Keywords

Circular tubes mostly have the wavy or herringbone fin and the offset fin or parallel louvre as the major enhanced surface geometries. Wavy fins typically have 50–70% higher heat transfer coefficient than that of a plain fin. In this case, the combination of tubes and a special surface geometry establishes very complex flow geometry.

Two basic wave fin geometries—smooth wave and herringbone wave —are in use (Fig. 4.1). Number of investigations made with herringbone wave geometry is much more than that with smooth wave geometry.

Fig. 4.1
figure 1

Two basic geometries of the wavy fin: (a) herringbone wave, (b) smooth wave (Webb and Kim 2005)

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Tao et al. (2007a, b) numerically investigated the performance of wavy fin used for heat transfer augmentation. They used wavy fin (fin A) and plain fin (fin C) and observed that for both the fins, the local Nusselt number decreased along the length of the pipe. The local Nusselt number upstream was almost ten times that of downstream. Thus, they suggested a new fin pattern in which wave is located only in the upstream and referred to it as fin B. The schematic of fin A, fin B and fin C has been shown in Fig. 4.2.

Fig. 4.2
figure 2

Schematic of (a) fin A, (b) fin B and (c) fin C (Tao et al. 2007a, b)

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The Nusselt number variation for fin A, fin B and fin C has been presented in Fig. 4.3. The Nusselt number for fin B was about 45% greater than that of fin C and 4% lower than that of fin A. Figure 4.4 shows the friction factor variation with Reynolds number for all the three fins used in the analysis. The plain fin (fin C) as expected has the minimum friction factor. The pressure drop in the case of fin B was found to be less than that of fin A. The friction factor for fin B was 26% higher and 18% lower than that of fin C and fin A, respectively. The overall performance evaluation index, Nu/f, for these three fins has been plotted and shown in Fig. 4.5. The overall performance of fin B has been observed to be the best among the three fins used for the analysis. The Nu/f for fin B has been reported to be 12.4–18.5% and 14.9–20% greater than that of fin C and fin A, respectively.

Fig. 4.3
figure 3

Nusselt number variation for fin A, fin B and fin C (Tao et al. 2007a, b)

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Fig. 4.4
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Friction factor variation with Reynolds number (Tao et al. 2007a, b)

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Fig. 4.5
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Overall performance evaluation index, Nu/f vs. Re (Tao et al. 2007a, b)

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Nishimura et al. (1987), Xin and Tao (1988), Patel et al. (1991a, b), Rutledge and Sleicher (1994), Comini et al. (2002), Yoshii et al. (1973), Beecher and Fagan (1987), Mirth and Ramadhyani (1994), Xin et al. (1994), Wang et al. (1997, 2002a, b, c), Somchai and Yutasak (2005), Jang and Chen (1997), Tao et al. (2007b), Kuan et al. (1984), Zabronsky (1955), Chen and Liou (1998), Saboya and Sparrow (1974), Jones and Russell (1980), Rosman et al. (1984) and Ay et al. (2002) have studied the performance of fins.

Goldstein and Sparrow (1977) have observed that, for herringbone wave geometry , enhancement is due to Goetler vortices formed on concave wave surfaces. Beecher and Fagan (1987) worked with 20, three-row fin-and-tube geometries having wavy fin geometry. Webb (1990) used their data and developed multiple regression correlation.

$$ {Nu}_{\mathrm{a}}=0.5{Gz}^{0.86}{\left(\frac{S_{\mathrm{t}}}{d_0}\right)}^{0.11}{\left(\frac{s}{d_0}\right)}^{-0.09}{\left(\frac{e_{\mathrm{w}}}{S_{\mathrm{l}}}\right)}^{0.12}{\left(\frac{p_{\mathrm{w}}}{S_{\mathrm{l}}}\right)}^{-0.34}\kern1em Gz\le 25 $$
(4.1)
$$ {Nu}_{\mathrm{a}}=0.83{Gz}^{0.76}{\left(\frac{S_{\mathrm{t}}}{d_0}\right)}^{0.13}{\left(\frac{s}{d_0}\right)}^{-0.16}{\left(\frac{e_{\mathrm{w}}}{S_{\mathrm{l}}}\right)}^{0.25}{\left(\frac{p_{\mathrm{w}}}{S_{\mathrm{l}}}\right)}^{-0.43}\kern1em Gz>25 $$
(4.2)

The Nusselt numbers are sometimes based on arithmetic mean temperature difference (AMTD) and sometimes, as usual, on log mean temperature difference (LMTD) . Equation (4.3) gives a relation between Nul and Nua.

$$ {Nu}_{\mathrm{l}}=\frac{Gz}{4}\ln \left(\frac{1+2{Nu}_{\mathrm{a}}/ Gz}{1-2{Nu}_{\mathrm{a}}/ Gz}\right) $$
(4.3)

Torii and Yang (2007) theoretically studied thermo-hydraulic characteristics of flow over slot-perforated flat fins. The impact of fin pitch on heat transfer and pressure drop characteristics has been elaborated. Similar works have been carried out by Gan et al. (1990), Lee (1995), Biber (1996), de Lieto Vollaro et al. (1999), Anand et al. (1992), Ledezma and Bejan (1996), Leon et al. (2002), Culham and Muzychka (2000) and Furukawa and Yang (2002). Liang and yang (1975a, b), Liang et al. (1977), Lee and Yang (1978), Fujii et al. (1988) and Hwang et al. (1996) studied the effect of perforations on extended surfaces for internal turbine blade cooling.

Bilir et al. (2010) studied the heat transfer and pressure characteristics of fin-tube heat exchanger with three different types of vortex generator configurations. They numerically investigated the effects of location of vortex generators on the heat transfer and pressure drop characteristics. Each type vortex generators were placed at four different locations on the fin to find optimal location so that maximize the heat transfer and minimize the pressure drop. They made two different types of numerical model to optimize the heat transfer characteristics after finding the best location of vortex generators on the fin. They analysed the cumulative effect of three different vortex generators together on the heat transfer rate. After computational analysing and then compared with existing experimental and numerical results in literatures, they found that the use of three different vortex generators together increases heat transfer rate with a moderate increase in pressure drop.

Table 4.1 shows the location of vortex generators and model names. They compared the average heat transfer coefficient results obtained from the numerical analysis with the experimental and computational results of Wu and Tao (2008) as shown in the Fig. 4.6. Table 4.2 shows the numerical results of heat transfer and pressure drop in the heat exchanger. It was found that fin heat transfer rate was ten times the segment heat transfer rate. They concluded that location 4 was best for all the vortex generators in terms of maximum heat transfer rate as well as minimum overall pressure drop. Table 4.3 shows the heat transfer and pressure drop values of the fins with three types of winglet vortex generators . Abu Madi et al. (1998), Chen et al. (2000), Chen and Shu (2004), Elyyan et al. (2008), Kundu and Das (2007), Kwak et al. (2003), Leu et al. (2004), Lozza and Merlo (2001), Méndez et al. (2010), Wang et al. (2002a, b) and Wu and Tao (2008) investigated the effect of fin spacing with vortex generator on heat transfer rate and pressure drop.

Table 4.1 Model names and location of vortex generators (Bilir et al. 2010)
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Fig. 4.6
figure 6

Comparison of the numerical results of the present study with the results of Wu and Tao (2008): (a) for a plate fin; (b) for the fin with winglet with a 45° angle of attack (Bilir et al. 2010)

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Table 4.2 Numerical results of heat transfer and pressure drop across the heat exchanger (Bilir et al. 2010)
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Table 4.3 Heat transfer and pressure drop values of the fins with three types of vortex generators (Bilir et al. 2010)
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Wang et al. (1997, 1998, 1999a, c) and Abu Madi et al. (1998) worked with herringbone wave fin geometry, mostly on staggered layout. The effect of fin pitch and the effect of the rows were studied. General j and f correlations for the herringbone wave configuration were developed by Kim et al. (1997). A procedure in the line of Gray and Webb (1986) was taken for the development of the correlation. Wang et al. (1999d) also developed correlations for the herringbone wave geometry. Kim et al. (1997) correlations are given below:

$$ {j}_3=0.394{{\mathit{\operatorname{Re}}}_{\mathrm{D}}}^{-0.357}{\left(\frac{S_{\mathrm{t}}}{S_{\mathrm{l}}}\right)}^{-0.272}{\left(\frac{s}{d_0}\right)}^{-0.205}{\left(\frac{e_{\mathrm{w}}}{s}\right)}^{-0.133}{\left(\frac{p_{\mathrm{w}}}{2{e}_{\mathrm{w}}}\right)}^{-0.558} $$
(4.4)
$$ \frac{j_N}{j_3}=0.978-0.01N\kern1em {\mathit{\operatorname{Re}}}_{\mathrm{d}}>1000 $$
(4.5)
$$ \frac{j_N}{j_3}=1.35-0.162N\kern1em {\mathit{\operatorname{Re}}}_{\mathrm{d}}<1000 $$
(4.6)
$$ {f}_{\mathrm{f}}=4.467{{\mathit{\operatorname{Re}}}_{\mathrm{D}}}^{-0.423}{\left(\frac{S_{\mathrm{t}}}{S_{\mathrm{l}}}\right)}^{-1.08}{\left(\frac{s}{d_0}\right)}^{-0.034}{\left(\frac{p_{\mathrm{w}}}{2{e}_{\mathrm{w}}}\right)}^{-0.672} $$
(4.7)

Kim et al. (1997) used Zukauskas (1972) correlation for the friction factor due to tubes.

Zhang et al. (2019) used Taguchi method to study the influence of geometric parameters of three-dimensional finned tube on the gas-side heat transfer and pressure drop characteristics in the air cross flow. The effect of four factors such as the fin height, fin width, axial fin pitch and circular fin pitch in compact heat exchanger had been investigated. They developed empirical correlations for Nusselt number and friction factor in the experimental range for the evaluation of heat transfer performance. They found that thermo-hydraulic performance of three-dimensional finned tube was 2.7–2.9 times more than smooth tube in the field of heat transfer criterion. Air and water were used as working medium in the shell side and the tube side, respectively. They worked in heat exchanger with air velocity ranging from 2.9 to 8.3 m/s and the Reynolds number ranging from 4000 to 11,500.

Figure 4.7 shows that coupling effect of different fin parameters on Nusselt number and friction factor. It was cleared from the figure that at the higher value of Reynolds number, heat transfer can be maximized with minimum frictional loss in the finned tube heat exchanger. They experimentally measured that the impact of fin height, axial fin pitch and circular fin pitch on performance evaluation criterion were approximately 47%, 31% and 16%, respectively. Han et al. (2013), Khoshvaght-Aliabadi et al. (2016), Benmachiche et al. (2017), He et al. (2012), Jin et al. (2013), Liao (1990), Anoop et al. (2015), Lemouedda et al. (2012) and Bouzari and Ghazanfarian (2016) had studied about the effect of different types of fins such as circular fins, spiral fins, H-type fins, plate fins, etc. on the hydrothermal performance.

Fig. 4.7
figure 7

An overview of the changes of (a) Nusselt number and (b) friction factor with increasing Reynolds number (Zhang et al. 2019)

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Mirth and Ramadhyani (1994) investigated and developed correlation for smooth wave configuration for the staggered tube layout. Youn et al. (1998) generated data for two-row heat exchangers. Kang and Webb (1998) studied offset strip fins or slit fins applied to fin-tube heat exchangers (Fig. 4.8). Hitachi (1984) used convex louvre fin geometry in commercial plate fin-and-tube heat exchangers. The flow acceleration and fluid mixing in the wake of the tube provide a substantial enhancement. Hatada et al. (1989) generated performance data of the convex louvre fin geometry for a one-row heat exchanger (Figs. 4.9 and 4.10).

Fig. 4.8
figure 8

Comparison of the heat transfer coefficient for the OSF and plain fin geometries for 9.5 mm diameter tubes, 525 fins/m and 0.2 mm fin thickness (Nakayama and Xu 1983)

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Fig. 4.9
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Convex louvre plate fin-and-tube geometry tested (Hatada et al. 1989)

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Fig. 4.10
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Performance data for convex louvre surface geometries (Hatada et al. 1989)

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The reduced louvre angle near the tube allows more air flow in the vicinity of the tubes. Hatada and Seshu (1984) studied the plate-and-fin geometry. The effect of fin pitch and tube rows on the j and f factors of the convex louvre geometry have been investigated by Wang et al. (1996, 1998). j factors were independent of the fin pitch. The j factors were independent of fin pitch. The row effect on the j factors was relatively weak compared with that of the plain fin geometry. The friction factors were independent of the number of tube rows. The friction factors of the convex louvre fin geometry showed 21–41% and 60–72% increase as compared to the corresponding wavy fin geometry. Convex louvre geometry performance was the best, followed by the louvre and wavy fin geometries.

Tao et al. (2007a, b) numerically investigated the performance of wavy fin used for heat transfer augmentation. They used wavy fin (fin A) and plain fin (fin C) and observed that for both the fins, the local Nusselt number decreased along the length of the pipe. The local Nusselt number upstream was almost ten times that of downstream. Thus, they suggested a new fin pattern in which wave is located only in the upstream and referred to it as fin B. The schematic of fin A, fin B and fin C has been shown in Fig. 4.11.

Fig. 4.11
figure 11

Schematic of (a) fin A, (b) fin B and (c) fin C (Tao et al. 2007a, b)

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The Nusselt number variation for fin A, fin B and fin C has been presented in Fig. 4.12. The Nusselt number for fin B was about 45% greater than that of fin C and 4% lower than that of fin A. Figure 4.13 shows the friction factor variation with Reynolds number for all the three fins used in the analysis. The plain fin (fin C) as expected has the minimum friction factor. The pressure drop in the case of fin B was found to be less than that of fin A. The friction factor for fin B was 26% higher and 18% lower than that of fin C and fin A, respectively. The overall performance evaluation index, Nu/f , for these three fins has been plotted and shown in Fig. 4.14. The overall performance of fin B has been observed to be the best among the three fins used for the analysis. The Nu/f for fin B has been reported to be 12.4–18.5% and 14.9–20% greater than that of fin C and fin A, respectively.

Fig. 4.12
figure 12

Nusselt number variation for fin A, fin B and fin C (Tao et al. 2007a, b)

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Fig. 4.13
figure 13

Friction factor variation with Reynolds number (Tao et al. 2007a, b)

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Fig. 4.14
figure 14

Overall performance evaluation index, Nu/f vs. Re (Tao et al. 2007a, b)

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Generalized empirical correlations for j and f versus Re have not been developed for OSF geometry on round tubes. However, Nakayama and Xu developed an empirical correlation. In offset fin geometry, the direction of the strip relative to the air flow direction is very important. Several OSF geometry studies have been done (Wang and Chang 1998; Wang et al. 1999b; Kang and Webb 1998; Yun and Lee 2000; Du and Wang 2000). Youn et al. (2003) investigated the performance of the radial strip geometry. Radial strips perform better than the normal strips since the former have better heat conduction path, and this improves the heat transfer. However, radial strips face the air flow at an oblique angle; this lengthens the effective strip width and slightly reduces the heat transfer.

Nakayama and Xu (1983), Kang and Webb (1998), Wang et al. (1999b), Du and Wang (2000) and Youn et al. (2003) dealt with j and f correlations of OSF heat exchangers . However, the applicability of these correlations is very limited. The louvre geometry is applied to fin-tube heat exchangers. The louvre fin must be designed carefully since the louvers can cut the conduction path from the tube. The air-side performance of louvred fin heat exchangers has been investigated by Chang et al. (1995) and Wang et al. (1999a, 1999d). The j factors were independent of fin pitch. The effect of the number of tube rows was negligible for Red > 2000. However, significant reduction of the j factor with increasing number of tube rows was observed for the lower Reynolds number. Rich (1975) studied the row effect. Wang et al. (1999d) developed j and f correlations based on their data.

Muzychka and Kenway (2009) investigated the performance of offset-strip fin arrays for heat transfer augmentation in liquids having large Prandtl number. They proposed this model for the wake regions of laminar and turbulent regions. The correlations for j factor have been presented to study the effect of Prandtl number suppression on j factor. The schematic of offset-strip fins has been shown in Fig. 4.15. The results have been presented for water, polyalphaolefin and SAE5W30 engine oil considered as working fluids.

Fig. 4.15
figure 15

Schematic of offset-strip fins (Muzychka and Kenway 2009)

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Wang et al. (2001) studied slit and louvred fins and observed that performance depends on the louvre or slit pitch, and the fraction of the fin area on which louvres or slit exists. Fujii et al. (1991) studied a plate-fin geometry made of corrugated, perforated plates, and the surface had a one-row having 0.5 mm thick copper fins (Fig. 4.16). The friction performance is not that good compared to the other high-performance fin geometries. The data of the figure are scalable to other tube diameters.

Fig. 4.16
figure 16

(a) Illustration of one-row fin-tube heat exchanger tested; (b) air-side test results (Fujii et al. 1991)

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Elyyan and Tafti (2009) investigated the performance of dimpled multilouvred fins for heat transfer augmentation. They used a novel fin configuration with dimples, louvres and perforations. Thus, the combined effect of interrupted surface, surface roughness and small-scale discontinuities has been studied. The louvre geometries with dimples have been studied under case 1 and case 2. The fins considered under case 1 have dimples with larger imprint diameter than those in case 2. Case 3 considers perforations on the dimpled louvre fins. The heat transfer enhancement characteristics of fins have been studied by using direct and large eddy simulation.

They observed from the results of case 1 and case 2 that the influence of imprint diameter of the dimples on heat transfer was negligible. The presence of perforation on the dimpled louvre fins redirects the flow from the dimple side to the protrusion side of the fin. Thus, the recirculation in the dimple region is reduced. Further, more flow is observed to be drawn into the dimple cavity resulting in increased vorticity generation. Also, the perforation edges are the regions of high heat transfer coefficients which act as boundary layer regenerators. The flow redirected towards the protruded side and ejecting from there helps in mixing of the flow, and the heat transfer in the wake region of the protrusion is enhanced. They concluded that there was a 12–50% and a maximum 60% increase in heat transfer coefficient and friction factor due to the addition of perforations.

Webb and Trauger (1991), Tafti et al. (1999), Tafti and Zhang (2001), Zhang and Tafti (2001), Lyman et al. (2002), DeJong and Jacobi (2003), Mahmood et al. (2000), Burgess and Ligrani (2004), Ekkad and Nasir (2003), Wang et al. (2003), Ligrani et al. (2001, 2005), Chyu et al. (1997), Moon et al. (2000), Lin et al. (1999), Isaev and Leont’ev (2003), Park et al. (2004), Won and Ligrani (2004), Park and Ligrani (2005), Patrick and Tafti (2004), Elyyan et al. (2006) and Fujii et al. (1988) studied the heat transfer enhancement using louvred fins.

The mesh fin geometry can be applied to circular fin-tube heat exchangers. Ebisu (1999) observed as much 100% higher heat transfer at the same pumping power than that of conventional louvre fin heat exchangers. Ebisu (1999) extended the work of Torikoshi and Kawabata (1989) for mesh fin heat exchanger with in-line fin configuration, and he investigated the effect of offsetting the fin array. Figure 4.17 shows the flow visualization results of three-row tube bundles having different tube offsets. Figure 4.18 compares the performance of copper mesh finned heat exchangers with copper or aluminium louvre fin heat exchangers. The hA/v values of mesh fin having offset fin array and staggered tube layout may be as much as twice that for aluminium louvre fin heat exchanger at the same pumping power.

Fig. 4.17
figure 17

Flow visualization results of three-row tube bundles having different tube offsets: (a) y/P = 0, (b) y/P = 0.1, (c) y/P = 0.25, (d) y/P = 0.5 (Ebisu 1999)

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Fig. 4.18
figure 18

Heat transfer per unit volume (E) vs. pumping power per unit volume (P) for mesh fin heat exchangers. Louvre fin and plain fin data shown as lines (Ebisu 1999)

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A low heat transfer coefficient exists in the wake region behind the tubes, particularly at low Reynolds numbers for circular finned tubes. Vortex generators on the fin surface reduce the width of the wake zone and improve heat transfer in the wake region. However, the performance improvement with vortex generators is not great since there is no longitudinal horseshoe vortex which can make significant enhancement on the fins, relative to that provided by vortex generators.

Fiebig et al. (1990) studied vortex generators. The heat transfer enhancement was up to 20% and also the pressure drop decreased up to 10%. This was so because of boundary layer separation on the tube by longitudinal vortices generated by the vortex generators, which give high momentum fluid into the region behind the cylinder. Fiebig et al. (1993) extended their earlier study to three-row heat exchanger geometry (Fig. 4.19); the vortex generators were in common flow-down configuration.

Fig. 4.19
figure 19

The three-row fin-and-tube geometry tested by Fiebig et al. (1993); (a) in-line, (b) staggered arrangement, (c) shape of the vortex generator, d = 32 mm, H = 7 mm, 45° angle of attack (Fiebig et al. 1993)

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Torii et al. (2002) investigated the three-row geometry with vortex generators mounted in common flow-up configuration, and they observed pressure loss decrease and minor impairment in heat transfer. They attributed this to the boundary layer separation delay, reduction of form drag and removal of poor heat transfer zone behind the tube.

Kotcioglu and Caliskan (2008) investigated the performance of a cross-flow heat exchanger having wing-type vortex generators . The wing-type vortex generators in particular are convergent-divergent longitudinal vortex generators which are referred to as CDLVGs. An increase in heat transfer rate up to 120% was observed in the heat exchangers due to the presence of vortex generators. They observed a twofold to fourfold increase in pressure drop in case of vortex generators than that in the case of no vortex generators. They evaluated the effectiveness of the cross-flow heat exchanger using the ε-NTU method and observed that the effectiveness was about 60–80% higher in case of heat exchanger with vortex generators than that in the case without CDLVG. The NTU was in the range of 3.32–3.85. The secondary flow was reported in the space between wing cascades due to difference in pressure and velocity which prevails across the space between the converging and diverging pair of winglets.

Garg and Maji (1988) and Maughan and Incropera (1987) used fin, rib and wing configurations as vortex generators. Tahat et al. (2000) presented the spanwise and streamwise fin spacing for in-line and staggered arrangement of fins. El-Sayed et al. (2002) studied the effects of geometrical parameters of the fin, such as fin height, fin thickness, fin spacing, number of fins and fin tip-shroud clearance of fins. Kotcioglu et al. (1998) presented the heat transfer and pressure drop in a rectangular channel using wing-type vortex generators for heat transfer enhancement. Jubran and Al-Salaymeh (1996), Kakaç et al. (1999), Ogulata et al. (2000), Chen and Shu (2004) and Sahin et al. (2005) presented similar work on wing-type vortex generators. Numerical investigation of V-shaped vortex generators has been presented by Sohankar (2007). Tiwari et al. (2003) have also numerically studied the forced convection heat transfer enhancement in a rectangular channel having a built-in oval tube along with delta winglet-type vortex generators. They compared the heat transfer performance using one, two and three winglet vortex generator pairs and concluded that the performance was better for more number of winglet pairs.

Wang et al. (2002a, b, c) studied the fin-and-tube heat exchanger with vortex generators and compared its performance to that of a heat exchanger without vortex generators. They used two types of vortex generators, namely annular winglet type and delta winglet type . The longitudinal vortices have been observed in the case of annular winglet vortex generators. The intensity of counter-rotating vortices was found to increase with the increase in height of the annular winglets. The strength of longitudinal vortices was found to be more intense in case of delta winglet vortex generators. The longitudinal vortices may also be called the stream wise vortices. They explained that the use of vortex generators induces vortices which help in mixing the fluid at the wall with the mainstream flow by disturbing the boundary layer formation at the wall. Also, the form drag caused by slender bodies like winglet-type vortex generators is very less. They concluded that the vortex generators enhanced the heat transfer rate with moderate pressure drop.

Mittal and Balachandar (1995) showed that production and orientation of the vortices depends on the vortex generator types. They observed that the spanwise vortices are oriented parallel to the vortex generator axis. The longitudinal vortices are those which orient along the direction of the flow (Chen et al. 1998). Grossegorgemann et al. (1995) experimentally studied pin-fin array performance. The numerical study on unsteady flow has been taken up by Saha and Acharya (2003, 2004a, b). They used pin-fin arrays for heat transfer enhancement. They observed the enhancement due to three effects: increased surface area due to the presence of fins, boundary layer interruption and enhanced mixing due to the presence of vortex generators which cause vortex shedding and secondary flow. Amon et al. (1992) studied oscillatory flows. Wang and Vanka (1995) and Zhang et al. (1997) have also investigated the performance of periodic pin-fin arrays.

Lozza and Merlo (2001) investigated two-row fin-tube heat exchangers having various enhanced geometries and vortex generators (Fig. 4.20). The addition of winglet vortex generators to louvre fin geometry is not as good as giving the same area to louvres. Lozza and Merlo (2001) got greater enhancement than that found by Fiebig et al. (1990), who used vortex generators in the tube wake region. Vortex generators do not provide greater enhancement than that can be obtained from conventional slit or louvre fin geometries, when applied to round tubes. Advanced fin geometries reduce the fin efficiency by cutting the fins to form louvres, slits, vortex generators, etc. O’Brien et al. (2003) tested four-row individually finned bundles having annular fins (Fig. 4.21).

Fig. 4.20
figure 20

Fin configurations tested by Lozza and Merlo (2001): (a) louvre fin A, (b) louvre fin B, (c) louvre fin with vortex generator (Lozza and Merlo 2001)

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Fig. 4.21
figure 21

Individual fins having a pair of winglet vortex generators: (a) common flow-down, (b) common flow-up configuration (O’Brien et al. 2003)

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Figures 4.22 and 4.23 show enhanced circular fin geometries and segmented or spine fin geometries used in air-conditioning applications, respectively (Webb 1980). All geometries provide enhancement by the periodic development of thin boundary layers on small diameter wires or flat strips, followed by their dissipation in the wave region between elements. The segmented fin is used in a wide range of applications.

Fig. 4.22
figure 22

Enhanced circular fin geometries : (a) plain circular fin; (b) slotted fin; (c) punched and bent triangular projections; (d) segmented fin; (e) wire loop extended surface (Webb 1987)

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Fig. 4.23
figure 23

Segmented or spine fin geometries used in air-conditioning applications. (a) From La Porte et al. (1979). (b) Described by Abbott et al. (1980) and tested by Eckels and Rabas (1985)

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Figure 4.24 shows j and f versus Red curves for a four-row staggered and a seven-row in-line tube segmented fin geometry (Weierman et al. 1978). It also shows the j and f curves for a staggered plain fin geometry having the same geometrical parameters as the staggered segmented geometry. Weierman (1976), Rabas et al. (1986) and Breber (1991) studied steel segmented and plain fin geometries for staggered and in-line tube layouts. Steel fin geometries are used for high-temperature applications like boiler economizers and heat recovery boilers to avoid corrosion by combustion products. Breber (1991) also recommended appropriate correlations to predict the heat transfer coefficient and friction factor.

Fig. 4.24
figure 24

Comparison of segmented fins (staggered and in-line tube layouts) with plain, staggered fin tube geometry as reported: St /do = 2.25, e/do = 0.51, s/e = 0.12, w/e = 0.17 (Weierman et al. 1978)

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Holtzapple and Carranza (1990) and Holtzapple et al. (1990) studied spine fin tube made of copper tubes and fins. The fins are integral to the tube wall, but these are expensive. Data are provided on several tube pitch layouts. Carranza and Holtzapple (1991) gave an empirical pressure drop correlation. Benforado and Palmer (1964) worked with wire loop fin geometry. They also studied plain circular fin geometry having the same fin pitch and height, and they observed 50% increase in heat transfer coefficient and the same pressure drop as the plain fin.