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The influence of artificial roughness shape on heat transfer enhancement: corrugated tubes, dimpled tubes and wire coils

A. Garcíaa, J.P. Solano*,a, P.G. Vicenteb, A. Viedmaa

aUniversidad Politécnica de Cartagena, Departamento de Ingeniería Térmica y de Fluidos,

Campus Muralla del Mar, 30202 Cartagena, Spain bUniversidad Miguel Hernández, Departamento de Ingeniería de Sistemas Industriales, Avenida

de la Universidad, 03202 Elche, Spain

Abstract

This work analyzes the thermal-hydraulic behaviour of three types of enhancement

technique based on artificial roughness: corrugated tubes, dimpled tubes and wire coils.

The comparison has been performed from the three best specimens selected among the

wide range of geometries investigated by the authors in previous works. Heat transfer

and pressure drop experimental data in laminar, transition and turbulent regimes are

used in this investigation.

Results show that the shape of the artificial roughness exerts a greater influence on the

pressure drop characteristics than on the heat transfer augmentation. Likewise, this

shape strongly affects the advance of the transition to turbulence and its characteristics:

smooth or sudden. The study concludes that for Reynolds numbers lower than 200, the

use of smooth tubes is recommended. For Reynolds numbers between 200 and 2000, the

employment of wire coils is more advantageous, while for Reynolds numbers higher

than 2000, the use of corrugated and dimpled tubes is favoured over the wire coils

because of the lower pressure drop encountered for similar heat transfer coefficient

levels.

                                                            * Corresponding author. Tel.: +34 968325938; fax: +34 968325999.

E-mail address: juanp.solano@upct.es (J.P. Solano)

 

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Keywords: Heat transfer enhancement, wire coil inserts, corrugated tubes, dimpled tubes, turbulence promotion.

Nomenclature

cp fluid specific heat (J kg-1 K-1)

d tube inner diameter (m)

e wire coil diameter (m)

h corrugation/dimple height (m)

l length between dimples (m)

lh length of the heat transfer test section (m)

lp length of the pressure drop test section (m)

p helical/corrugation/dimple pitch (m)

ΔP pressure drop across the test section (Pa)

Q overall electrical power added (W)

Qℓ heat losses in the test section (W)

q" heat flux (Q-Qℓ)/(πdlh) (W m-2)

v mean fluid velocity (m s-1)

Dimensionless groups

f Fanning friction factor, ΔP·d/(2ρv2lp )

Gr Grashof number, gβd4q"/υ2λ

Nu Nusselt number, αd/λ

Pr Prandtl number, μcp/ λ

Ra Rayleigh number, Gr·Pr

Re Reynolds number, ρvd/μ

Greek symbols

α heat transfer coefficient (W m-2 K-1)

β thermal expansion coefficient (K-1)

λ thermal conductivity (W m-1 K-1)

μ dynamic viscosity (kg m-1 s-1)

υ  kinematic viscosity (m2 s-1) 

ρ fluid density (kg m-3)

Subscripts

a augmented tube

s smooth tube

∞ asymptotic

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1. Introduction

Enhancement techniques based on artificial roughness are used in numerous

applications of heat exchangers. The choice of an enhancement technique depends on

variables such as: the flow regime (Reynolds number), the fluid properties (Prandtl

number), the existence or not of fouling, the allowable pressure drop and the existence

or absence of natural convection.

The use of an enhancement technique may be conditioned by the specific application:

for example, wire coils are not applicable in the food industry due to hygiene problems

but corrugated and dimpled tubes are. In the petrochemical industry, the use of

mechanically deformed tubes is not allowed for safety reasons. However, the use of

wire coils does not present any problem. In boilers and heat recovery systems, wire

coils are frequently used because of their easy removal for cleaning operations.

In the fully laminar regime, the use of artificial roughness techniques does not

significantly improve the heat transfer coefficients as they only promote mixing in the

boundary layer near the wall. Instead, devices that mix the gross flow are suitably

employed for heat transfer enhancement in this flow regime [1], [2].

In fully developed internal turbulent flow, the velocity and temperature profiles across

the tube are similar in shape and relatively flat until very close to the wall. Artificial

roughness techniques are particularly appropriate for heat transfer augmentation in this

flow regime, as they contribute to disturbing the thermal boundary layer.

With regard to the transition from laminar to turbulent flow, experimental evidence

proves that these techniques promote the advance of transition [3]. As a result of the

flow perturbation in the viscous sub-layer, turbulence spots at Reynolds numbers below

2300 lead to early turbulence phenomena. When the transition takes place, the heat

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transfer rate can be five times higher than the one for the laminar flow in a smooth tube

[4]. The use of the best enhancement technique will bring about an important increase

of the heat transfer rate in the transition region, this presenting a high potential in

applications with highly viscous fluids, e.g. in the petrochemical and food industries.

2. Background

The use of wire coils to enhance heat transfer in tubular heat exchangers goes back to

the works by Joule in the middle of the XIX century. In fact, those works are considered

the pioneers in the field of heat transfer enhancement. The technology which allows the

manufacture of low-cost deformed tubes was developed in the last third of the XX

century. The patent of the corrugated tubes dates back to 1977 [5]. The patent of a

method for manufacturing dimpled tubes by cold external deformation dates back to

1989 [6].

In the field of enhanced heat transfer, there are very few experimental studies on

laminar flow. Here, the entrance effects and the secondary flow induced by buoyancy

forces greatly complicate the analysis. On wire coils, the work of Uttarwar and Raja

Rao [7] has been widely mentioned in the open literature [3], [8]. However, their heat

transfer results were strongly influenced by the entry region. Recently, Akhavan-

Behabadi et al. [9] studied the heat transfer augmentation in laminar flow in tubes with

different wire coil inserts. The experiments were carried out in a double-pipe

configuration with constant wall temperature, and did not account for entry region

effects nor mixed convection.

Barba et al. [10] published an experimental paper on heat transfer enhancement in a

corrugated tube for laminar and transitional flow. They reported pressure drop increases

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of 2.5 times for Re=800 and Nusselt number augmentations of about 17 times at

Pr=200, compared to the smooth tube.

Experimental studies on surface roughness enhancement techniques have been usually

carried out for turbulent flow at low Prandtl numbers (water and air). Ravigururajan and

Bergles [11] compiled a great amount of experimental data from seventeen sources and

seven different enhanced tubes. They developed general correlations for the friction

factor and for the Nusselt number for turbulent flow. They concluded that roughness

shape exerts a higher influence on pressure drop than on heat transfer. Zhang et al. [12]

obtained very similar results in wire coils of circular and square section. On the other

hand, Zimparov et al. [13] studied corrugated tubes with the same dimensionless

geometrical parameters but different shape and observed differences up to 25% in the

friction factor. Chen el al. [14] performed an experimental investigation of different

dimpled tube geometries in turbulent flow, providing accurate correlations for heat

transfer and pressure drop analysis. They concluded that the size and weight of the heat

exchanger could be reduced by a factor of almost 2 without affecting any other system

conditions. Wang et al [15] have studied the thermal-hydraulic characteristics in tubes

with outward-facing and raised dimples in staggered and aligned configurations, for

Reynolds number in the range 15000-60000 and using air as working fluid.

Further to the well known interest in using corrugated tubes in turbulent flow, the most

interesting region is undoubtedly the transition region [4,16,17]. A heat exchanger can

partially work in the laminar regime: in viscous fluids, the flow can be laminar in the

entrance, where the fluid is cold and its viscosity is high. Transition takes place at an

undefined point of the heat exchanger. Because of this, the transition point (critical

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Reynolds number) is an important parameter to bear in mind in all enhancement

techniques.

The use of a surface roughness in the transition region (Re=250-3000) can be very

effective to increase heat transfer [4], [18]. Oliver and Shoji [19] studied different insert

devices in the laminar and transition region. Although their work only covered

Reynolds numbers below 700, it was proven that in this region, wire coils increase heat

transfer in a much more efficient way than other insert devices such as mesh inserts and

twisted tapes. Ravigururajan and Bergles [20] and Li et al. [21] demonstrated through

visualization experiments that the presence of artificial roughness promotes turbulent

flow at Reynolds numbers below 2000. The paper of Olsson and Sundén [22] was

focused on the laminar-transitional region (Re=500–6000). They studied rib-roughened,

dimpled and offset strip fin small tubes for radiators, employing air as test fluid

(Pr≈0.7). Their measurements were highly influenced by the entry region. Since the

flow behaviour presented a smooth transition, both friction factor and Nusselt number

results were fitted to Reynolds number by a simple power series correlation. To extend

the validity of heat transfer results, it was assumed that Nusselt number was

proportional to Pr1/3. Meyer and Olivier [23,24] obtained heat transfer coefficients, and

diabatic and adiabatic friction factor data for four helical finned tubes for fully

developed and developing flow, covering the laminar, transitional and fully turbulent

flow. They analyzed the influence of secondary flows on the advance of transition, and

the impact of different inlet geometries.

Compound enhancement techniques have been recently studied by several authors.

Thianpong et al [25] investigated the thermal-hydraulic performance of combinations of

three twisted tapes and two dimpled tubes. They found experimental correlations of heat

transfer and pressure drop as a function of the pitch ratio and twist ratio. The effects of

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the entrance length and mixed convection were not considered. Saha adopted new

configurations in square ribbed channels with wire coil inserts, and studied separately

the laminar [26] and turbulent [27] flow regimes.

The aim of the present work is to perform a well-reasoned comparison of the thermal-

hydraulic behaviour of three types of enhancement technique based on artificial

roughness: corrugated tubes, dimpled tubes and wire coils. The authors have revisited

their own results on dimpled tubes [28,29], corrugated tubes [30,31] and wire coils [32],

where a wide range of geometrical parameters of each artificial roughness technique

was investigated. The specimens which yielded the best thermal-hydraulic performance

for each shape have been chosen in the present investigation. The heat transfer and

pressure drop experimental data obtained by the authors in laminar, transition and

turbulent regimes have been analyzed on a comparative basis. The main advantage of

this approach is that the range of Reynolds and Prandtl numbers investigated is similar

for the three techniques, as well as the thermal boundary condition and development

lengths. This prevents an ambiguous interpretation when data from different sources are

analyzed. The criterion for the choice of the three specimens allows us to establish

general conclusions on the best eligibility of an artificial roughness shape with regard to

the flow regime.

3. Artificial roughened tubes analyzed

Surface roughness is the most common and successful technique for enhancing tube-

side heat transfer in single phase turbulent flow. Large scale production of roughened

tubes can be manufactured through cold rolling. In corrugated and dimpled tubes the

roughness height and pitch are controlled by the roller geometry, the feed rate and the

pressure applied during the process. A tube with a wire coil insert is another simple and

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cheap method of creating a roughened tube. Fig. 1 shows a sketch of the three

enhancement techniques analyzed in this work: corrugated tubes, dimpled tubes and

wire coil inserts.

The dimensionless numbers characterizing the geometry of corrugated tubes are

dimensionless roughness height (h/d) and dimensionless pitch (p/d). For dimpled tubes,

the dimensionless roughness height (h/d) and dimple density (d²/pl) are employed and

for wire coil inserts, wire diameter (e/d) and dimensionless pitch (p/d). Table 1 shows

the geometrical and the dimensionless parameters of the mechanically deformed tubes

and the wire coil analyzed in this work. The geometrical parameters analyzed in the

works from which the test specimens have been chosen, as delivering the best thermal-

hydraulic performance, cover the next ranges: for the corrugated tubes

0.024<h/d<0.057 and 0.608<p/d<1.229; for the dimpled tubes 0.083<h/d<0.119 and

1.650<d2p/l<2.639; for the wire coils 0.074<e/d<0.101 and 1.173<p/d<2.684. Further

information on the measurement technique, data reduction and uncertainties of the

results can be found in [28,29],[30,31] and [32].

3.1. Pressure drop results

Fig. 2 shows the experimental results of isothermal pressure drop for the wire coil, the

corrugated tube and the dimpled tube selected, obtained in the hydrodynamically

developed region. The experimental set-up was adjusted and verified through pressure

drop experiments with a smooth tube. Laminar results were compared to the analytical

solution (fs=16/Re) while results in the turbulent region were compared to Blasius

equation (fs=0.0791Re-0.25). An excellent agreement with the mentioned correlations is

observed: ±3% for 95% of the experimental data.

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The three roughened tubes show the typical behaviour of artificial roughness

techniques: advance of transition to turbulence and high pressure drop increase in

turbulent regime [33]. In laminar regime, at Reynolds numbers below 350, the three

devices under study increase pressure drop around 30% as a result of an increase of the

skin friction drag: this is due to the reduction of the cross-sectional area and to the

increase of the wet perimeter (decrease of the hydraulic diameter).

At Reynolds numbers higher than 3000, the friction factor curve corresponding to any

of the three devices has the typical trend of the turbulent flow in roughened tubes: fa ∝

Re−0.2. This implies that the flow is fully turbulent and the pressure drop is

approximately proportional to the square of the flow velocity. The wire coil produces

higher pressure drop than the deformed tubes: at Re=10000, the friction factor increase

is fa/fs=5 as compared to fa/fs=3.7 obtained in corrugated and dimpled tubes.

It can be stated that the three roughened tubes studied in this paper present similar

behaviour both in pure laminar and turbulent regimes. However, roughness shape plays

an important role in how transition occurs. During the performance of the pressure drop

experiments, it was observed that the transition to turbulence in the dimpled tube took

place with strong flow instabilities. These instabilities were not so strong in the

experiments carried out in the corrugated tube. In wire coils, transition occurred

smoothly and without any kind of fluctuation. Fig. 2 illustrates the different behaviours:

the friction factor curve of the dimpled tube presents a high jump within a limited

Reynolds number range, which goes between 1200 and 1600. For the wire coil, the

critical Reynolds number cannot be clearly identified as the jump is very small and it

takes place within a wider Reynolds range that extends from 350 to 2000. However,

flow visualization tests in this wire coil performed by the authors [34] demonstrate that

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at Re=700 the flow has turbulent characteristics and that at Reynolds numbers between

350 an 700, the laminar flow is strongly disturbed.

Pressure drop results of the three roughened tubes are qualitatively different and it can

be affirmed that this is due to the roughness shape. Wire coils produce two effects in the

flow structure: rotation of the core flow and flow separation downstream of the wire. It

is reasonable to affirm that corrugated tubes produce a slight rotation of the core flow

and no flow separation downstream of the corrugations. On the other hand, the three-

dimensional artificial roughness of dimpled tubes is similar to natural roughness, which

does not generate either rotating flow or large-scale separations. It can be stated that the

rotation of the core flow affects mainly the advance of transition from laminar to

turbulent flow and its characteristics: smooth or sudden. Moreover, coil inserts of round

wire shape produce flow separations that yield high friction factor coefficients in

turbulent flow, suggesting that bluff body drag exceeds the skin friction drag on the

wall.

3.2. Heat transfer results

This section aims to compare the increase in the heat transfer coefficient produced by

the different enhancement techniques in laminar, transition and turbulent regimes.

Experimental results are presented in terms of Nusselt number versus Reynolds number.

Firstly, experimental results of Nusselt number for a smooth horizontal tube are

presented in Fig. 3.

Heat transfer in the laminar regime can occur either in forced convection (continuous

line) or in mixed convection (dashed line). Experimental results in the laminar regime

were obtained in mixed convection and at Rayleigh numbers from 2 ⋅107 to 7.5⋅107 .

These results agree with the correlation of Petukhov and Polyakov [35]. Experiments

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for the turbulent flow were carried out at five different Prandtl numbers from 2.8 to 74.

The results agree to a great extent with the Gnielinski equation [36].

The different heat transfer regions for each of the three enhanced tubes under study are

illustrated in Fig. 4 (dimpled tube), Fig. 5 (wire coil), and Fig. 6 (corrugated tube).

Results are confronted with the correlations for the smooth tube presented in Fig. 2.

In laminar flow, heat transfer in horizontal tubes can occur either in forced convection

(entry region) or in mixed convection (fully developed region), where the flow is

affected by the existence of two buoyancy-driven recirculations. The results shown in

Figs. 4-6 for the pure laminar region (Region I) are for mixed convection flow. Here,

the three roughened tubes have a similar behavior to that of the smooth tube. However,

the onset of the buoyancy-driven recirculations is greatly affected by the roughness

shape. In the wire coil, the appearance of a rotational component of the velocity was

observed [34], which delays the appearance of the mixed convection: it only occurs at

Reynolds numbers below 200 and at higher Rayleigh numbers than for the smooth tube.

In corrugated tubes, this rotational component is weaker and mixed convection flow

does not occur at Reynolds numbers above 700. Finally, in the dimpled tube, viscous

flow occurs in a similar way to the smooth tube, and there is not a significant delay in

the development of mixed convection flow.

Figs. 4-6 clearly show great differences in how each enhanced tube promotes the

transition (Region II) from laminar to turbulent regime. Transition from the fully

laminar to the turbulent flow takes place smoothly in the wire coil in the Reynolds

number range from 200 to 700. Visualization tests showed that at Re=700 the flow is

turbulent. For Reynolds numbers between 200 and 700, the flow remains laminar, but

separation occurs downstream of the wire. The fluid near the wall is mixed and the heat

transfer coefficient increases significantly. Conversely, in the dimpled tube, fully

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developed laminar mixed-convection flow is found up to Reynolds number 1200. The

rotational component on the core flow produced in corrugated tubes hinders the

establishment of the two buoyancy-driven recirculations: at Reynolds numbers above

700 heat transfer takes place under forced convection.

In the turbulent regime at Reynolds numbers above 2000 (Region III), the assertions by

Ravigururajan and Rabas [37] are validated: wire coil inserts have approximately the

same heat transfer coefficient as integral surface roughness. Bergles [38] affirms that

with these techniques, maximum Nusselt number augmentations of 250% can be

expected at low Prandtl numbers.

4. Discussion of results and conclusions

Fig. 7 presents the Nusselt number correlations proposed by the authors [28-32] for the

corrugated tube, the dimpled tube and the wire coil at Prandtl number 200 in the

Reynolds number range from 20 to 20000.

At Reynolds numbers below 200, the use of roughened tubes will not produce higher

heat transfer coefficients than those produced by smooth tubes. Moreover, wire coils

and to a lesser extent corrugated tubes, can even reduce the heat transfer rate when they

delay the establishment of mixed convection flow. Therefore the use of these

enhancement techniques is not recommended within this range of Reynolds numbers.

For Reynolds numbers between 200 and 2000, the authors recommend the use of wire

coil inserts. In this region, Nusselt number and friction factor curves are continuous and

therefore it is possible to obtain reliable correlations. Wire coils are the best choice for

heat exchangers working in this region since they produce the best heat transfer

enhancement and they have a predictable behaviour.

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At Reynolds numbers above 2000, the deformed tubes produce slightly higher heat

transfer coefficients than the wire coil: at Re=10000 and Pr=200, Nua/Nus = 2.9 for

mechanically deformed tubes and Nua/Nus = 2.4 for the wire coil. The correlations

employed offer the next influence of Prandtl number on Nua/Nus: for dimpled tubes,

01.0sa PrNuNu ; for corrugated tubes, 05.0

sa PrNuNu ; for wire coils, 02.0sa PrNuNu

. These relations yield negligible differences between the heat transfer augmentations

reported above and the values averaged over the range of Prandtl number investigated.

Since wire coil inserts produce the highest friction factor coefficients in the turbulent

regime, it is obvious that they perform worse than corrugated and dimpled tubes. In any

case, wire coils would find use in many applications since they are easy to install on

existing smooth-tube heat exchangers.

The conclusions of this comparative analysis can be summarized in the next points:

The roughness shape determines the existence or absence of a rotational velocity

component in the flow and its magnitude. The core flow rotation affects mainly

the advance of transition from laminar to turbulent flow and its characteristics:

smooth or sudden.

In coil inserts, transition from the fully laminar to the turbulent flow takes place

smoothly. In the Reynolds number range from 200 to 700 the flow remains

laminar, but separation occurs downstream of the wire. This separation promotes

heat transfer enhancement and eventually yields bluff body drag and high

friction factors in turbulent flow.

In the pure laminar region, heat transfer in roughened tubes is very similar to

that observed in smooth tubes. The rotational velocity component induced in

wire coils and corrugated tubes hinders the appearance of mixed convection: For

wire coils, the buoyancy-driven recirculations only occur at Reynolds numbers

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below 200 and at high Rayleigh numbers. In corrugated tubes, mixed convection

is not produced at Reynolds numbers above 700.

At Reynolds numbers above 2000 the three roughened tubes produce similar

heat transfer coefficients, but wire coils have higher friction factor coefficients.

The roughness shape is the key factor in the selection of roughened tubes: at

Reynolds numbers below 200, the use of roughened tube is not recommended:

smooth tubes will produce the same results; at Reynolds numbers between 200

and 2000, the use of wire coils is recommended; at Reynolds numbers above

2000, the use of corrugated and dimpled tubes is recommended. In any case,

wire coils would find use in many applications since they are easy to install on

existing smooth-tube heat exchangers.

The conclusions reported in this work aim to ease the eligibility of an artificial

roughness technique for a given application, provided that the flow conditions are

known. For example, this knowledge is being at present employed for the tube-side

enhancement of flat plate solar collectors with coil inserts [39], that typically operate

with transitional flow Reynolds numbers.

Acknowledgements

This research has been partially financed by the DPI2007-66551-C02 grant of the

Spanish Ministery of Science and the company ”HRS Spiratube”.

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[36] V. Gnielinski, New equations for heat and mass transfer in turbulent pipe and

channel flow, International Chemical Engineering, 16 (1976) 359-368.

[37] T.S. Ravigururajan, T.J. Rabas, Turbulent flow in integrally enhanced tubes, Part 1:

Comprehensive review and database development, Heat Transfer Engineering, 17

(1996) 19-29.

[38] A.E. Bergles, ExHFT for Fourth Generation Heat Transfer Technology,

Experimental Thermal and Fluid Science, 26 (2002) 335-344.

[39] R. Herrero Martín, J. Pérez-García, A. García, F.J. García-Soto, E. López-Galiana,

Simulation of an enhanced flat-plate solar liquid collector with wire-coil insert devices,

Solar Energy 85-3 (2011) 455-469.

20 

 

Figure captions

Figure 1. Types of surface roughness that this paper contemplates. (a) Wire coils:

helical pitch p, wire diameter e; (b) Corrugated tubes: corrugation pitch p, corrugation

height h; (c) Dimpled tubes: corrugation pitch p, length between dimples l, dimple

height h.

Figure 2. Fanning friction factor vs. Reynolds number. Experimental results for the wire

coil, the corrugated tube and the dimpled tube.

Figure 3. Nusselt number vs. Reynolds number in laminar, transition and turbulent flow.

Experimental smooth tube results compared with Petukhov and Polyakov [19] and

Gnielinski [20] equations.

Figure 4. Nusselt number vs. Reynolds number. Experimental results for the dimpled

tube in the: laminar region (I), transition region (II) and turbulent region (III).

Figure 5. Nusselt number vs. Reynolds number. Experimental results for the wire coil in

the: laminar region (I), transition region (II) and turbulent region (III).

Figure 6. Nusselt number vs. Reynolds number. Experimental results for the corrugated

tube in the: laminar region (I), transition region (II) and turbulent region (III).

Figure 7. Nusselt number vs. Reynolds number. Experimental correlations for the wire

coil, the corrugated tube and the dimpled tube.

21 

 

Table captions

Table 1. Characteristic dimensions of the roughened tubes

Enhancement

technique

d

[mm]

h (e)

[mm]

p

[mm]

l

[mm]

h/d (e/d)

[-]

p/d

[-]

d2p/l

[-]

dimpled, D05 16.0 1.83 14.50 9.02 0.114 0.906 1.957

corrugated, C01 18.0 1.03 15.95 - 0.057 0.886 -

wire-coil, W01 18.0 1.34 21.12 - 0.074 1.173 -

Table(s)

Figure(s)

101

102

103

104

105

10−3

10−2

10−1

Reynolds number, Re

Fric

tion

fact

or, f

f=16/Re

f=0.079 Re

Wire coil: W01Dimpled tube: D05Corrugated tube: C01Smooth tube −0.25

Figure(s)

102

103

104

105

101

102

103

Reynolds number, Re

Nus

selt

num

ber,

Nu

Pr=74Pr=33.5

Pr=16.8Pr=4.4

Pr=2.8

− − −

Ra=2.0−7.5 107 , Nu=15.4−19.5

Gnielinski [36]

TURBULENT FLOW

LAMINAR FLOW

Petukhov & Polyakov [35]

Figure(s)

102

103

104

105

101

102

103

Reynolds number, Re

Nus

selt

num

ber,

Nu

D05: Pr=2.9, 4.1D05: Pr=92, 59, 37Smooth tube, Pr=2.9, 4.1Smooth tube, Pr=92, 59, 37Smooth tube, Ra=constant

Pr=92Pr=59 Pr=37

Pr=4.1Pr=2.9

Ra=15 10Ra=7.4 10Ra=3.5 10

6

66

IIIIII

Figure(s)

102

103

104

105

101

102

103

Reynolds number, Re

Nus

selt

num

ber,

Nu

W01: Pr=168, 23, 4.3

W01: Pr=76, 11, 2.8Smooth tube, Pr=168, 23, 4.3Smooth tube, Pr=76, 11, 2.8Smooth tube, Ra=constant

Pr=168

Pr=76Pr=23

Pr=11 Pr=4.3 Pr=2.8

Ra=7.5 10

Ra=2.0 10

7

7

IIIIII

Figure(s)