,11

1,80

1,85

7,74

7,76

23,36

25,04

8,78

33,81

5,12

5,12

1,89

1,87

7,82

7,77

24,56

27,17

8,38

35,55

5,18

5,19

1,69

1,82

7,73

7,84

24,82

29,59

8,79

38,38

5,20

5,20

1,65

1,73

7,97

8,04

26,16

31,88

9,67

41,55

5,27

5,27

1,66

1,54

7,74

7,59

34

Table 3. Some of the findings regarding with the solution of ANN a) Performance results of the corresponding networks R

MSE

Training

Neuron

hr

hc

ht

Epoch

number

Configuration 1

0.0396

0.9957

0.7193

0.9286

12

17

Configuration 2

0.0179

0.9948

0.9447

0.9521

10

5

Configuration 3

0.0750

0.9985

0.8050

0.7746

10

19

b) Obtained linear correlation and its constants at different wall configurations ℎ = 𝑎1 𝑇𝑤 + 𝑎2 𝑇𝑠 + 𝑎3 𝑇𝑓𝑙𝑜𝑜𝑟 + 𝑎4 𝑇𝑐𝑒𝑖𝑙𝑖𝑛𝑔 + 𝑎5 𝑇𝑎 + 𝑎6 𝑇𝑜𝑝 + 𝑎7 𝐴𝑈𝑆𝑇 + 𝑏 Conf.

𝑎1

𝑎2

𝑎3

𝑎4

𝑎5

𝑎6

𝑎7

𝑏

ℎ𝑟

0.00011

-0.01887

-0.07164

-0.25489

-0.03475

-0.08778

0.56746

3.00986

ℎ𝑐

-0.76704

2.18388

0.16263

0.63664

0.33091

-0.49099

-2.49409

7.20603

ℎ𝑡

-1.23106

3.37128

0.09426

0.63673

0.09677

0.15969

-3.70884

13.10813

𝑎1

𝑎2

𝑎3

𝑎4

𝑎5

𝑎6

𝑎7

𝑏

ℎ𝑟

0.06154

-0.21108

-0.49860

-0.25398

0.21689

0.06899

0.70275

3.51571

ℎ𝑐

0.66063

-1.94943

-0.85361

1.83388

-0.23551

0.14964

0.41927

5.90195

ℎ𝑡

0.69677

-2.07681

-1.04635

1.12227

-0.57380

1.60153

0.36888

9.56686

𝑎1

𝑎2

𝑎3

𝑎4

𝑎5

𝑎6

𝑎7

𝑏

ℎ𝑟

0.00011

-0.01610

-0.04968

-0.16910

-0.02460

-0.05975

0.38366

3.60786

ℎ𝑐

-2.44466

6.11396

0.36993

1.38539

0.76839

-1.09614

-5.53097

10.44463

ℎ𝑡

-2.61321

6.28613

0.14282

0.92285

0.14966

0.23744

-5.47800

14.47944

1

Conf. 2

Conf. 3

35

Table 4. Comparison between experimental/numerical literature and determined heat transfer coefficients for a radiant heated wall in cavities hr (W/m2K)

hc (W/m2K)

ht (W/m2K)

Radiant ceiling cooling

5.6

4.4

13.2

Acikgoz [34]b

Radiant wall heating

5.5

3.5

10.5

Cholewa et al. [21]a

Radiant floor heating

5.6

2.8

10.1

Chicote et al. [22]a

Radiant ceiling cooling

5.4

4.2

8.5

Present studyb

Radiant wall heating

5.0

2.7

9.0

Reference source

Heating type

Causone et al. [17]

a Average values referred from corresponding experimental research b Average values referred from corresponding numerical study

36