Experimental and numerical investigation of air-side forced convection on wire-on-tube condensers

International Journal of Thermal Sciences 151 (2020) 106241

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Experimental and numerical investigation of air-side forced convection on wire-on-tube condensers € € _ €nül *, Ozden �ra, S¸. Ozgür Alis¸an Go Ag Atayılmaz, Hakan Demir, M. Kemal Sevindir, Ismail Teke Department of Mechanical Engineering, Yildiz Technical University, 34349 Istanbul, Turkey

A B S T R A C T

In this study, wire-on-tube condensers used frequently in industrial cooling applications have been investigated experimentally and numerically, which are exposed to forced convection. Five different coils with different geometric properties were studied in the experimental study. The numerical study has been validated by the experimental data obtained through these coils. After validation, the effect of wire diameter (Dw), tube diameter (Dt), wire pitch (Sw) and tube pitch (St) have been investigated parametrically for five different air velocities (0.5, 1.0, 1.5, 2.0 and 2.5 m/s). The parametric study was performed for the variation for wire diameter (1.2 mm–2.0 mm), tube diameter (4.2 mm–7.2 mm), wire pitch (5.5 mm–9.5 mm) and the tube pitch (20 mm–50 mm) to determine their effects on wire-on-tube condensers in terms of heat transfer. It is observed that the increase of the wire diameter decreased the heat transfer coefficient on the wire by 10–12% while the heat transfer coefficient on the tube increased by 10–15%. It is determined that the effect of increasing tube diameters on the convection coefficient on the wire is very low. When the distance between the wires is increased from 5.5 mm to 9.5 mm, the average convection coefficient on both tubes and wires is decreased by 5%. When the distance between the tubes is increased from 20 mm to 50 mm, it is concluded that there is a decrease in the convection heat transfer coefficient on both the tube and the wires by approximately 7–8% depending on the velocities. As a result, the correlations are proposed to determine the amount of heat transfer generated over both the wire and the tube. The proposed correlations yield accurate results in the error range of 10% with CFD results and %15 with experimental results.

1. Introduction Today, the studies on heat exchangers used in air conditioning and cooling systems aim to increase energy efficiency, reduce production costs and present innovative designs. In industrial and domestic cooling systems, wire-on-tube condensers manufactured with steel tubes and wires are generally used. These type of condensers consists of wires welded to a tube on a double side and perpendicular to the tube, usually welded to each other in parallel. They are operated according to the place of use as forced convection or nat­ ural convection. In such heat exchangers, heat is transferred from the outer surfaces of the wires and tubes to the external environment. The characteristic geometric properties of the wire-on-tube con­ densers are expressed by wire diameter (Dw), tube diameter (Dt), centerline to centerline wire spacing for same side (Sw), centerline to centerline tube spacing (St), total wire length (Lw) and a tube passage length (Lt), when tube bending and the thermal constriction between tube and wires are ignored as seen on Fig. 1 When the literature is examined, it is seen that the studies are pre­ dominately aimed at examining the wire-on-tube condensers which are subjected to natural convection. This is surprising despite the fact that today’s used wire-on-tube condensers operate on a largely forced regime

basis. Witzell and Fontaine examined the heat transfer with natural con­ vection for different wire diameters in their study in 1957 [1]. Witzell and Fontaine investigated the effect of the change of wire pitch on ra­ diation and natural convection. They suggested a correlation to deter­ mine the heat transfer rate on these kinds of condensers [2]. Collicott et al. investigated the radiation heat transfer and determined the view factors on the wire-on-tube condensers based on Witzell et al.’s previous studies [3]. Similarly, experimental studies with different geometric parameters to determine natural convection heat transfer were con­ ducted by Cyphers et al. [4], Witzell [5], Melo and Hermes [6]. Tagliafico and Tanda [7]. Also, they proposed many empirical correla­ tions depending on their experimental results. Quadir et al. [8] and Ameen et al. [9] used the finite element method to determine the performance of the wire-on-tube condenser in the household refrigerators. Hoke et al. [10] carried out the effect of both natural and forced convection heat transfer regimes on the horizontal and inclined con­ densers. Experimental studies were performed on wire-on-tube con­ densers having six different geometric specifications. But, just one of them positioned perpendicular to the flow for both wires and tubes like this study. They especially highlighted that the effect of the angle of attack on heat transfer was quite high. They suggested a correlation by

* Corresponding author. E-mail addresses: [email protected], [email protected] (A. G€ onül). https://doi.org/10.1016/j.ijthermalsci.2019.106241 Received 3 June 2019; Received in revised form 21 November 2019; Accepted 20 December 2019 Available online 6 January 2020 1290-0729/© 2019 Elsevier Masson SAS. All rights reserved.

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International Journal of Thermal Sciences 151 (2020) 106241

Nomenclature At At,R AT Aw At,R C CDkω cp Dt Dw,b Dw, f Dw

ηw

he hw hw,b hw,f ht Jta Jwa k k ks kt L Lt Lw m m m_ n Nt Nw Nuw Nut P Pr Prs

Rew Ret Q_ C Q_ C;t Q_ C;bw

Area of tubes Selected area of tubes for radiation heat transfer calculation Area of tubes and wires Area of wires Selected area of wires for radiation heat transfer calculation Constant Positive portion of the cross-diffusion term of Constant-pressure specific heat Tube outer diameter Back wire diameter Front wire diameter Wire diameter Fin efficiency Average equivalent heat transfer coefficient on the coils Average heat transfer coefficient on the wires Average heat transfer coefficient on the back wire Average heat transfer coefficient on the front wires Average heat transfer coefficient on the tube Radiosity from tube to medium Radiosity from wire to medium Turbulence kinetic energy The thermal conductivity of the fluid The thermal conductivity of solid The turbulent thermal conductivity of the fluid Half-length of centerline-to-centerline spacing between tubes or tube pitch Tube length Wire length Constant Number determining the temperature gradient on the wires Mass flow rate Constant Number of tubes Number of wires Nusselt number according to wire diameter Nusselt number according to tube diameter Pressure Prandtl number by film temperature Prandtl number by surface temperature

Q_ C;fw Q_ C;w

Q_ total Q_ total;CFD Q_ ps Q_ R qrad;in qrad;out ! r ! s ’ ! s St

Sw T Tc Teq Th Tt Tw Vf ui ΔTm ΔT

σ Ω Ωij ϵ ϵapp

μ μt ω

considering wire diameter as the characteristic length. Lee et al. [11] conducted experimental and analytical studies to determine the air-side heat transfer coefficient of the single-layer heat exchanger. In the experimental study, the wire-on-tube condensers were positioned hori­ zontally and vertically according to the direction of flow in a wind tunnel for the forced convection regime. According to these situations, they tried to make analytical analysis by adding correction coefficients � to the Zukauskas equation [12] as considering characteristic length both wire and tube diameter. They used three different coils having the same wire and tube diameter, also they did not mention wire spacing (Sw) in the paper. Resistance wire were inserted to the tube so as to supply needed heat like this study. Islamoglu [13] employed artificial neural networks (ANN) to point out the amount of heat transfer of the wire-on-tube condenser based on the study of Lee et al. [11]. Similarly, Hayati et al. carried out the Adaptive Neuro-Fuzzy Inference System (ANFIS) model to estimate the heat transfer rate on wire-on-tube condensers in forced regimes [14]. Barbosa Jr. and Sigwalt investigated the thermal-hydraulic

Reynolds number according to wire diameter Reynolds number according to tube diameter Total heat transfer rate with convection Heat transfer rate with convection on tubes

Heat transfer rate with convection on back wires

Heat transfer rate with convection on front wires Heat transfer rate with convection on wires

Total heat transfer rate Total heat transfer rate from selected region for CFD calculation The supplied heat transfer rate on coils by means of PowerMeter Total heat transfer rate with radiation Incident radiation heat flux Outgoing radiation heat flux Position vector Direction vector

Scattering direction vector Centerline-to-centerline spacing between tubes or tube pitch Centerline-to-centerline spacing between wires or wire pitch Temperature Incoming air temperature Coil surface mean temperature (equivalent temperature) Outgoing air temperature Tube outer surface temperature Wire outer surface temperature Free-stream velocity Velocity components in a generalized coordinate system (m/s) Logarithmic temperature difference Temperature difference between inlet and outlet Stefan–Boltzmann constant (W/m2K4) Solid angle Mean rate of rotation tensor (s 1) Surface thermal emissivity Surface apparent thermal emissivity Fluid dynamic viscosity Fluid turbulent dynamic viscosity Specific dissipation rate

performance spiral wire-on-tube condensers. They tested the condensers in 16 different geometries at air velocities ranging from 0.2 to 2.0 m/s in an open-loop wind tunnel [15]. Zhang et al. examined the airflow area under the actual operating conditions in a refrigerator and the effect of this area on the cooling performance of spiral wire-on-tube condensers [16]. As a result of the literature research, it is clear that there are few studies for wire-on-tube condensers at forced convection regimes. By means of this study, both experimental and numerical studies are per­ formed to point out heat transfer under forced convection regime. In the study, the wire-on-tube condensers are positioned perpendicular to both the wire and the tubes to the flow as used in industrial applications. Ansys Fluent program is used for numerical study by selecting k- ω SST model. Numerical results illustrate similar results with the experimental results. After verification, the parametric study is fulfilled according to changing values of Dw, Dt, Sw, and St to point out their effects on heat transfer. While air velocity ranged between 0.5, 1.0, 1.5 and 2.0 in the experimental study, 2.5 m/s is analyzed in addition to these values in the 2

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International Journal of Thermal Sciences 151 (2020) 106241

numerical study. By means of the studies, correlations have been sug­ gested depending on the wire and tube diameter. 2. Experimental study The experimental study was performed by means of a wind tunnel. The wind tunnel is located in the Thermodynamic laboratory of Yıldız Technical University and consists of five basic sections. Part A refers to smooth the airflow by decreasing turbulence intensity in incoming air into the test chamber (B). The test chamber consists of 30.6 cm � 30.6 cm section and 60 cm dimensions manufactured with plexiglass mate­ rial. The fan unit is inside section C, a damper unit in section D and section E refers to the part of the silencer. The schematic is clearly seen in Fig. 2 after some equipment is inserted into the tunnel. The equipment used for measurements and data collection is given in Table 1. Air temperatures are measured instantaneously with RTDs before and after the test sample placed in the test section. The pressure drop is similarly measured by the data obtained before and after the test sample. In order to ensure the heat transfer at a constant temperature from the condenser surface, resistance wires covered with non-flammable mate­ rials are placed inside the condenser tubes. The desired surface tem­ peratures are reached with the help of an adjustable DC power supply. A high-precision multimeter for power measurement is placed in the inlet and outlet of the Coil to make delicate. In this study, the effect of the tube bending that provides the

Fig. 1. Schematic representation of an exemplary wire-on-tube condenser (a) Front view, (b) Side view.

Fig. 2. Schematic illustration of the experimental apparatus. 3

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International Journal of Thermal Sciences 151 (2020) 106241

heat transfer rate. Condenser surface temperatures are measured using four T-type thermocouples mounted on the condenser surface. Also, two T-type thermocouples are placed in the wire at St/2 to measure up temperature of wires. The data obtained from T-type thermocouples and RTD ther­ mocouples are instantaneously transferred to the computer via a data logger unit. In-duct air velocities are changed by means of a frequency inverter connected to the fan, while the air velocity is measured by a duct-mounted hot wire probe prior to the sample. Experimental studies were carried out for coils having 5 different geometric properties in Table 2 at four different free-stream velocities (0.5, 1.0, 1.5, and 2.0 m/s) and at two different surface temperatures (40 and 50 � C). In order to examine the sensitivity of the experimental study, heat transfer through a single tube with a diameter of 4.75 mm, an average surface temperature of 50 � C and average air temperatures of 22.7 � C were studied experimentally at a velocity range of 0.5–2.0 m/s. The radiation heat transfer rate was calculated with the assumption that the surface of the tube was the gray body and the surrounding was the black body. Thus, the convection heat transfer rates were computed by subtracting the radiation heat transfer rate from total heat transfer rate and convection heat transfer coefficients were calculated. The results of these studies were compared with the correlations of � Hilpert [17,18], Zukauskas [12,18] and Churchill-Bernstein [18,19] which are frequently used in the literature for the related flow condi­ tions. The results are demonstrated to be quite compatible as seen in Fig. 4. All three correlations were obtained from experimental data and it was stated that the experimental studies remained within �15% un­ certainty range [18]. Moreover, uncertainty analyses are performed for the experimental study for wire-on-tube condensers and the uncertainty rates are presented in the Appendix.

Table 1 List of wind tunnel sections and equipment in the experimental apparatus. No

Equipment/Section

Brand

Model

Feature/ Sensitivity

A

–

–

–

C

Fan Section

–

–

D

Damper Section

–

–

E

Silencer Section

–

–

1 2

Test sample Power supply

Woods of Air Movement Woods of Air Movement Woods of Air Movement Woods of Air Movement Woods of Air Movement – Agilent

–

B

Incoming Air Section Test Section

– N5767A

3 4 5

Datalogger Multimetre Frequency Invertor

Agilent AATech Siemens

6 7

Computer Fan

8

Damper

9

Silencer

10

Hotwire

HP Woods of Air Movement Woods of Colchester LTD Woods of Air Movement Testo

34970 A ADM-3055 MicroMaster 420 – –

– 60 V/25 A, 1500 W – %0.015 0.12–11 kW

11

Differential Pressure Transmitter RTD T Type Thermocouple

12 13

– –

–

–

BB191D

–

440

Dwyer

MS2-W101

� (0.03 m/sn þ %4) � %1.00

Watlow TermoElectric

– NN 24 TT

� %0.10 � %0.25

connection between the inline tubes is ignored. The related parts are cut and replaced with copper elements of 2.0 mm diameter. As can be seen in Fig. 3, the copper tubes are covered with macaron cable. That’s why coils potentially are prevented in spite of electrical current. In Fig. 3, Detail A shows the curve with the resistance wire, while detail B shows the curve with a copper piece. The curves are then completely insulated with 1 cm thick rubber insulating material and 5 cm thick XPS material and kept outside the test chamber. Thus, it is ensured that the supplied thermal power is transferred from the coil surface to the air only. Two thermocouples were placed on the outer surface of the insulation. After the measurements with these thermocouples, heat transfer from the resistance wire to the copper curves is determined as 1–1.5% of the total

Table 2 Geometric properties of the coils used in the experiments. Coil

Dw (mm)

Dt (mm)

Sw (mm)

St (mm)

Nw (mm)

Nt (mm)

Lw (mm)

Lt (mm)

1 2 3 4 5

1.4 1.4 1.4 1.8 1.8

4.95 4.95 6.20 4.95 4.95

7.5 6.5 5.0 5.0 5.0

25 25 25 50 25

82 94 122 122 122

12 12 12 6 12

30.5 30.5 30.5 30.5 30.5

30.5 30.4 30.5 30.4 30.4

Fig. 3. Details of the curves connecting inline tubes. 4

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�

�

∂ω ∂ ∂ω ðρωui Þ ¼ Γω þ Gω ∂xi ∂xj ∂xj

(6)

Yω þ Dω þ Sω

Here Gk is the generation of turbulent kinetic energy because of the mean velocity gradient and Gω is the generation of specific dissipation rate. Γk and Γω are the effective diffusivities of k and ω respectively. Yk and Yω are the dissipation of k and ω respectively. Sk and Sω are userdefined source terms, while Dω is the cross-diffusion term. There was no change in model coefficients and calculations were performed ac­ cording to the values in the program. The ideal gas was accepted for the fluid. The heat transfer equation for the ideal gas is expressed below. (7)

pV ¼ ρRT

Fig. 4. Comparison of experimental results and correlations in literature for a single tube.

For detailed information about the model, Menter et al. [24] study can be examined. The Discrete Ordinate (DO) model is utilized to determine radiation heat transfer. This model takes into account scattering, absorption, and emissivity. General equation [23];

3. Numerical study

dIð r ; s Þ σT 4 σs ⇀ ⇀ þ ða þ σ s ÞIð r ; s Þ ¼ an2 þ ds π 4π

⇀ ⇀

ρu j

∂ðui Þ ¼ ∂xj

4π

⇀ ⇀ı

⇀

⇀ı

Ið r ; s ÞΦð s ; s ÞdΩı 0

qrad;out ¼ n2 εσ T 4 þ ð1

εÞqrad;in

Here qrad;in is the heat flux from, as follows; Z ⇀⇀ qrad;in ¼ Iin s :n dΩ

�

s : n >0

(2)

(3)

The energy equation for solid, ks

∂2 T ¼0 ∂x2j

(10)

The calculations are performed in the domain seen in Fig. 5. As the geometry of the related area repeats each other continuously on the coil surfaces, analyses are performed by taking the solution domain seen in Fig. 5 only. As demonstrated in Fig. 6, the air domain is placed on the selected condenser region. The distance between the output and the condenser is

�

The energy equation for fluid, � � � � ∂T ∂ ∂T ¼ ðk þ kt Þ ρcp ui ∂xj ∂xj ∂xj

(9)

⇀⇀

(1)

∂P ∂ ∂ui ðμ þ μt Þ þ ∂xi ∂xj ∂xj

(8)

The net heat transfer on gray surfaces is according to the following equation;

ANSYS Fluent 18.2 program is used for the numerical study. Although single-tube and single-wire flow conditions are in the laminar range, boundary-layer interactions and wire-on-tube condenser geom­ etry cause distortion in the characteristic of the flow and therefore, the turbulence models are analyzed by considering that the flow cannot be completely laminar. In the literature, due to similar situations, there are many studies using turbulence models due to flow disturbances in low Re [20–22]. It was determined that the best results for experimental studies were calculated with the k-ω SST model and parametric studies were performed according to this model. Since the heat transfer in wire-on-tube condensers is based on the conjugate heat transfer mech­ anism, the energy equations are computed for both conduction in the solid and convection and radiation in the fluid side together so that the temperature field obeys the laws of thermodynamics. RANS equations are obtained by taking the time average of transport and energy equations. Continuity, momentum, and energy equations for both fluid and solid are written in steady-state conditions as follows, respectively [23]:

∂ui ¼0 ∂xj

Z

(4)

xj represents the x, y and z coordinates in the Cartesian coordinate system for j ¼ 1, 2, 3. In this study, it is assumed that the flow is three dimensional, steady-state and the physical value of the density of the fluid is ideal gas and viscosity and thermal conductivity are constant. The transport equations under steady-state conditions for the k-ω SST model are as follows [23,24]: � � ∂k ∂ ∂k Γk þ Gk Yk þ Sk ðρkui Þ ¼ (5) ∂xj ∂xi ∂xj

Fig. 5. Condenser geometry used in the CFD model. 5

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International Journal of Thermal Sciences 151 (2020) 106241

Fig. 6. Surfaces in the CFD model.

chosen as 20D of the tube diameter when selecting the input geometry distance 5D of tube diameter in order to be able to examine the flow correctly. Symmetry boundary conditions are given for repetitive sur­ faces. Thus, both the resolution time and computing power are consid­ erably reduced. Since the flow in condensers is dominantly in two-phase zones, the constant temperature boundary condition is applied to the internal surface of the tube. The heat thus obtained reaches the outer surface of the tube first and then the wires. As a result, the heat to be removed in the wire-on-tube condensers is discharged from the system by the conjugate heat transfer mechanism. The surface temperature was determined as 50 � C. When selecting constant velocity as input bound­ ary condition, the input velocities are entered as between 0.5 and 2.5 m/ s. Because the inlet temperature is around 22.5 � C in experimental studies, this temperature is entered as inlet air temperature in numerical analysis. Since the wind tunnel was designed to reduce turbulence in the air entering the test chamber, both turbulent intensity and turbulent viscosity ratio are considered 5%. Because the air heated from the condenser surfaces is thrown into the atmospheric environment, the pressure outlet is selected such that gage pressure is 0 Pa for the output boundary condition. Boundary condition on the surface of tube and wires is coupled which means that fluid and solid interface temperatures are equal and velocity equal to zero because of non-slip condition. The hybrid mesh method is used to decrease the number of elements and nodes in the meshing method used for the solution as illustrated in Fig. 7. Tetra, hexa, wedge and pyramid mesh types are used in hybrid meshing. The average skewness and orthogonal quality values are around 0.2 and 0.8, respectively while the max skewness value is 0.78. As illustrated in Fig. 7b) and c), the inflation layer is formed with prisma mesh consisting of 7 layers on the surface of pipes and wires. Thus, a sensitive analysis zone is formed within the boundary layer. A mesh independence analysis was performed to reduce the computational time in addition to guarantee a minimum discretization error for the numerical study. Coil 1 given in Table 3 for air inlet velocity of 2 m/s. The change in total heat transfer in selected region for CFD analysis and output temperature read through analysis is less than 1% when the number of the mesh is increased to 10 times as seen in Table 3. Para­ metric studies were performed according to B case meshing conditions.

The values used in the parametric study are shown in Table 4. In the simulation, the air is used as the fluid and the density is taken according to the ideal gas assumption, while the heat transfer coefficient and the specific temperature are entered according to the film temperature. The methods chosen for the disintegration of the differential ex­ pressions used in the analysis are summarized in Table 5 [23]. Under-relaxation values are taken as in the program and no changes are performed. The convergence criteria were determined as 10 5 for continuity equation, 10 6 for radiation and 10 9 for energy. 4. Data reduction The heat transfer is due to both radiation and convection on wire-ontube condensers. In this case, the total heat transfer is expressed as follows. Q_ total ¼ Q_ C þ Q_ R

(11)

The radiation heat transfer rate is calculated for the experimental studies similarly to Tagliafico and Tanda’s study [7]. Radiation heat transfer was performed with the calculation of view factors over the area shown in Fig. 8. The Coil surface temperature is converted to an equivalent temper­ ature in order to simplify the calculations. It is accepted that the radiosities are uniform in Eq. (18). The surface of the body and the tube are assumed to be exhibit. The surfaces of the wire and tube are assumed to exhibit gray body behavior while the surrounding is accepted as a black body. The radiation heat transfer from related surfaces is calcu­ lated by means of Eq. (12).; � � �i ε h � 4 Q_ R ¼ ðNt 1Þ At;R σ T eq Jta þ Aw;R σ T 4eq Jwa (12) 1 ε Where At,R ¼ π DtSt, Aw,R ¼ πDwSwNw. View factors are calculated by considering the symmetry, enclosure, summation rules and view factors between cylinder pairs. Apparent thermal emittance (ϵapp) is calculated with the data obtained as a result of view factor calculations over the related areas. Thus, the heat transfer by radiation has been converted to the form seen in Eq. (13). 6

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International Journal of Thermal Sciences 151 (2020) 106241

Table 5 Solution methods used in the domain used for simulation. Pressure-Velocity relation Gradient Discretization Pressure Discretization Momentum Discretization Turbulent Kinetic Energy Discretization Specific Dissipation Rate Discretization Initialization

� Q_ R ¼ εapp σ AT T 4eq

� T 4c

Coupled Least Squares Cell Based PRESTO Second-Order Upwind Second-Order Upwind Second-Order Upwind Hybrid Initialization

(13)

The equivalent surface temperature in Equations (18) and (19) can be calculated from the following equation. Teq ¼

At Tt þ Aw Tw AT

(14)

If the fin efficiency is known, Tw can be found simply by using the following equation approximation [7]. Where At ¼ π DtStNt, Aw ¼ πDwSwNwNt

ηw ¼

Tw Tt

Tc Tc

(15)

However, since this value is not known, two thermocouples placed in St/2 position were measured in this experimental study. Assuming that the temperature across the wire surface changes linearly, the mean wire surface temperature can be calculated according to Eq. (16). Tw ¼

Tt þ Tw;up 2

(16)

As a result of these equations, the radiation heat transfer rate is subtracted from Eq. (11) and the convection heat transfer is discretized. The heat transfer calculations by convection are expressed according to the following equation based on the temperature difference between the inlet-outlet air temperature and the surface temperature. Q_ C ¼ Q_ C;t þ Q_ C;w ¼ ðht At þ ηw hw Aw ÞΔTm

(17)

where ΔTm is the logarithmic temperature difference, expressed as follows. ΔTm ¼

Table 3 Mesh independency analysis data. Node Numbers

Element Number

Qtotal,CFD (W)

Th (K)

A B C

105787 410247 1365120

431463 1476709 3966211

0.762 0.759 0.758

297.60 297.56 297.55

Dw (mm)

Dt (mm)

Sw (mm)

St (mm)

0.5 1.0 1.5 2.0 2.5

1.20 1.40 1.60 1.80 2.00

4.25 4.95 5.65 6.35 7.05

5.50 6.50 7.50 8.50 9.50

20.00 25.00 30.00 40.00 50.00

(18)

ηw ¼

tanhðmLÞ mL

(19)

m2 ¼

4hw kw Dw

(20)

where m expresses the temperature gradient on wires, L expresses as St/ 2. When Eq. (17) is examined, ht, hw and ηw are unknown to this equation. The ηw value can be obtained according to the adiabatic boundary condition assumption on fin tip and hw value. But, the math­ ematical calculation of ht and hw is very difficult from experimental data since only the heat transfer rate is known. Hoke et al. [10] suggested an empirical expression according to the relationship between the tube and the wire diameters. However, heat transfer on both wire and tube can be separately calculated with CFD analysis. In terms of the reliability of the data obtained from the numerical study, experimental studies were

Table 4 Geometric parameters for CFD analysis. Velocity

Tc Þ ðTt Th Þ � � In TTtt TThc

The temperature change on the wire along the distance between tubes is expressed by the fin efficiency. The fin efficiency is one of the most important factors affecting thermal performance in wire-on-tube condensers. Lee et al. [11] suggested the following equations to calcu­ late fin efficiency by accepting the adiabatic boundary condition.

Fig. 7. Mesh structure used in the analysis (a) General meshing view, (b) Tube surface detail (c) Wire surface detail.

Case

ðTt

7

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International Journal of Thermal Sciences 151 (2020) 106241

Fig. 8. Selected region for radiation view factor calculation.

conducted on Coils having five different geometries and compared with the numerical results. That’s why, ht and hw are calculated as follows equations by means of numerical study. Q_ C;t ht ¼ At ΔTm hw ¼

Q_ C;w ηw Aw ΔTm

Nut ¼

(21)

(23)

ρVf Dw μ

(24)

Rew ¼

hw Dw ks

(26)

Also, total heat transfer can be calculated by means of Eq. (27) as experimentally and numerically.

(22)

ρVf Dt μ

(25)

Nuw ¼

_ p ðTh Q_ total ¼ mc

Tc Þ ¼ mc _ p ΔT

(27)

The convection heat transfer is calculated by subtracting this value from the total heat transfer rate.

The average Nusselt and Reynolds numbers used for both wire diameter and tube diameter are defined as follows to evaluate the re­ sults. Reynolds numbers are calculated according to free stream air velocity. Ret ¼

ht Dt ks

5. Results and discussion As a result of the calculations, it is observed that the heat transfer with radiation has an effect of 3–11% in total heat transfer depending on the variation of velocity values. Similar results are found in CFD ana­ lyses. Results obtained from the experimental and numerical study for the coil geometries given in Table 2 are shown in Fig. 9. The results are quite compatible. The CFD results generally were in good agreement with less than

Nusselt numbers are expressed by considering wire and tube diam­ eter as characteristic length as below.

Fig. 9. Comparison of numerical and experimental results a) Total heat transfer rate b) Radiation heat transfer rate. 8

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10% error with experimental results. Also, the radiation heat transfer rate ranges also are acceptable between numerical and experimental results since many assumptions are applied during the analytical calculation. According to this information, the compatibility of CFD analysis is seen on a good tool to calculate heat transfer on wire-on-tube condensers. When Hilpert correlation [17]is calculated for a single circular cyl­ inder by considering tube and wire diameter used for Coil 1 as charac­ teristic lengths, it is calculated as ht ¼ 62.7 W/m2K and as hw ¼ 123.2 W/m2K at 2 m/s. However, as a result of the study ht ¼ 94.5 W/m2K, hw ¼ 112.7 W/m2K are found for Coil 1, respectively. When Coil 1 is considered, the air velocity on the tube increases due to the wires wel­ ded side by side to the tube surface and then the convection heat transfer coefficient on the tube is improved. However, similar results are not on the wires. In order to examine this situation, the flow is examined on the planes as below. Fig. 10 demonstrates the planes formed to determine the velocity, temperature and pressure behavior during the airflow through the wireon-tube condensers. The red X-axis, the green Y-axis, and the blue axis refer to the Z-axis in the coordinate system shown on the page plane. Accordingly, Plane A (blue plane) shows the cross-section on XY plane, while Plane B (green plane) shows cross-section on XZ plane. Plane C (red plane) is shifted by St/4 from the XZ plane in the þ Y direction, while Plane D (white axis) is shifted St/2 in a similar manner. The airflow is in the -X direction and the first contact with the air is called the front wire and the other is called the back wire. Fig. 11 indicates the pressure, velocity and temperature contours on the Plane A in order to visualize the flow, respectively. Fig. 12a–c show the velocity contours of Plane B, Plane C, and Plane D, respectively. When it is looked at the images formed in Figs. 10 and 11, it is seen that the wake region formed by the front wire decreases the velocity of the air reaching the back wire. In order to understand this situation, in the literature, studies on cross-flow conditions of low Reynolds numbers on two tandem circular cylinders were investigated [25–29]. In the studies, the circular cylinder diameter is denoted by D, the distance between the circular cylinders is expressed by L. The flow patterns are named according to the L/D (pitch ratios) ratios as extended body (L/D ¼ 1–2), reattachment (L/D ¼ 2–5) and co-shedding L/D > 5, respectively [25,27]. It has been stated that two cylinders acted like a single body in the extended body regimes. The reason for this is that the

downstream cylinder remains in the wake region as a result of the flow separation in the upstream cylinder. In addition, it has been shown that the flow separated from the shear layer of upstream circular cylinder wraps the downstream cylinder without re-attaching the boundary layer of it. Then, the Karman vorticity streets occur behind the downstream circular cylinder. In the reattachment regime, it is determined that the flow separation from the upstream does not wrap the downstream cyl­ inder. However, it is principally comprehended that the flow separated from the upstream cylinder adheres to the boundary layer of the downstream circular cylinder. By means of this situation, it is observed shedding of eddies inside the gap between them. In the co-shedding regime, both the upstream and the downstream circular cylinder form the Karman vortex shedding back of them due to increasing space be­ tween them [25,27]. In all three flow regime conditions, the gap and the region behind the downstream cylinder were determined to have a high-density turbulent zone [29]. According to the above statements, Dw represents D, and Dt corresponds to L in single-layer condensers in this study. The Dt/Dw ratio in the wire-on-tube condensers used in the application is mostly in the range of 2.5–4.5 in terms of Dt/Dw ratio. Therefore, the reattachment regime patterns are originated in the tandem sequence for wires on wire-on-tube condensers. However, the flow characteristic between the wires is relatively difference because of tubes which the wires are wel­ ded. Figs. 11(b) and 12 shows that the air velocity reaching the back wire under the influence of the air striking the tube partially disrupts the reattachment conditions. However, it is observed that this effect is reduced when the tubes are removed along the back wire, so the back wire remains under the influence of the front wire in larger proportions. Similarly, the effect of the tube on the flow characteristic is also observed in the temperature contours of Fig. 12. Fig. 13a–c are temperature distributions in Plane B, Plane C, and Plane D, respectively. An increase in the temperature of the air con­ tacting the front wire and the tube leads to an increase in the air tem­ perature reaching the back wire. As a result of increasing temperature and decreasing velocity in the gap reduces the heat transfer rate from the back wires. It is very difficult to measure this temperature experimen­ tally without disturbing the flow without CFD analysis or PIV etc. In practice, it is convenient to use the wires as a whole without separating the wires as front wire or back wire. However, considering the wires as front wire and back wire, the convection heat transfer

Fig. 10. Four planes assigned to determine the contours of velocity, temperature, and pressure. 9

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Fig. 11. (a) Pressure contours, (b) Velocity contours, (c) Temperature contours on Plane A according to the result of CFD analysis.

Fig. 12. Velocity contours on different planes (a) on Plane B, (b) on Plane C, (c) on Plane D.

coefficients can be calculated according to the following manner. Although it is different in the convection heat transfer coefficient depending on the temperature of the air accessing the back wire, the

logarithmic temperature difference is calculated by considering the inlet-outlet temperature for the purpose of simplification.

10

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Fig. 13. Temperature contours on different planes (a) on Plane B, (b) on Plane C, (c) on Plane D.

According to these equations, CFD analysis results for Coil 1 are given in Fig. 13. In Fig. 14 the variation of the average convection heat transfer co­ efficient of the tube and the front, back wires according to the different Reynolds numbers are given. It is observed that, as the Reynolds number increases, the heat transfer coefficient on both the tube and the wires increases as well. At the same time, it is seen that the average heat transfer coefficient of the wires is higher than the tube because the tube diameter is larger than the wire diameter. In the data in Fig. 14, it is found that the average heat transfer coefficient on the wires was 1.5 times higher than on the tube. The convection heat transfer coefficient on the front wire is very high compared to that of the back wire ac­ cording to the free stream air velocity. It is stated that the cause of this situation is decreasing velocity and increasing temperature in the gap

between the front and the back wire as seen in Figs. 11 and 12. Fig. 15 shows the pressure drop for the reference geometry according to free stream air velocity. One of the biggest advantages of wire-on-tube condensers is that the pressure drop is relatively low compared to the finned tube condensers used in cooling systems. As can be seen in Fig. 15, even if the air velocity in the single-layer condensers is 2.0 m/s, the pressure drop is around 2.2 Pa. Since the pressure drop in singlelayer wire-on-tube condensers is quite low, thus heat transfer is mainly studied in this study. In the following section, the effects of Dw, Dt, Sw, and St on heat transfer have been investigated. Coil 1 has been taken as reference geometry and one of the Dw, Dt, Sw, and St values were changed in parametric studies while the other values were kept constant. When Fig. 16 (a) is examined, the convection heat transfer coeffi­ cient on the tube increases with increasing air velocities and the heat transfer coefficient for smaller diameters is higher as expected. Fig. 16 (b) shows a reduction of about 10% of the convection coefficient on the tube when the diameter of the tube increases from 4.25 mm to 7.05 mm. The effect of increasing the tube diameter on heat transfer from the wires is quite small. Due to the expansion of the tube diameter, the air

Fig. 14. The variation of convection heat transfer coefficient on wires and tube according to the variation of Rew numbers for Coil 1.

Fig. 15. Effect of Rew on the pressure drop based on experimental and CFD results for Coil 1.

hw;f ¼

hw;b ¼

Q_ C;fw ηw Afw ΔTm

(28)

Q_ C;bw

(29)

ηw Abw ΔTm

11

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Fig. 16. (a). Rew versus hw for different wire diameters, 16 (b). Dt versus hw and ht at 2 m/s.

velocity passing through the coil is relatively increased as a result of the partial contraction in the area where the air pass. As a result of this, the air velocity reaching the back wire is partly high and the heat transfer on the wires is around 1–2%. Fig. 17 (a) shows the variation of the heat transfer coefficient on the wires corresponding Reynolds numbers, Fig. 17 (b) shows the variation of average heat transfer coefficient on the tube and wires for the air velocity of 2 m/s for different wire diameters. As expected, with increasing airflow rates, the heat transfer coefficients on both the tube and the wires have been increased. As seen in Fig. 17 (b), the increasing wire diameter decreases the heat transfer coefficient. The convection heat transfer coefficient at the free stream air velocity of 2.0 m/s over the 1.2 mm diameter wire is about 120 W/m2K, while at the same flow conditions it is 105 W/m2K for the diameter of 2.00 mm. The decrease in the heat transfer coefficient is around 15%. Although the diameter of the wire increased by 68%, the decrease in the convection coefficient is small due to the increased wire diameters and the narrowing of the cross-sectional area through which the flow passes and thus the velocity increase. As a result, when the wire diameter is increased from 1.2 mm diameter to 2.0 mm diameter, the convection heat transfer coefficient on the tube and wire decreases up to 5% and 15% as seen in Fig. 16 (b), respectively. Fig. 18(a) demonstrates the change in the average heat transfer co­ efficient on the wires to determine the effect of tube pitch varying from

20 mm to 50 mm. As data given in Fig. 18 is examined, it is seen that the distance between the tubes does not affect the convection heat transfer coefficient on the wires at low speeds and the heat transfer coefficient changes due to the increasing velocities. In Fig. 17 (b), the effect of distance between the tubes on the wires and the convection heat transfer coefficient is examined for a velocity of 2 m/s. Referring to Fig. 18 (b), the transport coefficients on the wires and the tube appear to exhibit a similar trend. When the distance between tubes (St) is increased from 20 mm to 50 mm, it is seen that there is a decrease in the heat transfer coefficient on both the tube and the wires by approximately 7–8% depending on the velocities. The main reason for this is the expanding of the section due to the increasing distance between the tubes. As can be seen from Fig. 11 (b) and Fig. 12, the airflow impinging on the tube slightly increases the velocity on the back wire surfaces. In this way, it partially disrupts the accretionary streams originating from the front wire and increases the convection coefficient on the back wire. How­ ever, increased St values reduce the area at which the tube affects the flow on the back wire. The back wire remains largely in the area of the wake region originating from the front wire, depending on the increased tube pitches. Fig. 19 (a) obviously shows the change in the heat transfer coefficient on the wires for the distance between the wires ranging from 5.50 mm to 9.50 mm. Fig. 19(a) shows that the convection heat transfer coefficients increase with similar trends versus increasing velocities. The variation of

Fig. 17. (a) Ret versus hw for different wire diameters, 16 (b) Dw versus hw and ht at 2 m/s. 12

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International Journal of Thermal Sciences 151 (2020) 106241

Fig. 18. (a) Rew versus hw for different tube pitches, 18 (b) St versus hw and ht at 2 m/s.

Fig. 19. (a). Rew versus hw for different tube pitches, 19 (b). Sw versus hw and ht at 2 m/s.

the distance between the wires is one of the most important parameters affecting the thermal performance of the wire-on-tube condensers. As previously mentioned, when the distance between the wires is reduced, the heat transfer coefficients increase for both wires and tubes, as the air velocities reaching the back row due to narrowing the cross-section and increase in tube surface. When the distance between the wires is increased from 5.50 mm to 9.50 mm, there is a 5% decrease in the heat transfer coefficient on the wires. The effect of the distance between the wires for the velocity of 2 m/s is shown in Fig. 19(b). The same phe­ nomenon is observed at other velocity values. It is seen that the heat transfer coefficient on wires and tubes decreases by 5% due to the increasing area, which is perpendicular to flow direction, depending on increasing wire pitch according to Fig. 19(b). As already mentioned in the literature, there is a correlation [10] and a correlation correction factor [11] for the heat transfer investigation of the wire-on-tube condenser where both wires and tubes are positioned perpendicular to the flow. Hoke et al. [10] only one coil positioned perpendicular to the flow and proposed a correlation accordingly in spite of working with 6 different coils, Similarly, Lee et al. [11] proposed a correction factor by conducting only a tube and wire diameter anal­ ysis. It is observed that the two correlations are quite different. It would be appropriate to propose a new correlation in terms of both having a low number of geometric features and giving quite deviant values

between each other. In this context, in addition to the parametric studies conducted with CFD analysis, more than 400 analyzes were employed in different combinations of parameters. The obtained data is examined with Excel Solver and two Nusselts correlations are proposed for both wire and tube as follows. � � 0:32 � �0:31 Sw Dw Nut ¼ 0:72Ret 0:53 (30) Dt Dt � Nuw ¼ 0:70Rew 0:49

Sw Dw

�

0:25

(31)

Ranges of the parameters used in the correlation, 38.7 � Rew � 322.8, 135.6 � Ret � 1162.2, 1.2 mm � Dw � 2.0 mm, 4.2 mm � Dt � 7.2 mm, 5.0 mm � Sw � 10.0 mm, 20 mm � St � 50 mm. Fig. 20 shows the estimation error range of Hoke et al., Lee et al. and the proposed correlations in this study versus the ht in Fig. 20(a) and hw in Fig. 20(b) values obtained from the CFD results. As can be seen from the Figures, the h values on both the wires and the tube give the closest results with the proposed correlations between �10% error. The 13

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International Journal of Thermal Sciences 151 (2020) 106241

Fig. 20. hCFD versus hCorr. (a) ht (b) hw.

6. Conclusions

correlation suggested by Lee et al. [11] yields 60% for both ht and hw. hw is estimated in the error range up to �15%, while ht is estimated in the error range reaching 30% according to the correlations proposed by Hoke et al. [10]. The results of the heat transfer by means of the proposed correlation are compared with the experimental results. The experimental results were also compared with Hoke et al. [10] and Lee et al. [11] in Table 6. When the data given in Table 6 is examined, it is seen that the results found with the correlations proposed in this study and Hoke et al.’s correlations give the closest results to the experimental studies [10]. On the other hand, it is observed that the values found with Lee et al.’s correction factor suggest results in error range up to 55% [11].

The thermal behavior of wire-on-tube condensers is investigated experimentally and numerically. The parametric study has been per­ formed numerically as a result of the validation of the CFD analysis by the experimental studies. Calculations are done with k-ω SST model for CFD analysis. The parametric studies have conducted the basis of forced convection in order to determine the effect of tube diameter, wire diameter, tube, and wire pitches. The obtained results are pointed out below. � Experimental studies are conducted for Coils with 5 different geometries.

Table 6 Comparison of the correlations found in the literature and proposed correlations with experimental results. Coil

Ret

Rew

Tt

Tc

Th

QC,exp

QC, proposed corr.

Error %

QC, Hoke

1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3 4 4 4 4 4 4 4 4 5 5 5 5

153.7 320.6 471.4 638.7 153.0 320.0 470.1 638.2 153.7 320.5 471.4 638.7 152.7 319.1 470.0 636.8 196.2 396.7 602.8 153.6 314.7 475.6 643.1 153.1 313.4 475.0 642.1 152.9 313.4 473.9 641.2

43.5 90.7 133.3 180.6 43.3 90.5 133.0 180.5 43.5 90.6 133.3 180.6 43.2 90.3 132.9 180.1 44.3 89.6 136.1 55.9 114.4 172.9 233.9 55.7 114.0 172.7 233.5 55.6 114.0 172.3 233.1

40.0 40.3 39.8 39.8 49.6 49.8 49.7 49.8 40.2 39.8 39.6 39.7 49.1 49.4 49.4 50.0 39.7 40.1 39.4 40.8 40.2 40.1 40.8 50.3 50.5 50.2 50.9 39.9 39.8 40.2 40.1

22.4 22.5 22.6 22.7 22.5 22.5 22.7 22.7 22.7 22.7 22.7 22.7 22.7 22.6 22.7 22.7 22.7 22.7 22.7 22.6 22.6 22.7 22.7 22.6 22.7 22.6 22.7 22.7 22.6 22.6 22.6

24.7 24.7 24.1 23.7 25.8 25.2 24.9 24.5 25.1 24.2 24.0 24.1 26.8 25.5 25.2 24.8 25.6 24.6 24.1 25.8 24.7 24.2 24.0 27.1 25.8 24.9 24.6 26.6 25.3 24.8 24.5

117.8 162.2 185.1 209.5 178.6 245.8 296.8 338.4 131.2 183.0 217.7 256.7 191.9 281.5 338.8 399.4 167.2 231.7 259.3 142.0 187.5 215.1 238.8 213.0 287.6 329.0 384.1 192.3 280.6 357.7 406.4

117.7 170.1 197.2 226 182.7 261.4 309.8 357.4 134.3 187.9 220 253.3 200.5 291.8 348 409.5 171.4 249 290.4 163.6 212.6 247.2 277.6 245.4 331.8 382.6 448.2 199.2 289.3 359.7 411.9

0.1 4.9 6.5 7.9 2.3 6.3 4.4 5.6 2.4 2.7 1.1 1.3 4.5 3.7 2.7 2.5 2.5 7.5 12.0 15.2 13.4 14.9 16.2 15.2 15.4 16.3 16.7 3.6 3.1 0.6 1.4

112.5 164.4 191.6 222.2 174.0 252.4 301.7 350.7 123.9 176.6 210.0 241.9 185.0 273.8 328.9 389.6 150.4 222.6 262.5 140.9 187.4 220.4 258.4 213.4 295.0 347.9 399.6 164.8 243.0 308.2 356.1

14

et al.

Error %

QC, Lee et

4.5 1.4 3.5 6.1 2.6 2.7 1.7 3.6 5.6 3.5 3.5 5.8 3.6 2.7 2.9 2.5 10.0 3.9 1.2 0.8 0.1 2.5 8.2 0.2 2.6 5.7 4.0 14.3 13.4 13.8 12.4

175.7 244.6 278.1 316.5 271.7 375.5 437.8 499.4 193.6 262.9 305.0 344.7 289.2 407.5 477.6 555.0 234.5 331.2 380.2 212.8 270.8 311.3 359.1 322.2 426.3 491.3 555.3 255.8 359.9 444.4 503.9

al.

Error % 49.2 50.8 50.2 51.1 52.1 52.8 47.5 47.6 47.6 43.7 40.1 34.3 50.7 44.8 41.0 39.0 40.3 42.9 46.6 49.9 44.4 44.7 50.4 51.3 48.2 49.3 44.6 33.0 28.3 24.2 24.0

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International Journal of Thermal Sciences 151 (2020) 106241

� Both the radiation and convection heat transfer rates calculated experimentally and numerically. It is determined that the radiation heat transfer rates are between 3% and 11% in total heat transfer rates. � The heat transfer coefficient on the front wire is approximately 50% higher than on the back wire at the velocities studied. � It is pointed out that the convection heat transfer coefficient on the tube decreases as expected as increasing the tube diameters. How­ ever, the effect of the increase in the tube diameter on the narrowing of the cross-section was observed to be very small. Thus, the convective heat transfer coefficients on the wires do not affect owing to varying tube diameters. � It is found that the variation of the wire diameter is very important for heat transfer. The parametrical study is performed for 5 different values between 1.2 mm and 2.00 mm. When the wire diameter in­ creases from 1.20 mm to 2.00 mm, the average convection heat transfer coefficient on the wires decreases by 10–12%. However, the convection heat transfer coefficient on the tube increases by about 15–20% according to air velocities. � Five different values between 20 mm and 50 mm are analyzed for the determination of the effect of the tube pitch. It is observed that the tube pitch does not affect the convection heat transfer coefficient both on the wires and on the tube at low velocities. But, the heat transfer coefficient on both wires and tube decreases by 7–8% by

increasing the tube pitch from 20 mm to 50 mm depending on increased free stream air velocities. � In order to determine the effect of heat transfer for wire pitches, five different values ranging from 5.5 mm to 9.5 mm were analyzed. When the wire pitch is varied from 5.5 mm to 9.5 mm, the convection heat transfer coefficients on the tube and wires is decreased by 5%. � Two correlations are proposed to determine the convection heat transfer coefficient both on the wires and on the tube. The proposed correlations based on Nuw and Nut values obtained from CFD studies provide strong estimation ability in the range of �10% error. � The results in the heat transfer calculations according to these cor­ relations are quite consistent with experimental studies. Declaration of competing interest On behalf of all authors, the corresponding author states that there is no conflict of interest. Acknowledgment This project is supported by Yildiz Technical University Scientific Research Projects Coordination Department with FBA-2017-3063 proj­ ect number. Also, the authors would like to express their appreciation to ATM Beyaz Esya Parcalari San. Tic. Ltd. S¸ti providing the coils used in experimental studies.

Appendix Uncertainty analysis [30] was employed on two different equations in order to find out the effect of uncertainty on all measurement equipment used in the experimental studies. The energy balance in the wind tunnel was first investigated for the uncertainty analysis. The heat transfer rate to the Coil with the power source was calculated and the difference in the energy balance was observed �10% with these calculations. Then, the uncertainty analysis was performed according to both the airside and the coil heat transfer rate. The uncertainties of the measurement devices are given in Table 1. Furthermore, the dimensional error range of the wire and tube diameters are determined as �0.5%, while the tube pitch and the wire pitch are about �1%. The uncertainty in the air-side heat transfer rate is found according to the following equation. sffiffiffiffiffiffiffi� ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi� ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X ∂Q_ total; exp �2 X ∂Q_ total; exp �2 2 uQ_ total; exp ¼ (32) um_ þ u2ΔT ∂m_ ∂ΔT i i The following equation is defined to find the heat transfer on the coil. (33)

Q_ ps ¼ heq Atotal ΔTm

Here, the heq value is considered as the equivalent heat transfer coefficient on the coil, including the effect of the fin efficiency and Atotal is Atotal ¼ At þ Aw . That’s why, the uncertainty of heq can be found by Eq. (34). sffi� ffiffiffiffiffiffiffiffiffiffiffiffi� ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi� ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi� ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi� ffiffiffiffiffiffiffiffiffiffiffiffiffiffi� ffiffiffiffiffiffiffiffiffiffiffiffiffi ∂heq 2 2 ∂heq 2 2 ∂heq 2 2 uheq ¼ (34) uQ_ þ uAtotal þ uΔTm ps ∂Atotal ∂ΔTm ∂Q_ ps The uncertainty analysis showed that the uncertainty in the air-side heat transfer was between 5% and �10%, while the uncertainty of heq was around �1% in Fig. 21. The uncertainty of heq is very small because both power-meter and thermocouple sensitivities are quite high. As a result, experimental uncertainties are up to %10–11.

15

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International Journal of Thermal Sciences 151 (2020) 106241

Fig. 21(a) %uQtotal,exp versus Qtotal,exp, (b) %uheq versus heq according to the data of experimental studies.

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