experimental investigation of forced convection heat · experimental investigation of forced...

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Experimental Investigation of Forced Convection Heat

Transfer over Horizontal Tube with Conical Fins for Different Fin Spacings and Different Inclination Angles

Journal: Transactions of the Canadian Society for Mechanical Engineering

Manuscript ID TCSME-2017-0129.R2

Manuscript Type: Article

Date Submitted by the Author: 18-May-2018

Complete List of Authors: Yakar, Gülay; pamukkale university, mechanical;

Keywords: forced convection, inclination angle, conical fin, heat transfer

Is the invited manuscript for consideration in a Special

Issue? : N/A

https://mc06.manuscriptcentral.com/tcsme-pubs

Transactions of the Canadian Society for Mechanical Engineering

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1

Experimental Investigation of Forced Convection Heat

Transfer over Horizontal Tube with Conical Fins for Different

Fin Spacings and Different Inclination Angles

Gülay Yakar*

Department of Mechanical Engineering, Pamukkale University, 20070 Kınıklı, Denizli,

Turkey

Abstract

This paper was performed to experimentally studied the heat transfer over the horizontal

tube with conical fins for different fin spacings and different inclination angles. The air

entering the test section first contacts the large surface of the conical fin. Therefore, the

conical fin both directs the air towards the heating surface and increases the heat transfer

surface area. The experiments were conducted for three different inclination angles (45º, 60º

and 80º) and three different fin spacings (10, 12 and 15 mm). Water and air were used as hot

and cold fluid in these experiments, respectively. The temperature of water, which was the

heating fluid, was kept fixed at 65 °C. The cold fluid entered the test section at eight different

air flow velocities (2 – 20 m/s). The experimental results indicated that the Nusselt number at

each inclination angle for the 10-mm fin spacing was almost the same. Moreover, for the 15-

mm fin spacing, the highest Nusselt number was obtained at 80º and lowest at 60º for Re >

5x104, while the Nusselt number was almost the same at each inclination angle for Re <

5x104. It was determined that the lowest pressure drop was obtained at 80º for both 10 and 15

mm.

Key words: forced convection, inclination angle, conical fin, heat transfer

* Corresponding author. Tel: +90-258-2963097. Fax: +90-258-2963262. E-mail address: [email protected].

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1. Introduction

The most effective method for increasing the efficiency of heat exchangers is to improve

the heat transfer coefficients on the hot and cold fluid side. In order to increase the heat

transfer coefficient, different enhancement techniques are used, both active and passive.

Petracci et al. (2016) studied numerically the average heat transfer on a finned cylinder

cooled by a rectangular jet of height. H. Change et al. (2016) measured axial Nusselt number

distributions and tube averaged fanning friction factors for the tubular flows enhanced by twin

or four twist – fin inserts with five twist ratios and ∞ (straight fins) at Reynolds numbers of

750 – 70,000. Al – Asadi et al. (2016) numerically analyzed three-dimensional conjugate heat

transfer under laminar flow conditions within a micro-channel to explore the impact of a new

design of vortex generator positioned at intervals along the base of the channel. Zhang et al.

(2016) experimentally studied the steady state laminar flow and transition flow heat transfer

performance of two types of wavy fin heat exchangers with different Reynolds numbers on

both air and water sides. Peng et al. (2016) numerically and experimentally investigated the

thermos-hydraulic performances of an internally finned tube with innovative wave fin arrays.

Dong et al. (2016) presented an efficient and low resistant circumferential overlap trisection

helical baffle shell-and-tube heat exchanger with folded baffles (cothHXf). Khoshvaght –

Aliabadi (2016) studied the effects of vortex-generator (VG) and Cu/water nanofluid flow on

performance of plate – fin heat exchangers. His results indicated that the VG channel is more

effective than the nanofluid on the performance of plate-fin heat exchangers. Behfard and

Sohankar (2016) performed a numerical simulation to investigate the heat transfer and

pressure drop characteristics of three-row inline tube bundles as a part of a heat exchanger.

Ahmed et al. (2015) carried out numerical and experimental investigation to study the laminar

heat transfer and fluid flow characteristics in an equilateral triangular duct using combined

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vortex generator and nanofluids. They found that both numerical and experimental results

show a good enhancement in heat transfer by using vortex generator with base fluid. Tian et

al. (2015) performed three-dimensional numerical simulations to investigate the flow and heat

transfer characteristics of the plain fin with multi-row delta winglets punched out from the fin.

Kiatpachai et al. (2015) investigated the effect of fin pitches on the air-side performance of

serrated welded spiral fin-and-tube heat exchangers having z-shape flow arrangement and the

number of tube rows of 2 in range of high Reynolds number (4000 – 15,000).

The aim of the study is to study the effect of conical fins on heat transfer enhancement.

Unlike other studies in the literature, conical fins are used in this study instead of traditional

circular fins. Because they increase both the heat transfer area and extend the residence time

of air flow in the heating tube. Moreover, conical fins that are an enhancement mechanism

have an effect to accelerate the boundary layer separation.

2. Experimental design

The experimental design is shown in Fig. 1. In this experimental design, the air was

directed to the air channel by an adjustable speed fan. The channel length before the test

section is long to obtain a fully developed flow at the entrance to the test section. That is,

experimental measurements were made at the points where the flow reached fully developed

conditions. The measurement of mass flow of the air at the entrance and exit of body was

determined by a propeller – type flow meter. The air flow velocity was adjusted by the fan.

The entrance and exit temperatures of air were quantified by T-type copper-constant

thermocouples. The air temperatures of the fin bottom (Ts) and between the fins (T∞) were

measured by the same type thermocouples 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. 2a. The air pressure at the input and output of the body was determined with a differential

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manometer. The material of the heating tube is galvanized steel. Moreover, the pressure,

temperature and volumetric flow rate of the hot fluid was determined for the entrance and exit

of the finned tube. The hot fluid was carried to the test section by a pump. The heating fluid

was heated by the electrical heaters placed in the 250 liter water tank and carried to the test

section by a tube. The external body was insulated with an insulating material of 10 mm

thickness to reduce the heat loss to surroundings. In addition, the deflectors that placed in the

inner surface of the external body extended the residence time of air flow on the heating tube.

In this paper, the diameter of the external body was 154 mm and the diameter of the tube

with conical fin was 27 mm. The fin's circular diameter was 87 mm. The inclination angles of

the conical fins to the tube axis were 45°, 60° and 80°. The thickness of conical fin was 0.6

mm. The length of tube with conical fin was 900mm. Besides, the heights (H) of the conical

fins were 35 mm for α = 45°, 33 mm for α = 60° and 31 mm for α = 80°.

Figure 2 shows the schematic diagram (a) and photograph (b) of the heating tube with

conical fins. Also, Figure 3 illustrates photographs of conical fins.

The heating tube with conical fins was exposed to a cross air-flow in the external body.

Experimental studies were conducted at eight different air flow velocities (2–20 m/s). All

measurements were recorded by using software, PLC.

The uncertainties of the measured values are as follows: temperature for air is ± 0.5 °C,

heating tube diameter is ±2 mm, pressure difference for air is ± 0.16 mbar, velocity for air is

±0.2 m/s, pressure for water is ± 0.2 mbar, temperature for water is ± 0.1 °C and water flow is

± 0.4 L/h.

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Also, the uncertainties of the calculated values were determined by using Moffat (1988).

The uncertainty of Reynolds number was obtained as % ± 7.41 and the uncertainty of the

Nusselt number was obtained as % ± 7.43.

3. Mathematical Formulation

As the external body was well insulated, the heat loss to surroundings was found very

small. Therefore, the following equation can be written:

�� = �� = �� = �� (1)

in which

�� = �� ,��,�� − �,�� (2)

and

�� = �� ,�� − ��,�� (3)

The convection heat transfer can be written as follows

�� = ℎ�� − �� (4)

where A� �!" is the total heat transfer surface area on the circular tube with conical fins.

�� = # $�� + η& �& ' (5)

in which A( is the surface area of the tube between two fins and η)*+ represents the fin

efficiency. Moreover, n specifies the number of fins.

The heat transfer coefficient is expressed as

ℎ = ,�-./012.234�56758� (6)

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The Nusselt number can written as follows

9: = ;<= (7)

Reynolds number is written as

?@ = AB3C<D (8)

This experimental study investigated cross-flow over a heating tube with a conical fin

configuration. The heated fluid (air) flows between the conical fins. Therefore, as in the case

of cross-flow over tube banks, maximum velocity is also defined in this study:

EF�G = F� 3HIJ3HI1K

(9)

in which Vmax is the maximum velocity (velocity between two fins) and Ap is the area of

section vertical to the direction of flow between to fins.

Heat transfer effectiveness (ɛ) is defined as follows Çengel (2006)

L = ��;�� &��F�GFMF;�� &�� (10)

The energy equation gives

�� = �� ,�� − ��,�� = N��,�� − ��,�� (11)

and

�� = �� ,��,�� − �,�� = N��,�� − �,�� (12)

The maximum heat transfer is expressed as

��F�G = �� F ��,; − �,�� = N��,�� − �,�� (13)

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The heat transfer effectiveness is

L = ,�,�B3C

= OP32QI�5H,P32QI75.,P32QI�O3HI�5H,P32QI75H,3HI�

(14)

and

9�R = S12.234OBH/

(15)

where U is the total heat transfer coefficient (in W/m2°C), while NTU is the number of

transfer units.

4. Results and discussion

The experiments were performed at cross flow arrangements for three different inclination

angles (45º, 60º and 80º) and for three different fin spacings. The temperature of hot water

was 65 °C. The heated fluid (air) entered the test section at eight different air flow velocities

(2, 5, 8, 10, 13, 15, 18 and 20 m/s).

Also, experimental data were obtained for a horizontal tube with conical fins (α = 45º and

p/D = 0.44) in order to testify the validity of the experimental set-up. The heat transfer

effectiveness obtained experimentally for the horizontal tube with conical fins (α = 45º and

p/D = 0.44) was compared with the effectiveness obtained from correlation of the

effectiveness of cross-flow heat exchangers Çengel (2006).

The effectiveness of cross-flow heat exchangers is

L = 1 − @UV $W5SX.ZZ

� [@UV�−�9�R\.]^� − 1_' (16)

They are used in the Eq. (16), which is c = OBH/OB3C

= O3HIOP32QI

.

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Figure 4 shows the comparison between the effectiveness obtained from the Eq. (16) and

the effectiveness of the experimental results.

It is seen in Fig. 4 that the experimental results of this study are in good agreement, ± 13.8

% compared to the correlation of the effectiveness of cross-flow heat exchangers.

Figure 5 shows the effect of the different fin spacings and Reynolds number on the Nusselt

number for α = 80º.

As seen in Fig. 5, the Nusselt number increases with the increment of Reynolds number for

all fin spacins. In addition, the best fin spacing for α = 80º is determined to be 15-mm in terms

of heat transfer. However, the difference between the Nusselt numbers of 15 mm and those of

10 and 12 mm increase for Re ˃ 5x104, while this difference for Re ˂ 5x10

4 is small. A reason

coming into mind is the formation of big vortices for large spacings, such as 15 mm, between

the fins. For larger values of Re = 5x10e, the ratio p/D = 0.56 gives the best heat transfer

coefficient. Fig. 6 illustrates change of pressure drop with fin spacing for α = 80º. It is seen

in Fig. 6 that the pressure drop of 15-mm fin spacing is bigger than those of the other fin

spacings. While the difference between the pressure drop values of three fin spacings for Re ˂

5x104 is very small, however, this difference increases for Re ˃ 5x104

. According to these

results obtained, we can define the Re = 5x104

value at α = 80º as critical Reynolds number.

Figure 7 shows the change of the fin efficiency with Reynolds number for three different

fin spacings.

Fin efficiency mainly depends on surface area, heat transfer coefficient and surface

temperature of fins. From the Fig. 7 one can conclude that efficiency diminishes with

Reynolds number. Such a decrease of efficiency is a result of increased air flow velocity

around fins. The increase of flow velocity leads to moderately low surface temperature along

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the fin, from the base to tip, and also lower fin efficiency. Although heat transfer coefficient

increases with Reynolds number for all p/D’s, the competing effects of heat transfer between

the actual case which lessens due to reduced surface temperature and ideal case (maximum

heat transfer) lead to such a decrease of fin efficiency. In other words, the more air velocity

causes the lower surface temperature due to the enhanced heat transfer coefficient and lower

fin efficiency. As seen in Fig. 7, the highest fin efficiency for α = 80º is at p/D= 0.37.

Figure 8 shows the change of effectiveness (ɛ) with NTU for (a) α = 80º (b) α = 45º.

As seen in Fig. 8, effectiveness (ɛ) increases with NTU for α = 80º and α = 45º. In

addition, both at α = 80º and at α = 45º, effectiveness of all the p/D ratios are almost the same

up to NTU= 1, while the discrepancy between them is explicit for NTU ˃ 1.

Figure 9 shows the change of Nusselt number with Reynolds number and three different

inclination angles for p/D = 0.37 (a) and p/D = 0.56 (b).

For p/D = 0.37, Nusselt numbers of 45º, 60º and 80º are almost the same (Fig. 9a).

However, for p/D = 0.56, Nusselt numbers of α = 45º and α = 80º are almost the same up to

Re = 5x104, while Nusselt numbers of α = 80º for Re ˃ 5x10

4 are higher than the other

inclination angles (Fig. 9b). Moreover, as seen in Fig. 10a and 10b, pressure drops of all the

inclination angles are almost the same for Re ˂ 5x104

both at p/D = 0.37 and at p/D = 0.56,

while the lowest pressure drop for Re ˃ 5x104 takes place at α = 80º. This case shows that the

best inclination angle at both fin spacings is α = 80º for Re ˃ 5x104.

Figures 11a and 11b shows the effect of NTU and different inclination angles on

effectiveness for p/D = 0.37 and p/D = 0.56, respectively.

As seen in Fig. 11a, while the effectiveness of all the inclination angles up to NTU= 1 are

almost the same, the difference between their effectiveness is obvious for NTU ˃ 1.

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Moreover, according to Fig. 11b, the effectiveness of α = 60º up to NTU= 0.7 is the lowest,

while the effectiveness of all the inclination angles for 0.7 ˂ NTU ˂ 1 are almost the same.

For NTU ˃ 1, the effectiveness of α = 80º is the highest.

Figures 12a and 12b shows the effect of OBH/OB3C

and different inclination angles on

effectiveness for p/D = 0.37 and p/D = 0.56, respectively.

As seen in Fig.12a and 12b, As OBH/OB3C

increases, the effectiveness decreases. For p/D = 0.37,

this decrease is almost the same at all inclination angles (Fig.12a). However, for p/D = 0.56,

The decrease in α = 60º is more than that of α = 45º and α = 80º (Fig.12b).

5. Conclusions

The conclusions obtained in this study are summarized below.

1. For α = 80º, the best fin spacing in terms of heat transfer is 15 mm.

2. Both for α = 80º and for α = 45º, the effectiveness of all p/D ratios up to NTU = 1 are

almost the same, while the difference between their effectiveness is obvious for NTU

˃ 1.

3. For p/D = 0.37, Nusselt numbers of 45º, 60º and 80º at all Reynolds numbers are

almost the same.

4. For p/D = 0.56, Nusselt numbers of α = 80º at Re ˃ 5x104 are higher than the other

inclination angles, while Nusselt numbers of α = 45º and α = 80º up to Re = 5x104 are

almost the same.

5. Both at p/D = 0.37 and at p/D = 0.56, the lowest pressure drop for Re ˃ 5x104 takes

place at α = 80º, while the pressure drops of all the inclination angles for Re ˂ 5x104

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are almost the same. This case indicates that the best inclination angle for Re ˃ 5x104

is α = 80º.

As a result, traditional circular fins and conical fins have the same performance in

terms of heat transfer and pressure drop at low air velocities. In addition, heating of

living areas usually takes place at low air velocities (mostly natural convection).

6. For p/D = 0.56, the effectiveness of α = 60º up to NTU = 0.7 is the lowest, while the

effectiveness of all the inclination angles for 0.7 ˂ NTU ˂ 1 are almost the same. For

NTU ˃ 1, however, the effectiveness of α = 80º is the highest.

Nomenclature

A� �!" total heat transfer surface area (mg)

A( surface area of tube between two fins �mg�

A)*+ area of the conical fin on the tube �mg�

Ah area of section vertical to the direction of flow between to fins �mg�

ch,!*j specific heat of air (kJ/kg°C)

ck!�lj specific heat of water (kJ/kg°C)

C capacity rate (W/°C)

airC capacity rate of air (W/°C)

waterC capacity rate of water (W/°C)

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D outer diameter of heating tube (m)

H height of conical fin (m)

h heat transfer coefficient (W/mgK)

k thermal conductivity (W/m°C)

L length of finned tube (m)

m� !*j mass flow of air (kg/s)

m� k!�lj mass flow of water (kg/s)

NTU number of transfer units

n number of conical fins

Nu Nusselt number

Pr Prandtl number

p distance between conical fins (m)

Q� Heat power transferred from hot fluid (W)

Q� n!o maximum heat transfer (W)

Q� !*j heat transfer of air (W)

Q� k!�lj heat transfer of water (W)

Q� p +q convective heat transfer (W)

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Re Reynolds number

T*,!*j inlet temperature of air into test section (°C)

T ,!*j exit temperature of air from test section (°C)

T*,k!�lj inlet temperature of water to test section (°C)

T ,k!�lj exit temperature of water from test section (°C)

T( temperature of heating tube surface (°C)

T� temperature of heated air (°C)

t conical fin thickness (m)

U total heat transfer coefficient (W/m2°C)

Vmax maximum velocity (velocity between two conical fins) (m/s)

Vi,air inlet velocity of air into test section (m/s)

Greek Symbols

ν kinematic viscosity (m2/s)

µ dynamic viscosity (kg/ms)

s conical fin inclination angle (°)

ɛ effectiveness

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η)*+ conical fin efficiency

∆p pressure drop (mbar)

Subscripts

air air side

fin fin

conv convection

i inlet

o exit

s tube wall

total total

water water side

References

Ahmed, H.E., Ahmed, M.I., and Yusoff, M.Z. (2015). Heat transfer enhancement in a

triangular duct using compound nanofluids and turbulators. Appl. Therm. Eng. 91: 191 –

201.

Al-Asadi, M.T., Alkasmoul, F.S., and Wilson, M.C.T. (2016). Heat transfer enhancement in a

micro – channel cooling system using cylindrical vortex generators. Int. Com. in Heat and

Mass Trans. 74: 40 – 47.

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Behfard, M., and Sohankar, A. 2016. Numerical investigation for finding the appropriate

design parameters of a fin – and – tube heat exchanger with delta – winglet vortex

generators. Heat and Mass Trans. 52: 21 – 37.

Çengel, Y. A. 2006. Heat and Mass Transfer: A Practical Approach. 3rd ed. McGraw – Hill,

New York, USA.

Chang, S.W., Cai, W.L., and Syu, R.S. 2016. Heat transfer and pressure drop measurements

for tubes fitted with twin and four twisted fins on rod. Exp. Thermal and Fluid Sci. 74:

220 – 234.

Dong, C., Li, D., Zheng, Y., Li, G., Suo, Y., and Chen, Y. 2016. An efficient and low resistant

circumferential overlap trisection helical baffle heat exchanger with folded baffles. Energy

Conv. and Manag. 113: 143 – 152.

Khoshvaght – Aliabadi, M. 2016. Thermal performance of plate – fin heat exchanger using

passive techniques: vortex – generator and nanofluid. Heat and Mass Trans. 52: 819 –

828.

Kiatpachai, P., Pikulkajorn, S., and Wongwises, S. 2015. Air – side performance of serrated

welded spiral fin – and – tube heat exchangers. Int. J. of Heat and Mass Trans. 89: 724 –

732.

Moffat, R.J. 1988. Describing the uncertainties in experimental results. Exp. Therm. and Fluid

Sci. 1: 3 – 17.

Peng, H., Liu, L., Ling, X., and Li, Y. 2016. Thermo – hydraulic performances of internally

finned tube with a new type wave fin arrays. Appl. Therm. Eng. 98: 1174 – 1188.

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Petracci, I., Manni, L., and Gori, F. 2016. Numerical simulation of the optimal spacing for a

radial finned tube cooled by a rectangular jet. I – Average thermal results. Int. J. of

Thermal Sci. 104: 54 – 67.

Tian, L., Liu, B., Min, C., Wang, J., and He, Y. 2015. Study on the effect of punched holes on

flow structure and heat transfer of the plain fin with multi – row delta winglets. Heat and

Mass Trans. 51: 1523 – 1536.

Zhang, X., Wang, Y., Cang, P., and Wang, R. 2016. Experimental investigation of thermal

hydraulic performance of heat exchangers with different Reynolds numbers on both air –

side and water side. Appl. Therm. Eng. 99: 1331 – 1339.

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List of Figure Captions

Figure 1. Schematic display of experimental design.

Figure 2. Heating tube with conical fins: (a) Schematic diagram and temperature

measurement points on the air side of the test section, and (b) photograph.

Figure 3. Photographs of conical fins.

Figure 4. Verification of effectiveness of horizontal tube with conical fins.

Figure 5. Effect of Reynolds number and fin spacing on Nusselt number.

Figure 6. Change of pressure drop according to Reynolds number.

Figure 7. Change of fin efficiency with Reynolds number.

Figure 8. Change of effectiveness (ɛ) with NTU for three different fin spacings for (a) α = 80º

(b) α = 45º.

Figure 9. Effect of Reynolds number and inclination angle on Nusselt number for (a) p/D =

0.37 (b) p/D = 0.56.

Figure 10. Change of pressure drop with Reynolds number for three different inclination

angles, (a) p/D = 0.37 (b) p/D = 0.56.

Figure 11. Effect of NTU and inclination angle on effectiveness (ɛ), (a) p/D = 0.37 (b) p/D =

0.56.

Figure 12. Effect of ��

��

and inclination angle on effectiveness (ɛ), (a) p/D = 0.37 (b) p/D =

0.56.

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Fig. 1. Schematic display of experimental design.

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DraftAir flow

D

p

α

1ST2ST

3ST

L=0cm L=15cm L=45cm L=75cm L=90cm

3T∞

2T∞ 1

T∞

Water flow

(a)

(b)

Fig. 2. Heating tube with conical fins: (a) Schematic diagram and temperature

measurement points on the air side of the test section, and (b) photograph.

(a) α = 45° (b) α = 60°

Fig. 3. Photographs of conical fins.

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Fig. 4. Verification of effectiveness of horizontal tube with conical fins.

Fig. 5. Effect of Reynolds number and fin spacing on Nusselt number.

Fig. 6. Change of pressure drop according to Reynolds number.

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Fig. 7. Change of fin efficiency with Reynolds number.

(a)

(b)

Fig. 8. Change of effectiveness (ɛ) with NTU for three different fin spacings for (a) α = 80º

(b) α = 45º.

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(a)

(b)

Fig. 9. Effect of Reynolds number and inclination angle on Nusselt number for (a) p/D = 0.37

(b) p/D = 0.56.

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(a)

(b)

Fig. 10. Change of pressure drop with Reynolds number for three different inclination angles,

(a) p/D = 0.37 (b) p/D = 0.56.

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(a)

(b)

Fig. 11. Effect of NTU and inclination angle on effectiveness (ɛ), (a) p/D = 0.37 (b) p/D =

0.56.

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(a)

(b)

Fig. 12. Effect of ��

��

and inclination angle on effectiveness (ɛ), (a) p/D = 0.37 (b) p/D =

0.56.

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