Energy Conversion and Management 52 (2011) 2785–2793
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Forced convection heat transfer and pressure drop for a horizontal cylinder with vertically attached imperforate and perforated circular fins Rasim Karabacak, Gülay Yakar ⇑ Department of Mechanical Engineering, Pamukkale University, 20070 Kınıklı, Denizli, Turkey
a r t i c l e
i n f o
Article history: Received 29 April 2010 Accepted 28 February 2011 Available online 21 April 2011 Keywords: Imperforate Perforated Finned heat exchanger Heat transfer
a b s t r a c t In this study, the effect of holes placed on perforated finned heat exchangers on convective heat transfer experimentally investigated. Six millimeter-diameter holes were opened on each circular fin on a heating tube in order to increase convective heat transfer. These holes were placed on the circular fins in such a way as to follow each other at the same chosen angle. The holes created turbulence in a region near the heating tube surface on the bottom of the fin. Some experiments were then performed to analyze the effect of this turbulence on heat transfer and pressure drop. These experiments were carried out at six different angular locations in order to determine the best angular location. In addition, a perforated finned heater was compared with an imperforate finned heater to observe the differences. In the cases of the Re above the critical value, Nusselt numbers for the perforated finned positions are 12% higher than the Nusselt numbers for the imperforate state. Moreover, a correlation has been obtained between the Re and Nu in the Re number above the critical value and the Re below the critical value. Meanwhile, correlations regarding pressure drops in the flow areas have been obtained. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Heat exchangers are widely used in many industrial and domestic applications. When one of the fluids is gas in a heat exchanger, liquid flows in the tube and gas flows over the tubes equipped with extended surfaces. In such an arrangement most of the thermal resistance is on the gas side and to reduce this thermal resistance many active and passive heat transfer enhancement techniques are applied. In their experimental study by using naphthalene sublimation technique Xiao and Tao [1] examined the heat transfer coefficients and friction factors for wavy plate-fin heat exchangers with different fin lengths. They applied thermal performance assessments for the same pumping power and pressure drop values; and found that both the Sherwood number and the friction factor increased while the mean heat transfer coefficient and pressure drop decreased with an increase in fin spacing. Karabacak [2] showed the effects of fin parameters on the heat transfer that occurred in the form of radiation and free convection in a horizontal cylindrical heater with rectangular sections and circular fins. Kayansayan’s [3] analysis displayed that boundary layer interaction between the fin and the plate leads to a reduction in the Nusselt number. Karabacak [4] also investigated the experimental relationships between heat flux, Nusselt number, and temperature ⇑ Corresponding author. Tel.: +90 258 2963261; fax: +90 258 2963262. E-mail address:
[email protected] (G. Yakar). 0196-8904/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2011.02.017
difference in a finned heater. Yan and Sheen [5], on the other hand, conducted experiments to determine the heat transfer and pressure drop characteristics of a plate (wavy and partitioned) fin heat exchanger. Wang et al. [6] studied plate-fin heat exchanger under crosscurrent and frictional current conditions, and then determined an experimental correlation describing the performance of the air side of the model fin. Souidi and Bontemps [7] studied the countercurrent gas–liquid flow in plate-fin heat exchangers with plain and perforated fins, and then compared their results with the experimental results in the literature for rectangular canals. Leu et al. [8] also analyzed the performances of the air sides of plate-fin heat exchangers with round and oval shapes. Their results showed that the pressure drop increases with the fin angle while heat transfer and friction increase with fin length. Wierzbowski and Stasiek [9] analyzed the heat transfer by using a liquid crystal technique in a plate-fin heat exchanger. Yakut and Sahin [10] experimentally investigated the flows that cause the vibration characteristics of the turbulators used to increase the heat transfer in heat exchangers. They found that the Nusselt number increases with the increase in Reynolds number. Zhang et al. [11] investigated the heat transfer characteristics of a helically baffled heat exchanger combined with one three – dimensional finned tube. They carried out the experiments in counter mode operation with hot oil in the shell side and cold water in the tube side. They used a commercial computational fluid dynamics (CFD) program called Fluent 6.0 to predict the flow and heat transfer performance in the heat
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Nomenclature A0 Aw As
RAf c cwater cair C Cair Cwater D d ebi Fij G_ hf hw h0 K, M, N L _ m _ water m _ air m NTU Nu Nuh Dp qc Qt Qc RQR Qw Qf q Re Reh Recr ri s t
total heat transfer area (m2) heating tube surface area except total fin surface area (m2) area of reference section perpendicular to the flow direction between two fins (m2) total area of the fins on the tube (m2) specific heat capacity (kJ/kg °C) specific heat capacity of water (kJ/kg °C) specific heat capacity of air (kJ/kg °C) _ capacity rate (W/°C) (C ¼ mc) capacity rate of air (W/°C) capacity rate of water (W/°C) fin diameter (m) outer diameter of heating tube (m) black body radiation power (W/m2) view factor between i surface and j surface mass flow velocity (kg/m2 s) heat convective coefficient around fin (W/m2 °C) heat convective coefficient around body (W/m2 °C) visible heat convective coefficient (W/m2 °C) coefficient of formulation length of heating tube (m) mass flow rate (kg/s) mass flow rate of water (kg/s) mass flow rate of air (kg/s) number of transfer units (NTU = AoU/Cmin) Nusselt number Nusselt number of perforated state pressure drop (mbar) convective heat flux (W/m2) heat power supplied from hot fluid (W) convective heat flow rate (W) total radiative heat flow rate (W) amount of the heat transferred by air over heating tube (W) amount of the heat transferred by air over fins (W) radiation heat flux (W/m2) modified Reynolds number modified Reynolds number of perforated state critical modified Reynolds number surface radiation (W/m2) distance between fins (m) fin thickness (m)
exchanger. Chen and Hsu [12] predicted the average heat transfer coefficient and fin efficiency on a vertical annular circular fin of finned – tube heat exchangers for various fin spacings in forced convection. They assumed the distribution of the heat transfer coefficient on the fin to be non – uniform, thus they divided the whole annular circular fin into several sub – fin regions in order to predict the average heat transfer coefficient and fin efficiency values. Tang et al. [13] experimentally investigated air – side heat transfer and friction characteristics of nine kinds of fin and tube heat exchangers, with a large number of tube rows (6, 9, and 12, respectively) and large diameter of tubes (18 mm). They acquired the heat transfer and friction factor correlations for all the heat exchangers with Reynolds numbers ranging from 4000 to 10,000. The goal of the present study is to investigate the heat transfer enhancement capacity of the holes opened on the circular fins. As an enhancement mechanism the holes have a potential to reduce the thickness of the boundary layer that is formed on the circular fins placed on the heating tube; thus, increasing heat transfer through convection in this area.
Tw T0 Tf T ftip T wateri T watero DTwater
DTair T airi T airo um U V_ wR
temperature of heating tube surface (°C) temperature of the heated air (°C) average fin temperature (°C) fin tip temperature (°C) input temperature of water to tube (°C) output temperature of water from tube (°C) difference between the input and output temperature of water in heating tube (°C) difference between the input and output temperature of air from heat exchanger (°C) input temperature of air into heat exchanger (°C) output temperature of air from heat exchanger (°C) average velocity of air (m/s) overall heat transfer coefficient (W/m2 °C) volumetric flow rate of air (m3/h) uncertainty
Greek symbols ei emissivity coefficient for surface e effectiveness k thermal conductivity (W/m °C) kf thermal conductivity of fin material (W/m °C) r Stefan–Boltzmann constant (W/m2 K4) g0 finned-surface efficiency gf fin efficiency m kinematic viscosity (m2/s) l dynamic viscosity (kg/ms) h angular location (°) Subscripts air air side c convection f fin i input o output R radiation tip fin tip t total water water side w tube wall
2. Experimental set-up Information on the experimental apparatus, devices used, and procedures followed were given in detail by Yakar [14]. A summary of that information is presented below. The schematic of the experimental set-up is shown in Fig. 1. As can be seen in Fig. 1, air is supplied to the test section by a variable speed fan (no. 2) which was installed on a table (no. 1). The channel (no. 3) length before the test section is long to obtain a fully developed flow at the entrance to the test section. The mass flow rate of the heated air at the entrance and at the exit of the test section was measured by a propeller – type flow meter (nos. 4 and 14). Inlet and exit air temperatures were measured by T – type copper – constantan thermocouples (nos. 5 and 13). The same type of thermocouples were used to measure the temperatures at the fin base, fin tip and between the fins at distances of 15, 45 and 75 cm from the entrance of 900 mm-long finned heating tube. Detailed temperature measurement points are shown in Fig. 2. A manometer was used to measure the input and output pressure
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Fig. 1. Schematic diagram of the experimental set-up.
Fig. 2. Temperature measurement points on the air side of the heat exchanger.
difference of the air (nos. 6 and 12). The tube side material in which water flows is galvanized steel (no. 8). The fin material was also galvanized steel. Moreover, the pressures (nos. 9 and 17), temperatures (nos. 10 and 18), and volumetric flow rate (nos. 11 and 19) of the heating water were measured at the inlet and the exit of the finned tube. The heat exchanger was installed on a table (no. 15). The heating water was carried to the heat exchanger by a tube (no. 16). The heating water, on the other hand, was heated by electrical heaters (no. 22) that are placed inside the 250 l water tank (no. 21). The water used to heat the air was carried from the water tank (no. 21) to heat exchanger by a pump (no. 20). The body into which the finned tube was placed was insulated with an insulating material (no. 24) of 10 mm thickness. Moreover, the route of the air around the heating tube was lengthened by means of deflectors (no. 25) placed in the inner surface of the external body. In this study, the external diameter of the body into which the finned tube was placed was 154 mm, the heating tube external diameter was kept fixed at 29 mm, the fin diameter was 87 mm, and the fin thickness was 0.5 mm. The distance between the fins, on the other hand, varied to be one of five different values; these were 4, 8, 10, 12 and 15 mm. The heating tube length was kept fixed at 900 mm. In accordance with the goal of the experimental
study, convective heat transfer was intended to be increased by reducing the thickness of the boundary layer on the fins by using 6 mm-diameter holes that were opened at different angles on the circular fin that was placed on the heating tube. These same-diameter holes on each fin could follow each other at the same selected angle. Experimental studies were carried out at six different angular locations; 0°, 15°, 30°, 45°, 60° and 90°. Fig. 3 shows the circular finned heating tubes that had 6 mm-diameter holes at angles 0°, 15°, 30°, 45°, 60° and 90°. To determine the effects of the flow directions of the heating and heated fluid to each other, experiments were carried out at parallel and counter flow arrangements and with the air mass flow rates of 0.04, 0.06 and 0.08 kg/s. All measurements recorded by a computer and analyzed by a program. 3. Uncertainty Each of the measurement devices used in experiments has a measurement uncertainty. Uncertainty analysis has been carried out according to the standard procedures in the literature. if R depends on ‘‘n’’ independent variables (x1, x2, . . . , xn), then the error in R, wR, depends on these variables according to:
wR ¼
"
@R w1 @x1
2
@R þ w2 @x2
2
@R þ w3 @x3
2
@R þ þ wn @xn
#1=2
ð1Þ The results of the error analysis can be seen in Tables 1 and 2. 4. Mathematical formulation and data reduction Total heat transfer rate (Qt) from the hot water to air consists of radiation (QR) and convective (Qc) components. When the temperature distribution along the fin is known, it is theoretically possible to calculate the amounts of both convective and radiative heat transfer from the cell realized by the two neighboring fins. If the energy balance is written for the elementary area dA, as shown in Fig. 4, then the following equation is obtained:
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Fig. 3. Finned heating tubes where 6 mm-diameter holes were opened at the angular locations of 0°, 15°, 30°, 45°, 60° and 90°.
Table 1 Uncertainties of the values measured in experiments. Measured value
Uncertainty in measurements
Pressure difference on the air side Temperature on the air side Velocity on the air side Tube diameter on the air inlet side Distance between two fins Fin diameter Flow on the water side Pressure on the water side Temperature on the water side
±0.16 mbar ±0.5 °C ±0.2 m/s ±2 mm ±1 mm ±0.5 mm ±0.4 l/h ±0.2 mbar ±0.1 °C
Table 2 Uncertainty in the values calculated with the units measured in the experiment.
2
d T dr
2
þ
Calculated value
% error
_ air (kg/s) m um (m/s) Qt (W) Qc (W) T0 (°C) Tw (°C) Tf (°C)
0.34 0.35 0.16 0.34 0.58 0.58 0.58
2hf 1 dT 2rei ¼ ðT T 0 Þ þ ½F drw ðT 4 T 4w Þ þ F dr0 ðT 4 T 40 Þ r dr kf t kf t Z ro 4 dF drdr0 ðT 4 T 0 Þ ð2Þ þ ri
The expression given in Eq. (2) is usually a nonlinear integro-differential equation. In addition, shape factors contain complex integral expressions depending on fin geometry thus making the equation
hard to solve. So in the current study by using the arithmetical averages of the experimentally determined fin base and tip temperatures as fin temperature, radiative and convective heat transfer rates are calculated as follows. 4.1. Heat transferred by radiation When calculating the amount of radiative heat transfer from the circular fin surfaces placed on the heating tube, it is necessary to first determine the shape factors of the surfaces. The shape factors depend on the fin parameters of the surface in the closed cell made by two neighboring fins, as shown in Fig. 5, and also given in Ref. [15]. To calculate the radiative heat transfer from the fin surfaces to the surrounding air, an analogous electrical circuit, as shown in Fig. 6, was used for the thermal interaction between the surfaces. Since the sum of currents in each node of the electrical circuit is zero, one can write for any point ri, i = 1, 2 and j = 1–4
ebi r i 1ei
ei
þ
X rj ri j
1 F ij
¼0
ð3Þ
where ebi ¼ rT 4i – black body radiation power (W/m2), ri – surface radiation (W/m2), ei – emissivity coefficient for surface. Radiation from (1) and (2) surfaces are the same according to Fig. 6; and (r1 = r3) and (r4 = eb4). Besides to the equality condition of q14 = q34, radiative heat transfer from the cell formed by two fins to outer air medium can be stated as:
q4 ¼ 2q14 þ q24
ð4Þ 2
where q – radiation heat flux (W/m )
q14 ¼ F 14 ðr 1 r 4 Þ
ð5Þ
q24 ¼ F 24 ðr 2 r 4 Þ
ð6Þ
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dA
q0
dqc
dqc
dq r
dq r qi r
ro
dr
d
r
r0 ri
D
ri
S
Fig. 4. Circular and horizontal finned tube heater.
Fig. 5. Closed cell component formed between two fins.
Fig. 6. Electrical analogy circuit for the closed cell formed between the two fins.
In the horizontal heater formed by n circular fins, radiative heat transfer from all of the heater cells is:
where A0 = Aw + RAf: total heat transfer area; and g0 represents the efficiency of the finned surface. The value of efficiency can be calculated by using the following equation [16]:
Q R1 ¼ ðn 1ÞA4 q4
ð7Þ
go ¼ 1
As a result of these equations [15]:
Q R1 ¼ K
4
Tw 100
þM
Tf 100
4
N
4
T0 100
ð8Þ
Tf is the average fin temperature; Tw is the heating tube surface temperature; and T0 is the temperature of the heated air from the upper part of the fin in the abovementioned equation. The values of the K, M, and N coefficients given in Eq. (8) were taken from reference [14]. For the galvanized steel fin and the galvanized steel heating tube material, emissivity coefficients were measured to be egal = 0.06 and ed = 0.15, respectively, were used for the solution of Eq. (8). Radiative heat transfer from fin tips is as follows:
Q R2
" 4 # X T ftip 4 T0 ¼ ðAF Þtip rei 100 100
ð9Þ
The total radiative heat transfer from all of the heating surfaces, on the other hand, is as below:
RQ R ¼ Q R1 þ Q R2
Af ð1 gf Þ A0
ð12Þ
Fin efficiency gf was given in Ref. [14] according to the fin parameters. Moreover, Aw is the area of the outer surface of heating tube while RAf represents the total surface area of the fin. The visible heat convective coefficient h0 is determined by the following equation when total power input Qt is known:
h0 ¼
Q t RQ R
g0 A0 ðT w T 0 Þ
ð13Þ
Eqs. (12) and (13) was solved simultaneously. Iteration is continued until the g0, gf, and h0 values converge to within 1%. Depending on the value of h0 obtained from the iteration, the Nusselt number is determined as follows (depending on the outer diameter of the heating tube):
Nu ¼
h0 d k
ð14Þ
ð10Þ
4.3. Modified Reynolds number
ð11Þ
The heated air flows through the spaces between the fins and the body inside the finned heat exchanger. Depending on the free flow area the air decelerates and accelerates. First it flows parallel, then vertical, and then parallel again. Because of the deflectors used in the system, flow direction of the air on the heating tube
4.2. Heat transferred by convection The convective heat transfer rate;
Q C ¼ h0 ðg0 A0 ÞðT w T 0 Þ
P
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changes continuously. Nonetheless, mass flow rate remains the same throughout the flow in the test section. Considering this, the Reynolds number that characterizes the air flow should be defined in terms of the mass velocity;
_ air m G_ ¼ As
ð15Þ
_ air is the mass flow rate of the air passing through the heater m while As represents the area of reference section perpendicular to the flow direction between two fins (As = Ds) in the abovementioned equation. On the other hand, not all of the air mass passes through the section between two fins under experimental conditions. Some of it passes through the intersection between the fin end and the outer body while some passes through the holes that are at certain angular locations. Therefore, the Reynolds number cannot be exactly defined as in the case of perpendicular flow to the tube. Reynolds number should contain the effects of the other flows. This case is rather complicated. So instead of Reynolds number, a new modified Reynolds number should be defined. The Reynolds number, which characterizes the flow, should take into account the convective heat transfer calculated for unit surface ðqc ¼ QA0c Þ since convective heat transfer is dependent on movement of the air. Consequently, the modified Reynolds number should be described according to ðqc ¼ QA0c Þ. After the required adjustments are made, the modified Reynolds number, which is obtained in such a way as to take the measured values into account, can be stated as follows (modified Reynolds number = Reynolds number Nusselt number): 2
Re ¼
_ qc Gd lkðT w T 0 Þ
ð16Þ
Physical properties of the air in the equation were obtained by using the film temperature as follows:
T film ¼
Tw þ T0 2
5. Experimental system validation To the knowledge of the authors, there is no experimental study to exactly compare the results of the current study with perforated fins. So by using imperforate fin results [14] at the same working conditions for the same geometrical parameters with the perforated fins at 30° and 60° angular locations, comparisons have been made in terms of effectiveness values. Imperforate fin results were in very good agreement with the values given in Ref. [16]. For counter flow arrangement with imperforate fins NTU, capacity rate ratios and effectiveness values in [16] are as follows.
NTU ¼ 0:295;
C min C min C air and ¼ 0:0087 ¼ C max C max C water
e ¼ 0:260
and the results from the current study gives:
NTU ¼ 0:295;
C min ¼ 0:0087 and C max
e ¼ 0:265
From the above values, it is clearly seen that imperforate fin results are in very good agreement with the literature. For the same geometrical parameters (D/d = 3, s/d = 0.345) at an angular location of 60° for a counter flow arrangement perforated fin effectiveness of e = 0.313 is 18.1% higher than the value of e = 0.265 obtained from imperforate fin geometry. 6. Results and discussion 6.1. Imperforate state The change in NuxRe according to Re for the imperforate state is shown in Fig. 7. Fig. 8, however, shows the Nu change according to Re for the imperforate state.
The significance of transition is that no boundary layer interference occurs at Re numbers above the critical value and the data points cluster on a single line. As shown in Fig. 8 Re > Recr (cr = critical), the effects of both diameter ratio (D/d) and the fin spacing pitch on Nusselt number become undetectable in the data presentation. Then a single equation relating the two principal parameters is determined from a least squares fit and is given by,
Nu ¼ 0:51
Re
0:77 ð17Þ
104
At Re numbers below the critical value, where the boundary layer interference prevails, strong dependence of Nusselt number on D/d and s/d is expected. Then in the low range critical Re numbers, a single equation relating the two principal parameters is determined from a least squares fit and is by:
Nu ¼ 0:58
Re
0:77
104
ð18Þ
6.2. Perforated state The change in NuxRe according to Re for the perforated state is shown in Fig. 9. The general sensitivity of Nu values to D/d is worthy of special note and Fig. 9 may be examined in this regard. Here NuxRe data for a fin diameter ratio of 3 are plotted as a function of Re. An interesting feature of this illustration is the existence of ‘‘discrete transition’’. At a particular diameter ratio D/d, the transition point is located by a change in the slope of the linear curves produced. The critical Re numbers at transition points are summarized in Table 3. As shown in this table, for h values in the 0°, 15°, 30°, 45°, 60° and 90°, the term ðsin h þ 2Þ1=3 Recrh , with a deviation of ±2% can be said to be constant for all h values and approximated to be, ðsin h þ 2Þ1=3 Recrh ¼ 7:478x106 For h values of 0°, 15°, 30°, 45°, 60° and 90°, the change of the Nusselt number according to Re is shown in Fig. 10. The significance of the transition is that no boundary layer interference occurs at Re numbers above the critical value and the data points for all a h values cluster on a single line. As shown in Fig. 10, for Re > Recr, the effects of h values both the diameter ratio and the fin – spacing pitch on Nusselt number become undetectable in the data presentation. Then a single equation relating the two principal parameters is determined from a least squares fit and is given by:
0:77 Reh Nuh ¼ 0:52 104
ð19Þ
This relation is found to be valid for the ranges of parameters indicated; 0°, 15°, 30°, 45°, 60° and 90°, s/d = 0.345, D/d = 3 and Re > Recr. At Re numbers below the critical value, where the boundary layer interference prevails, strong dependence of Nusselt number on h values is expected. The data for h values of 0°, 15°, 30°, 45°, 60° and 90° are presented in Fig. 10, in six separate groups, at fin spacing pitches of 0.345 and diameter ratio of 3. Then, in the low range critical Re numbers, a single equation relating the two principal parameters is determined from a least squares fit and is by,
0:77 Reh Nuh ¼ 0:45 104
ð20Þ
In Eqs. (17)–(20), the exponent being very close to sieder and Tate’s finding [17] at high Reynolds number signals, as expected, lessened the influence of fin cylinder interaction. Fig. 11 shows the change of the Nusselt numbers for the states in which the holes on the fins are organized under certain h angles
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d
D/d=3 s/d=0.345 Imperforate State
D
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S
1000
Re/10
4
800
Recr=540x104
600 400 200 0
0
20
40
60
80
100
(NuxRe)/107 Fig. 7. Discrete transition in forced convection heat flow horizontally oriented finned tube in closed duct.
d
140
S
Recr=540x104
120
Nu=0.51(Re/104)0.77
100
Nu
Table 3 Re numbers for discrete transition in heat flux (0–90°, D/d = 3, s/d = 0.345).
D
D/d=3 s/d=0.345 Imperforate State
80 Nu=0.58(Re/104)0.77
60
h
(sin h + 2)1/3Recr
0° 15° 30° 45° 60° 90°
6.91 106 7.20 106 7.44 106 7.64 106 7.78 106 7.90 106
40 20 0
250
500
750
and to the state in which the fins on the finned heater are imperforate according to Re numbers above the critical value and Re numbers below the critical value. In the cases of the Re below the critical value, it has been determined from Fig. 11 that Nusselt numbers in imperforate state finned position are 6% higher than the Nusselt numbers in perforated finned position. In the cases of flowing conditions above the critical,
1000
Re/104 Fig. 8. Nusselt number results of imperforate state for spacing ratio of s/d = 0.345 at different Re numbers.
900 850 800 750 700 650
d
D/d=3, s/d=0.345 θ(Perforated) symbol 0˚ 15˚ 30˚ 45˚ 60˚ 90˚
D
0
S
Recrθ=5.5x106
600
Re/104
550 500 450 400 350 300 250 200 150 100 50 0 0
5
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105110
(NuxRe)/107 Fig. 9. Discrete transition in forced convection heat flow for horizontally oriented perforated finned tube in closed duct.
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Fig. 10. Nusselt number results of perforated state for h values from 0°, 15°, 30°, 45°, 60°, 90° and for Re numbers.
Fig. 11. The change of the Nusselt numbers for the state in which the fins on the finned heater are imperforate and for the states in which the holes on the fins are arranged according to certain h angles according to the Re numbers above the critical and Re numbers below the critical.
Nusselt numbers for the perforated finned positions are 12% higher than the Nusselt numbers for the imperforate state. In the flowing conditions above the critical Re, it is seen that Nusselt number can increase more and more for the perforated state than for the imperforate state. 7. Conclusions The literature review showed that there was not such a study previously made in literature. Therefore, a total of 1000 experiments were conducted in order to attain reliable results. The conclusions obtained in this study are listed below: 1. When the change of Re numbers according to h angular arrangement of the holes on the fin is analyzed, a relationship between the Re numbers for the perforated state and Re numbers for the imperforate state was discovered as below:
Reimperforate ¼ Reh ðsin h þ 2Þ1=3 2. The critical Re for the imperforate state finned position was determined as Recr = 5.4 106 and the critical Re for the perforated state was found as Recr = 5.5 106.
3. It was determined that there were a lot of boundary layer interactions under the conditions of Re below the critical value, whereas this interaction was found out to decrease somewhat in the Re numbers above the critical value. Therefore, Nusselt number was determined to increase. 4. According to 1000 experiments, it was found out that i. In the Re numbers below the critical value, heat transfer on the finned heater of imperforate state was 6% higher than for the perforated finned state, ii. However, in the Re numbers above the critical value, heat transfer on the finned heater of perforated state was 12% higher than for the imperforate finned state. 5. When the pressure drops were analyzed for the flowing conditions for the imperforate and perforated state on the heater with the same geometric parameters, D/d = 3, s/d = 0.345, the following results were obtained; iii. For the imperforate state, the relationship between Re and pressure drop, Dp (mbar), was found as Dp = 6.17 107Re by ±6% error. iv. For the perforated state, the relationship between Re and pressure drop, Dp (mbar), was found as Dp = Reh( sin h + 2)m.
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v. Here, m exponent value was determined to be varying with the h angle. The values of m were determined as follows; h
m
0° 15° 30° 45° 60° 90°
20.90 17.27 16.18 14.25 13.36 13.16
Acknowledgments The authors would like to express their appreciation to the Pamukkale University Scientific Research Projects Council, Turkey, Report No. 2003/MHF005 for providing financial support for this study. References [1] Xiao Q, Tao WQ. Effect of fin spacing on heat transfer and pressure drop of two–row corrugated–fin and tube heat exchangers. Int Com Heat Mass Transf 1990;17:577–86. [2] Karabacak R. The effects of fin parameters on the radiation and free convection heat transfer from a finned horizontal cylindrical heater. Energy Convers Manage 1992;33:997–1005. [3] Kayansayan N. Thermal characteristics of fin-and-tube heat exchanger cooled by natural convection. Exp Therm Fluid Sci 1993;7:177–88.
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[4] Karabacak R. Experimental relationships for heat flux, Nusselts number and temperature difference in a finned heater. Energy Convers Manage 1996;37:591–7. [5] Yan WM, Sheen PJ. Heat transfer and friction characteristics of fin-and-tube heat exchangers. Heat Mass Transf 2000;43:1651–9. [6] Wang CC, Hwang YM, Lin YT. Empirical correlations for heat transfer and flow friction characteristic of herringbone wavy fin and tube heat exchangers. Int J Refriger 2001;25:673–80. [7] Souidi N, Bontemps A. Countercurrent gas–liquid flow in plate-fin heat exchangers with plain and perforated fins. Int J Heat Fluid Flow 2001;22:450–9. [8] Leu JSM, Liu S, Liaw JS, Wang CC, Numerical Investigation A. A numerical investigation of louvered fin and tube heat exchangers having circular and oval tube configurations. Int J Heat Mass Transf 2001;44:4235–43. [9] Wierzbowski M, Stasiek J. Liquid crystal technique application for heat transfer investigation in a fin-tube heat exchanger element. Exp Therm Fluid Sci 2002;26:319–23. [10] Yakut K, Sahin B. Flow-induced vibration analysis of conical rings used for heat transfer enhancement in heat exchangers. Appl Energy 2004;78:273–88. [11] Zhang Z, Ma D, Fang X, Gao X. Experimental and numerical heat transfer in a helically baffled heat exchanger combined with one three dimensional finned tube. Chem Eng Process 2008;47:1738–43. [12] Chen HT, Hsu WT. Estimation of heat transfer characteristics on a vertical annular circular fin of finned tube heat exchangers in forced convection. Int J Heat Mass Transf 2008;51:1920–32. [13] Tang LH, Min Z, Xie GN, Wang QW. Fin pattern effects on air-side heat transfer and friction characteristics of fin-and-tube heat exchangers with large number of large-diameter tube rows. Heat Transf Eng 2009;30:171–80. [14] Yakar G. The effect of turbulence created in fin-tube type heat exchangers with perforated fin on heat transfer and pressure drop. Ph.D. thesis, Pamukkale University, Denizli, Turkey; 2007. [15] Karabacak R. The effect of fin geometric parameters on natural convection from a horizontal cylinder. Ph.D. thesis, Dokuz Eylul University, Izmir, Turkey; 1989. [16] Holman JP. Heat transfer. 4th ed. Tokyo: McGraw-Hill; 1976. [17] Sieder EN, Tate CE. Heat transfer and pressure drop of liquids in tubes. Ind Eng Chem 1936;28:1429.