Advertisement

Round Tubes Having Plain-Plate Fins

  • Sujoy Kumar Saha
  • Hrishiraj Ranjan
  • Madhu Sruthi Emani
  • Anand Kumar Bharti
Chapter
  • 173 Downloads
Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)

Abstract

The performance characteristics of round tubes having plain-plate fins are discussed in this chapter. The concepts of wavy fins, louvred fins, multi louvred fins, fin numbering, etc. are explained in detail. Staggered and in-line arrangement of tube bundles and fin spacing are the other topics covered here. The correlations for configurations are also presented.

Keywords

Plain-plate fins Wavy fin Louvred fin Multi-louvred fin In-line arrangement Staggered arrangement 
Ohara and Koyama (2012) investigated the heat transfer and flow pattern experimentally in a plate-fin heat exchanger. They studied the thermo-hydraulic characteristics of falling film evaporation of pure refrigerant HCFC123 in a vertical rectangular channel with a serrated fin surface. The rear wall of the channel and evaporator was heated by electricity and liquid refrigerant flowing down vertically on it. The flow pattern was observed directly through transparent vinyl chloride resin plate during evaporation process. Experimental setup was supplied with constant mass velocity (G = 28–70 kg/m2s), heat flux (q = 20–50 kWw/m2) and pressure (P = 100 kPa). It was observed that when the vapour quality was more than equal to 0.3, heat transfer coefficient depended on the values of both mass velocity and heat flux. Figure 2.1 shows the variation of heat transfer coefficient with respect to vapour quality for heat fluxes of 20, 30, 40 and 50 kW/m2, respectively. Figure 2.2 shows the variation of Nusselt number with respect to Reynolds number for mass velocity of 28, 40, 55 and 70 kg/m2s, respectively.
Fig. 2.1

The relation between heat transfer coefficient and vapour quality (Ohara and koyama 2012)

Fig. 2.2

The relation between Nusselt number and Reynolds number (Ohara and Koyama 2012)

Thermo-hydraulic characteristics in air-cooled compact wavy fin heat exchanger was reviewed and analysed by Awad and Muzychka (2011). They developed the new model to simplify the existing studies of Fanning friction factor f and the Colburn j factor. These models were developed by establishing the correlation between low Reynolds number and laminar boundary layer regions. The prepared model was based upon the geometrical and thermophysical parameters such as fin height (H), fin spacing (S), wave amplitude (A), fin wavelength (λ), Reynolds number (Re) and Prandtl number (Pr). They compared the proposed model with numerical and experimental data of published literature for air. Figure 2.3 shows characteristic dimensions and top view of a basic cell of wavy fin geometry. Muley et al. (2002, 2006), Muzychka (1999), Muzychka and Kenway (2009), Sheik Ismail et al. (2009, 2010), Zhang (2005), Zhang et al. (2003, 2004), Junqi et al. (2007), Rush et al. (1999) and Lin et al. (2002) also studied the effect of fins in heat exchanger.
Fig. 2.3

Basic cell of wavy fin geometry: (a) characteristic dimensions of a wavy fin channel and (b) top view of a wavy channel (Awad and Muzychka 2011)

Bahrami et al. (2012) studied numerically and experimentally about the effect of geometric parameters of multi-louvred fins of compact heat exchangers on the heat transfer enhancement. They solved the three important thermophysical conservation equations of mass, momentum and energy using the finite volume method in various heat and flow conditions. Figure 2.4 shows the fin geometric parameters such as fin width (Fd) and fin pitch (Fp). Figure 2.5 shows the variation of pressure drop with inlet flow velocity or Reynolds number for the louvred angles of 18°, 24°, 26°, 28° 30° and 38° at the fin pitch of 1.3 mm. They observed that increasing the louvre angles resulted in more deviation of the fluid and that causes more pressure losses in the fins. They found from results that thermal capacity and pressure drop decreased with increase in fin pitch. Pressure drop and heat capacity were lesser affected by louvre angle than fin pitch.
Fig. 2.4

Geometric parameters of fin and louvres (Bahrami et al. 2012)

Fig. 2.5

The variations of pressure drop vs. flow velocities for different louvre angles (Bahrami et al. 2012)

They found that in the second row of louvres at low Reynolds number, more pressure loss and less heat transfer took place. Therefore, they recommended removing the second-half of louvres and studied the effect of this type of fin having 26° louvre angle. Figure 2.6 shows the semi-louvred fin. The results indicated that thermal heat capacity increased up to 22% in the semi-louvred fin at 2 m/s inlet velocity. Therefore, they strongly recommended this type of fin heat exchanger in stationary refrigeration and air-conditioning system. Atkinson et al. (1998), Chang and Hsu (2000), Chang and Wang (1996, 1997), Chang et al. (1994), Dillen and Webb (1994), Dong et al. (2007), Lawson and Thole (2008), Lyman et al. (2002), Perrotin and Clodie (2004) and Sunden and Svantesson (1992) also studied the effect of louvred fin and tube heat exchanger on thermo-hydraulic characteristics.
Fig. 2.6

Semi-louvred fin model (Bahrami et al. 2012)

Haghighi et al. (2018) conducted an experimental investigation in natural heat convection on thermal performance and convective heat transfer coefficient of plate fins and plate cubic pin-fin heat sink. He conducted the experimental investigation for Rayleigh number range of 8 × 106 to 9.5 × 106, heat input range of 10–120 W. Fin spacing and fin numbers were varied between 5 and12 mm and 5 and 9, respectively. They investigated the effect of fin spacing and number of fins of plate fins and plate cubic pin fin on thermal resistance and heat transfer. They found that plate cubic pin fin having 8.5 mm fin spacing and seven fins was better than plate-fin heat sink. They developed empirical correlations for average Nusselt number as a function of number of fin plates, fin spacing to height ratio as well as Rayleigh number.

Figure 2.7 shows the geometry of plate fin and plate cubic pin fin. Table 2.1 shows the dimensions of test fins. Figure 2.8 shows the variation of thermal resistance with fin spacing for plate pin fin and plate cubic pin fin. Figure 2.9 shows that Nusselt numbers were increasing with increase in Rayleigh numbers. The results of experimental investigation revealed that increasing the fin space caused lower thermal resistance but increase in fin number did not cause better heat transfer. They observed that thermal resistance of plate cubic pin fins were decreased by 15% compared to that of plate fin. Zaretabar et al. (2018), Mohammadian and Zhang (2017), Ji et al. (2018), Yang et al. (2017), Joo and Kim (2015), Yu et al. (2005), Yazicioğlu and Yüncü (2007), Yang and Peng (2009), Jeon and Byon (2017), Lee et al. (2016) and Micheli et al. (2016) investigated the effect of plate fins and pin fins on the hydrothermal characteristics.
Fig. 2.7

Geometry of plate fin and plate cubic pin fin (Haghighi et al. 2018)

Table 2.1

Dimensions of test fins (Haghighi et al. 2018)

Fin type

Fin shape

Fin number

Fin spacing (mm)

S/H

Type A

Plate pin fin

5

12

24/90

Type B

Plate pin fin

7

8.5

17/90

Type C

Plate pin fin

9

5

10/90

Type D

Plate cubic pin fin

5

12

24/90

Type E

Plate cubic pin fin

7

8.5

17/90

Type F

Plate cubic pin fin

9

5

10/90

Fig. 2.8

The variation of thermal resistance with fin spacing. (a) Plate pin fin heat sinks. (b) Plate cubic pin fin heat sinks (Haghighi et al. 2018)

Fig. 2.9

Variation of Nusselt number versus Rayleigh numbers. (a) Plate pin fin heat sink. (b) Plate cubic pin fin heat sink (Haghighi et al. 2018)

Didarul Islam et al. (2008) reported the performance of rectangular fins having different patterns and placed in duct flow in different arrangements. Co-angular, zigzag, co-rotating and co-counter rotating configurations as shown in Fig. 2.10 have been used for the analysis. The friction factor variation with Reynolds number for the four configurations of fins, for different Prandtl numbers, has been shown in Fig. 2.11. The heat transfer coefficient correlations for different fin patterns and pitch ratios for a given fin height of 10 mm have been tabulated in Table 2.2. Also, the variation of η (ratio of Nusselt number of enhanced surface to the Nusselt number of plain surface) with f1/3 Re has been plotted and presented in Fig. 2.12. They have observed that the friction factor for all four fin patterns were greater than that for the smooth rectangular duct for fully developed turbulent flow. The maximum pressure drop was seen in the duct with co-rotating fins.
Fig. 2.10

Co-angular, zigzag, co-rotating and co-counter rotating configurations. (a) Co-angular pattern. (b) Zigzag pattern. (c) Co-rotating pattern. (d) Co-counter rotating pattern (Didarul Islam et al. 2008)

Fig. 2.11

Friction factor variation with Reynolds number for the four configurations of fins, for different Prandtl numbers (Didarul Islam et al. 2008)

Table 2.2

Heat transfer coefficient correlations for different fin patterns and pitch ratios for a given fin height of 10 mm (Didarul Islam et al. 2008)

Pattern

\( {\overline{Nu}}_{\mathrm{overall}}=c{\mathit{\operatorname{Re}}}^{0.7} \)

c

PR = 2

PR = 3

PR = 3.5

Co-angular

0.163

0.153

0.149

Zigzag

0.175

0.176

0.168

Co-rotating

0.261

0.223

0.212

Co-counter rotating

0.191

0.169

0.191

Fig. 2.12

Variation of η (ratio of Nusselt number of enhanced surface to the Nusselt number of plain surface) with f1/3 Re (Didarul Islam et al. 2008)

This is because of strong flow interactions accompanied with vortex attack on the end wall and fin surface. The fins with co-angular pattern have showed minimum pressure drop. They have observed the smoke flow pattern around the fins and oil titanium oxide flow pattern on the end wall. They reported that they were both in good agreement. They have also observed that the flow over co-angular fin plate was governed by horseshoe vortices while wavy flow behaviour was dominant in the case of zigzag fin pattern. This is because the diverging fin pairs generate longitudinal vortices which attack the end wall and fin surfaces together. In case of co-counter rotating fin pattern, the flow was only slightly disturbed due to converging fin pairs. They concluded that the fin with co-rotating pattern with pitch ratio 2 and fin height 10 mm has shown the best thermal performance among all the fins considered. Also, the heat transfer using co-rotating fin pattern was noted to be threefold that of the duct without fins.

Torii and Yanagihara (1997) worked with vortex generators; Sparrow et al. (1982, 1983) studied rectangular fin arrays; and Kadle and Sparrow (1986), Turk and Junkhan (1986), Oyakawa et al. (1993), Molki et al. (1995), El-Saed et al. (2002) and Bilen and Yapici (2002) have carried out similar investigations for heat transfer enhancement and pressure drop characteristics. Fabbri (1998, 1999), Zeitoun and Hegazy (2004), Olson (1992), Alam and Ghoshdastidar (2002), Saad et al. (1997), Kumar (1997), Yu et al. (1999), Liu and Jensen (1999), Sarkhi and Nada (2005), Wang et al. (2008a, b, c), Eckert and Irvine (1960), Yu and Tao (2004), Shih et al. (1995) and Park and Ligrani (2005) have carried out similar works.

Sajedi et al. (2015) worked on optimization of fin numbering in a heat exchanger having external extended finned tube for natural convection. They carried out numerical investigation and presented the results for heat transfer rate and average Nusselt number. The experiment was carried out for fixed Reynolds number and varying Rayleigh number. They have compared the experimental results with the numerical results and developed correlation for Nusselt number. The fin geometry has been shown in Fig. 2.13. The comparison of surface temperatures of the heat exchanger for numerical and experimental results has been presented in Fig. 2.14 for different Rayleigh numbers. The number of fins was considered to be 20. The rate of entropy generation \( \left({\dot{S}}_{\mathrm{gen}}\right) \) and total heat loss (q) have been shown in Figs. 2.15 and 2.16, respectively.
Fig. 2.13

Fin geometry (Sajedi et al. 2015)

Fig. 2.14

Comparison of surface temperatures of the heat exchanger for numerical and experimental results (Sajedi et al. 2015)

Fig. 2.15

Rate of entropy generation in cases 1–4 as a function of fin numbers (Sajedi et al. 2015)

Fig. 2.16

Total heat loss in cases 1–4 as a function of fin numbers (Sajedi et al. 2015)

The variation of average Nusselt number with the number of fins has been shown in Fig. 2.17. Three graphs have been shown to clearly present the average Nusselt number variation for different ranges of number of fins. They explained that as heat transfer surface increases and heat transfer coefficient decreases with the increase in number of fins, there is a definite need to obtain the optimum number of fins. For different cases considered for the analysis, the optimum number of fins ranged from 10 to 12.
Fig. 2.17

Variation of average Nusselt number with the number of fins (Sajedi et al. 2015)

Atayılmaz and Teke (2009, 2010), Ahmadi et al. (2014), Taghilou et al. (2014), Park et al. (2014), An et al. (2012), Al-Arabi and Khamis (1982), Popiel et al. (2007), Na and Chiou (1980), Chae and Chung (2011), Qiu et al. (2013), Chen and Hsu (2007), Haldar et al. (2007), Mokheimer (2002), Elenbaas (1942) and Beckwith et al. (1990) have all worked with fins for natural convection heat exchanger applications.

Murali and Katte (2008) presented the performance of radiating pin fin having threads, grooves and taper on the outer surface. They concluded that the heat transfer rate from the radiator using threaded, grooved and tapered fin was about 1.2–3.7 times more than that from a solid radiating pin fin. Wilkins (1960), Kumar and Venkateshan (1994), Krishnaprakas (1996), Ramesh and Venkateshan (1997), Krikkis and Razelos (2002, 2003), Chung and Nguyen (1987), Schnurr et al. (1976), Black and Schoenhals (1968), Black (1973), Gorchakov and Panevin (1975, 1976), Bhise et al. (2002), Srinivasan and Katte (2004) and Holman (2000) have also worked on radiating fins.

In-line tube geometry is seldom used because it provides substantially lower performance than the staggered tube geometry. Effect of fin spacing is important (Fig. 2.18). Rich (1973, 1975) measured heat transfer and friction data for fin geometry. Equation (2.1) gives that the friction drag force which is the sum of the drag force on a bare tube bank and the drag caused by the fins (Rich 1973).
$$ {f}_{\mathrm{f}}=\left(\Delta p-\Delta {p}_{\mathrm{t}}\right)\frac{2{A}_{\mathrm{c}}\rho }{G^2{A}_{\mathrm{f}}} $$
(2.1)
Fig. 2.18

Heat transfer and friction characteristics of a four-row plain plate fin heat exchanger for different fin spacing (Webb and Kim 2005)

Both pressure drop contributions are evaluated at the same minimum area mass velocity. On many occasions, it may happen that Reynolds number based on hydraulic diameter will not correlate the effect of fin pitch.

Several investigators have observed conflicting behaviour of manifestation of flow: j factor may or may not have been affected by fin pitch, but also may or may not have been affected by row effect; Wang et al. (1996), Wang and Chi (2000), Yan and Sheen (2000), McQuiston (1978), Seshimo and Fujii (1991), Kayansayan (1993) and Abu Madi et al. (1998). Figures 2.19 and 2.20 show the j and f versus Redh and average heat transfer coefficients for plain plate-finned tubes, respectively.
Fig. 2.19

Plot of the j factor and the fin friction vs. Rest (Webb and Kim 2005)

Fig. 2.20

Average heat transfer coefficients for plain plate-finned tubes (571 fins/m) having one to six rows (Webb and Kim 2005)

McQuiston (1978), Gray and Webb (1986), Kim et al. (1999) and Wang et al. (2000) correlated j and f data versus Reynolds number for plain fins on staggered tube arrangements; the accuracy level of predictions, however, widely vary.

The Gray and Webb (1986) heat transfer correlation for four or more tube rows of staggered tube geometry is given by Eq. (2.2). The correlation for rows less than four needs a correction factor given by Eq. (2.3).
$$ {j}_4=0.14{{\mathit{\operatorname{Re}}}_{\mathrm{d}}}^{-0.328}{\left(\frac{S_{\mathrm{t}}}{S_{\mathrm{l}}}\right)}^{-0.502}{\left(\frac{s}{d_0}\right)}^{0.031} $$
(2.2)
$$ \frac{j_N}{j_4}=0.991{\left[2.24{{\mathit{\operatorname{Re}}}_{\mathrm{d}}}^{-0.092}{\left(\frac{N}{4}\right)}^{-0.031}\right]}^{0.607\left(4-N\right)} $$
(2.3)
McQuiston’s (1978) correlation assumes that the pressure drop is composed of two terms; the first term is for the drag force on the fins and the second term for the drag force on the tubes (Eqs. 2.4 and 2.5).
$$ f={f}_{\mathrm{f}}\frac{A_{\mathrm{f}}}{A}+{f}_{\mathrm{t}}\left(1-\frac{A_{\mathrm{f}}}{A}\right)\left(1-\frac{t}{p_{\mathrm{f}}}\right) $$
(2.4)
$$ {f}_{\mathrm{f}}=0.508{{\mathit{\operatorname{Re}}}_{\mathrm{d}}}^{-0.521}{\left(\frac{S_{\mathrm{t}}}{d_0}\right)}^{1.318} $$
(2.5)

The friction factor with the tubes is obtained from a correlation for flow normal to a staggered bank of plain tubes. Zukauskas (1972) and Incropera and Dewitt (2001) give the tube bank correlation. McQuiston (1978) correlation based on the same data, however, does a poor job.

Mon and Gross (2004) numerically examined the fin-spacing effects by three-dimensional simulation of four-row tube bundles placed in staggered and in-line arrangements. It is complicated and difficult to understand geometrically complex bundles related to heat transfer characteristics. Thus, numerical model may help in better understanding and explanation. Saboya and Sparrow (1974, 1976), Sheu and Tsai (1999), Xi and Torikoshi (1996), Fiebig et al. (1995), Torikoshi (1994), Kaminski (2002), Kaminski and Groß (2003) and Romero-Méndez et al. (2000) studied finned tube heat exchangers and evaluated the influence of fin spacing but neither of them worked for annular-finned tube heat exchangers. They used the K-ɛ turbulence model and adopted respective equations. They simulated for Reynolds number range of 8600 ≤ Re ≤ 43,000 and presented Table 2.3 for the dimension of bundle of testing tube.
Table 2.3

Dimensions of tube bundles (Mon and Gross 2004)

 

Staggered

In-line

s1

s2

s3

s4

s5

il

i2

i3

Tube outside diameter, d

24

24

24

24

24

24

24

24

Fin diameter, df

34

34

34

44

44

34

34

34

Fin height, hf

5

5

5

10

10

5

5

5

Fin thickness, tf

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

Fin spacing, s

1.6

2

4

0.7

2

1.6

2

4

Fin pitch, Sf = s + tf

2.1

2.5

4.5

1.2

1.2

2.1

2.5

4.5

Transverse tube pitch, St

40.8

40.8

40.8

52.8

52.8

40.8

40.8

40.8

Longitudinal tube pitch, S1

35.33

35.33

35.33

45.73

45.73

40.8

40.8

40.8

Number of rows, n

4

4

4

4

4

4

4

4

All dimensions are in mm

They simulated both the in-line and staggered arrangement of tubes and concluded global flow behaviour, local flow behaviour, thermal boundary layer development and fin spacing effects on heat transfer and pressure drop characteristics. The results of global velocity distribution are presented in Fig. 2.21, and it is found that main stream has been encountered by larger surface area in staggered array, whereas larger wake regions are in in-line array. Their simulated result shows that secondary vortex has developed. They plotted the results which included heat transfer coefficient versus fin spacing to height ratio in Fig. 2.22a and heat transfer coefficient versus pressure drop in Fig. 2.22b for both staggered and in-line bundles. The simulation presented that heat transfer coefficient increased to 19% in all cases with increased S/hf from 0.32 to 0.8 simultaneously, whereas in case of staggered arrangement, the heat transfer coefficient was found to be increased up to S/hf = 0.32 and remained constant for further increase in S/hf ratio. They found that boundary layers between fins departing from each other for staggered arrangement. Pressure drop found to be decreased with both the arrangement as S/hf increased.
Fig. 2.21

Global velocity distributions for (a) staggered and (b) in-line arrangements at Re = 8600 (Mon and Gross 2004)

Fig. 2.22

Effects of fin spacing to height ratio on (a) heat transfer coefficient and (b) pressure drop for staggered and in-line bundles (Mon and Gross 2004)

Seshimo and Fujii (1991) gave a more generalized correlation for staggered banks of plain fins having one to five tube rows. They correlated one- and two-row data in terms of entrance length by Eqs. (2.6) and (2.7).
$$ Nu=2.1{\left({X}_{\mathrm{Dv}}\right)}^n $$
(2.6)
$$ {fLD}_{\mathrm{v}}={c}_1+{c}_2\left({X}_{\mathrm{Dv}}\right)-m $$
(2.7)

For three or more rows, the entrance length-based correlations do not do justice to the data over the entire Reynolds number range (200 < ReDh < 800).

Use of smaller diameter finned tube heat exchanger is the recent trend; Kim et al. (1999) improved Gray and Webb (1986) correlation by including the data of Wang and Chi (2000) and Youn (1997) for heat exchangers having smaller diameter tubes. The improvement in prediction was noteworthy. A more general correlation is that of Wang et al. (2000).

The Kim et al. (1999) correlation (for three or more tube rows) is given by a set of Eqs. (2.8), (2.9) and (2.10).
$$ {j}_3=0.163{{\mathit{\operatorname{Re}}}_{\mathrm{d}}}^{-0.369}{\left(\frac{S_{\mathrm{t}}}{S_{\mathrm{l}}}\right)}^{0.106}{\left(\frac{s}{d_0}\right)}^{0.0138}{\left(\frac{S_{\mathrm{t}}}{d_0}\right)}^{0.13}\kern1em \left(N\ge 3\right) $$
(2.8)
$$ \frac{j_N}{j_3}=1.043\left[{{\mathit{\operatorname{Re}}}_{\mathrm{d}}}^{-0.14}\right]\cdot {\left[{\left(\frac{S_{\mathrm{t}}}{S_{\mathrm{l}}}\right)}^{-0.564}{\left(\frac{s}{d_0}\right)}^{-0.123}{\left(\frac{S_{\mathrm{t}}}{d_0}\right)}^{1.17}\right]}^{\left(3-N\right)}\kern1em \left(N=1,2\right) $$
(2.9)
$$ {f}_{\mathrm{f}}=1.455{{\mathit{\operatorname{Re}}}_{\mathrm{d}}}^{-0.656}{\left(\frac{S_{\mathrm{t}}}{S_{\mathrm{l}}}\right)}^{-0.347}{\left(\frac{s}{d_0}\right)}^{-0.134}{\left(\frac{S_{\mathrm{t}}}{d_0}\right)}^{1.23} $$
(2.10)
and they used the Jacob (1938) correlation. Equation (2.4) is used to calculate the friction factor of the heat exchanger. In-line tube geometries are not good because tube bypass effects substantially degrade the performance of an in-line tube arrangement (Schmidt 1963).

References

  1. Abu Madi M, Johns RA, Heikal MR (1998) Performance characteristics correlation for round tube and plate finned heat exchangers. Int J Refrig 21:507–517CrossRefGoogle Scholar
  2. Ahmadi M, Mostafavi G, Bahrami M (2014) Natural convection from rectangular interrupted fins. Int J Therm Sci 82(1):62–71CrossRefGoogle Scholar
  3. Alam I, Ghoshdastidar PS (2002) A study of heat transfer effectiveness of circular tubes with internal longitudinal fins having tapered lateral profiles. Int J Heat Mass Transf 45(6):1371–1376zbMATHCrossRefGoogle Scholar
  4. Al-Arabi M, Khamis M (1982) Natural convection heat transfer from inclined cylinders. Int J Heat Mass Transf 25(I):3–15CrossRefGoogle Scholar
  5. An BH, Kim HJ, Kim DK (2012) Nusselt number correlation for natural convection from vertical cylinders with vertically oriented plate fins. Exp Thermal Fluid Sci 41:59–66CrossRefGoogle Scholar
  6. Atayılmaz SO, Teke I (2009) Experimental and numerical study of the natural convection from a heated horizontal cylinder. Int Commun Heat Mass Transf 36:731–738CrossRefGoogle Scholar
  7. Atayılmaz SO, Teke I (2010) Experimental and numerical study of the natural convection from a heated horizontal cylinder wrapped with a layer of textile material. Int Commun Heat Mass 37:58–67CrossRefGoogle Scholar
  8. Atkinson KN, Drakulic R, Heikal MR, Cowell TA (1998) Two- and three-dimensional numerical models of flow and heat transfer over louvered fin arrays in compact heat exchangers. Int J Heat Mass Transf 41:4063–4080zbMATHCrossRefGoogle Scholar
  9. Awad M, Muzychka YS (2011) Models for pressure drop and heat transfer in air cooled compact wavy fin heat exchangers. J Enhanc Heat Transf 18(3):191–207CrossRefGoogle Scholar
  10. Bahrami S, Rahimian MH, Mohammadbeigi H, Hosseinimanesh H (2012) Thermal-hydraulic study of multi-louvered fins in compact heat exchangers and recommendations for improvement. J Enhanc Heat Transf 19(1):53–61CrossRefGoogle Scholar
  11. Beckwith TG, Marangoni RD, Lienhard JH (1990) Mechanical measurements, 5th edn. Addison-Wesley Publishing Company, New York, pp 45–112Google Scholar
  12. Bhise NV, Katte SS, Venkateshan SP (2002) A numerical study of corrugated structure for space radiators. In: 16th national and 5th ISHMT–ASME heat and mass transfer conference Kolkata, pp 520–526Google Scholar
  13. Bilen K, Yapici S (2002) Heat transfer from a surface fitted with rectangular blocks at different orientation angle. Heat Mass Transf 38:649–655CrossRefGoogle Scholar
  14. Black WZ (1973) Optimization of the directional emission from V-groove and rectangular cavities. J Heat Transf 95:31–36CrossRefGoogle Scholar
  15. Black WZ, Schoenhals RJ (1968) A study of directional radiation properties of specially pre pared ‘V’-groove cavities. J Heat Transf 90:420–428CrossRefGoogle Scholar
  16. Chae MS, Chung BJ (2011) Effect of pitch-to-diameter ratio on the natural convection heat transfer of two vertically aligned horizontal cylinders. Exp Thermal Fluid Sci 66:5321–5329Google Scholar
  17. Chang YJ, Hsu KC (2000) Generalized friction correlation for louver fin geometry. Int J Heat Mass Transf 43(12):2237–2243CrossRefGoogle Scholar
  18. Chang Y, Wang C (1996) Air-side performance of brazed aluminium heat exchangers. J Enhanc Heat Transf 3(1):15–28CrossRefGoogle Scholar
  19. Chang Y, Wang C (1997) A generalized heat transfer correlation for louvered fin geometry. Int Heat Transf 40(3):533–544MathSciNetCrossRefGoogle Scholar
  20. Chang Y, Wang C, Chang W (1994) Heat transfer and flow characteristics of automotive brazed aluminium heat exchangers. ASHRAE Trans 100(2):643–652Google Scholar
  21. Chen HT, Hsu WL (2007) Estimation of heat transfer coefficient on the fin of annular-finned tube heat exchangers in natural convection for various fin spacings. Int J Heat Mass Transf 50:1750–1761zbMATHCrossRefGoogle Scholar
  22. Chung BTF, Nguyen LD (1987) Thermal analysis and optimum design for radiating spine of various geometries. In: Proceedings of the international symposium on heat transfer science and technology Beijing People’s Republic of China October 15–18 198 (A87-33101 13-34). Hemisphere Publishing Corp, Washington, DC, pp 510–517Google Scholar
  23. Dillen EL, Webb RL (1994) Rationally based heat transfer and friction correlations for the louver fin geometry. SAE Tech Paper Ser 94050:600–607Google Scholar
  24. Dong J, Chen J, Chen Z, Zhang W, Zhou Y (2007) Heat transfer and pressure drop correlations for the multi-louvered fin compact heat exchangers. Energy Convers Manag 48:1506–1515CrossRefGoogle Scholar
  25. Eckert E, Irvine T (1960) Pressure drop and heat transfer in a duct with triangular cross-section. ASME J Heat Transf 83:125–136CrossRefGoogle Scholar
  26. Elenbaas W (1942) Heat dissipation of parallel plates by free convection. Physica 9(1):1–28zbMATHCrossRefGoogle Scholar
  27. El-Saed SA, Mohamed SM, Abdel-Latif AM, Abouda AE (2002) Investigation of turbulent heat transfer and fluid flow in longitudinal rectangular fin-arrays of different geometries and shrouded fin array. Exp Thermal Fluid Sci 26:879–900CrossRefGoogle Scholar
  28. Fabbri G (1998) Heat transfer optimization in internally finned tubes under laminar flow conditions. Int J Heat Mass Transf 41(10):1243–1253zbMATHCrossRefGoogle Scholar
  29. Fabbri G (1999) Optimum profiles for asymmetrical longitudinal fins in cylindrical ducts. Int J Heat Mass Transf 4(23):511–523zbMATHCrossRefGoogle Scholar
  30. Fiebig M, Gorsse-Georgemann A, Chen Y, Mitra NK (1995) Conjugate heat transfer of a finned tube part A: heat transfer behaviour and occurrence of heat transfer reversal. Numer Heat Transf Part A 28:133–146CrossRefGoogle Scholar
  31. Gorchakov VS, Panevin IG (1975) Effectiveness of radiating fins covered with V-shaped grooves. http://techreports.iarc.nasa.gov/egiin/ NTRS
  32. Gorchakov VS, Panevin IG (1976) Efficiency of radiating fins covered with V-shaped grooves. J High Temp 13(4):733–738Google Scholar
  33. Gray DL, Webb RL (1986) Heat transfer and friction correlations for plate fin-and-tube heat exchangers having plain fins. In: Heat transfer 1986. Proceedings of the eighth international heat transfer conference, pp 2745–2750Google Scholar
  34. Haghighi SS, Goshayeshi HR, Safaei MR (2018) Natural convection heat transfer enhancement in new designs of plate-fin based heat sinks. Int J Heat Mass Transf 125:640–647CrossRefGoogle Scholar
  35. Haldar SC, Kochhar GS, Manohar K, Sahoo RK (2007) Numerical study of laminar free convection about a horizontal cylinder with longitudinal fins of finite thickness. Int J Therm Sci 46:692–698CrossRefGoogle Scholar
  36. Holman JP (2000) Experimental methods for engineering. Ch. 2 and 3. McGraw-Hill, New YorkGoogle Scholar
  37. Incropera FP, DeWitt DP (2001) Fundamentals of heat mass transfer, 5th edn. Wiley, New YorkGoogle Scholar
  38. Islam MD, Oyakawa K, Yaga M (2008) Heat transfer enhancement from a surface affixed with rectangular fins of different patterns and arrangement in duct flow. J Enhanc Heat Transf 15(1):31–50CrossRefGoogle Scholar
  39. Jacob ML (1938) Heat transfer and flow resistance in cross flow of gases over tube banks. Trans ASME 60:384Google Scholar
  40. Jeon D, Byon C (2017) Thermal performance of plate fin heat sinks with dual-height fins subject to natural convection. Int J Heat Mass Transf 113:1086–1092CrossRefGoogle Scholar
  41. Ji C, Qin Z, Low Z, Dubey S, Choo FH, Duan F (2018) Non-uniform heat transfer suppression to enhance PCM melting by angled fins. Appl Therm Eng 129:269–279CrossRefGoogle Scholar
  42. Joo Y, Kim SJ (2015) Comparison of thermal performance between plate-fin and pin fin heat sinks in natural convection. Int J Heat Mass Transf 83:345–356CrossRefGoogle Scholar
  43. Junqi D, Jiangping C, Zhijiu C, Yimin Z, Wenfeng Z (2007) Heat transfer and pressure drop correlations for the wavy fin and flat tube heat exchangers. Appl Therm Eng 27(11–12):2066–2073CrossRefGoogle Scholar
  44. Kadle DS, Sparrow EM (1986) Numerical and experimental study of turbulent heat transfer and fluid flow in longitudinal fin array. ASME J Heat Transf 108:16–23CrossRefGoogle Scholar
  45. Kaminski S (2002) Numerische Simulation der luftseitigen Stromungs-und Warmetransportvorgange in Lamellenrohr-Warmeubertragern. Techn. Univ. Bergakad, FreibergGoogle Scholar
  46. Kaminski S, Groß U (2003) Luftseitige Transportprozesse in Lamellenrohrbundeln—numerische Untersuchung. Ki Luft und Kaltetechnik (5):220–224Google Scholar
  47. Kayansayan N (1993) Heat transfer characterization of flat plain fins and round tube heat exchangers. Exp Thermal Fluid Sci 6(3):263–272CrossRefGoogle Scholar
  48. Kim N-H, Youn B, Webb RL (1999) Air-side heat transfer and friction correlations for plain fin-and-tube heat exchangers with staggered tube arrangements. J Heat Transf 121(3):662–667CrossRefGoogle Scholar
  49. Krikkis RN, Razelos P (2002) Optimum design of spacecraft radiators with longitudinal rectangular and triangular fins. J Heat Transf 124:805–811CrossRefGoogle Scholar
  50. Krikkis RN, Razelos P (2003) The optimum design of radiating and convective-radiating circular fins. J Heat Transf Eng 24(3):17–41CrossRefGoogle Scholar
  51. Krishnaprakas CK (1996) Optimum design of radiating rectangular plate fin array extending from a plane wall. J Heat Transf 118:490–493CrossRefGoogle Scholar
  52. Kumar SS, Venkateshan SP (1994) Optimized tubular radiator with annular fins on a non-isothermal base. Int J Heat Fluid Flow 15:399–409CrossRefGoogle Scholar
  53. Kumar R (1997) Three-dimensional natural convective flow in a vertical annulus with longitudinal fins. Int J Heat Mass Transf 40(14):3323–3334zbMATHCrossRefGoogle Scholar
  54. Lawson MJ, Thole KA (2008) Heat transfer augmentation along the tube wall of a louvered fin heat exchanger using practical delta winglets. Int J Heat Mass Transf 51:2346–2360CrossRefGoogle Scholar
  55. Lee M, Kim HJ, Kim DK (2016) Nusselt number correlation for natural convection from vertical cylinders with triangular fins. Appl Therm Eng 93:1238–1247CrossRefGoogle Scholar
  56. Lin Y-T, Hwang Y-M, Wang C-C (2002) Performance of the herringbone wavy fin under dehumidifying conditions. Int J Heat Mass Transf 45:5035–5044CrossRefGoogle Scholar
  57. Liu XY, Jensen MK (1999) Numerical investigation of turbulent flow and heat transfer in internally finned tubes. J Enhanc Heat Transf 6(2–4):105–119CrossRefGoogle Scholar
  58. Lyman AC, Stephan RA, Thole KA, Zhang LW, Memory SB (2002) Scaling of heat transfer coefficients along louvered fins. Exp Thermal Fluid Sci 26:547–563CrossRefGoogle Scholar
  59. McQuiston FC (1978) Correlation of heat, mass, and momentum transport coefficients for plate-fin-tube heat transfer for surfaces with staggered tube. ASHRAE Trans 54(Part 1):294–309Google Scholar
  60. Micheli L, Reddy K, Mallick TK (2016) Experimental comparison of micro-scaled plate-fins and pin-fins under natural convection. Int Commun Heat Mass Transf 75:59–66CrossRefGoogle Scholar
  61. Mohammadian SK, Zhang Y (2017) Cumulative effects of using pin fin heat sink and porous metal foam on thermal management of lithium-ion batteries. Appl Therm Eng 118:375–384CrossRefGoogle Scholar
  62. Mokheimer EMA (2002) Performance of annular fins with different profiles subject to variable heat transfer coefficient. Int J Heat Mass Transf 45:3631–3642zbMATHCrossRefGoogle Scholar
  63. Molki M, Faghri M, Ozbay O (1995) A correlation for heat transfer and wake effect in the entrance region of an inline array of rectangular blocks simulating electronic components. ASME J Heat Transf 117:40–46CrossRefGoogle Scholar
  64. Mon MS, Gross U (2004) Numerical study of fin-spacing effects in annular-finned tube heat exchangers. Int J Heat Mass Transf 47(8–9):1953–1964CrossRefGoogle Scholar
  65. Muley A, Borghese J, Manglik RM, Kundu J (2002) Experimental and numerical investigation of thermal-hydraulic characteristics of wavy-channel compact heat exchanger. In: Proc. 12th international heat transfer conference France, vol 4, pp 417–422Google Scholar
  66. Muley A, Borghese JB, White SL, Manglik RM (2006) Enhanced thermal-hydraulic performance of a wavy-plate fin compact heat exchanger: effect of corrugation severity. In: Proc. 2006 ASME international mechanical engineering congress and exposition (IMECE2006), Chicago, IL, USA, IMECE2006-14755Google Scholar
  67. Murali JG, Katte SS (2008) Experimental investigation of threaded, grooved, and tapered radiating pin-fin. J Enhanc Heat Transf 15(3):199–209CrossRefGoogle Scholar
  68. Muzychka YS (1999) Analytical and experimental study of fluid friction and heat transfer in low Reynolds number flow heat exchangers. Ph. D Thesis. University of Waterloo, Waterloo, ONGoogle Scholar
  69. Muzychka YS, Kenway G (2009) A model for the thermal hydraulic characteristics of the offset strip fin array for large Prandtl number liquids. J Enhanc Heat Transf 16(1):73–92CrossRefGoogle Scholar
  70. Na TY, Chiou JP (1980) Turbulent natural convection over a slender circular cylinder. Warme Stoffubertrag 14:157–164CrossRefGoogle Scholar
  71. Ohara J, Koyama S (2012) Falling film evaporation of pure refrigerant HCFC123 in a plate-fin heat exchanger. J Enhanc Heat Transf 19(4):301–311CrossRefGoogle Scholar
  72. Olson DA (1992) Heat transfer in thin, compact heat exchangers with circular, rectangular, or pin-fin flow passages. ASME J Heat Transf 114:373–382CrossRefGoogle Scholar
  73. Oyakawa K, Furukawa Y, Taira T, Senaha I (1993) Effect of vortex generators on heat transfer enhancement in a duct. In: Proceedings of the experimental heat transfer, fluid mechanics and thermodynamics Honolulu, Hawaii, vol 1, pp 633–640Google Scholar
  74. Park J, Ligrani PM (2005) Numerical predictions of heat transfer and fluid flow characteristics for seven different dimpled surfaces in a channel. Numer Heat Transf Part A Appl 47(3):209–232CrossRefGoogle Scholar
  75. Park KT, Kim HJ, Kim DK (2014) Experimental study of natural convection from vertical cylinders with branched fins. Exp Thermal Fluid Sci 54:29–37CrossRefGoogle Scholar
  76. Perrotin T, Clodie D (2004) Thermal-hydraulic CFD study in louvered fin-and-flat-tube heat exchangers. Int J Refriger 27:422–432CrossRefGoogle Scholar
  77. Popiel CO, Wojtkowiak J, Bober K (2007) Laminar free convective heat transfer from isothermal vertical slender cylinder. Exp Thermal Fluid Sci 32(2007):607–613CrossRefGoogle Scholar
  78. Qiu Y, Tian M, Guo Z (2013) Natural convection and radiation heat transfer of an externally-finned tube vertically placed in a chamber. Heat Mass Transf 49:405–412CrossRefGoogle Scholar
  79. Ramesh N, Venkateshan SP (1997) Optimum finned tubular space radiator. Heat Transf Eng 18:69–87CrossRefGoogle Scholar
  80. Rich DG (1973) The effects of fin spacing on the heat transfer and friction performance of multi-row, smooth plate fin-and-tube heat exchangers. ASHRAE Trans 79(Part 2):137–145Google Scholar
  81. Rich DG (1975) Effect of the number of tube rows on heat transfer performance of smooth plate fin-and-tube heat exchangers. ASHRAE Trans 81(Part 1):307–319Google Scholar
  82. Romero-Méndez R, Sen M, Yang KT, McClain R (2000) Effect of fin spacing on convection in a plate fin and tube heat exchanger. Int J Heat Mass Transf 43(1):39–51CrossRefGoogle Scholar
  83. Rush TA, Newell TA, Jacobi AM (1999) An experimental study of flow and heat transfer in sinusoidal wavy passages. Int J Heat Mass Transf 42(9):1541–1553CrossRefGoogle Scholar
  84. Saad AE, Sayed AE, Mohamed EA, Mohamed MS (1997) Experimental study of turbulent flow inside a circular tube with longitudinal interrupted fins in the streamwise direction. Exp Thermal Fluid Sci 15(1):1–15CrossRefGoogle Scholar
  85. Saboya FEM, Sparrow EM (1974) Local and average transfer coefficients for one-row plate fin and tube heat exchanger configurations. J Heat Transf 96(3):265–272CrossRefGoogle Scholar
  86. Saboya FEM, Sparrow EM (1976) Transfer characteristics of two-row plate fin and tube heat exchanger configurations. Int J Heat Mass Transf 19(1):41–49CrossRefGoogle Scholar
  87. Sajedi R, Taghilou M, Jafari M (2015) Experimental and numerical study on the optimal fin numbering in an external extended finned tube heat exchanger. Appl Therm Eng 83:139–146CrossRefGoogle Scholar
  88. Sarkhi AA, Nada EA (2005) Characteristics of forced convection heat transfer in vertical internally finned tube. Int Commun Heat Mass Transf 32:557–564CrossRefGoogle Scholar
  89. Schmidt TE (1963) Der Warmeiibergang an Rippenrohre and die Berechnung von Rohrbundel-Warmeaustauschern, Kaltetechnik, Band 15, Heft 12Google Scholar
  90. Schnurr NM, Townsend MA, Shapiro AB (1976) Optimization of radiating fin arrays with respect to weight. ASME Trans J Heat Transf 98:643–648CrossRefGoogle Scholar
  91. Seshimo Y, Fujii M (1991) An experimental study on the performance of plate fin and tube heat exchangers at low Reynolds numbers. In: Proceedings of the ASME-JSME thermal engineering joint conference, vol 4, pp 449–454Google Scholar
  92. Sheik Ismail L, Ranganayakulu C, Shah RK (2009) Numerical study of flow patterns of compact plate-fin heat exchangers and generation of design data for offset and wavy fins. Int J Heat Mass Transf 52(17–18):3972–3983CrossRefGoogle Scholar
  93. Sheik Ismail L, Velraj R, Ranganayakulu C (2010) Studies on pumping power in terms of pressure drop and heat transfer characteristics of compact plate-fin heat exchangers—a review. Renew Sust Energ Rev 14(1):478–485CrossRefGoogle Scholar
  94. Sheu TW, Tsai SF (1999) A comparison study on fin surfaces in finned-tube heat exchangers. Int J Numer Methods Heat Fluid Flow 9(1):92–106zbMATHCrossRefGoogle Scholar
  95. Shih TH, Liou WW, Shabbrir A, Yang ZG, Zhu J (1995) A new k–e eddy viscosity model for high Reynolds number turbulent flows. Comput Fluids 24(3):227–238zbMATHCrossRefGoogle Scholar
  96. Sparrow EM, Niethammer JE, Chaboki A (1982) Heat transfer and pressure drop characteristics of arrays of rectangular modules encountered in electronic equipment. Int J Heat Mass Transf 25:961–973CrossRefGoogle Scholar
  97. Sparrow EM, Vemuri SB, Kadle D (1983) Enhanced and local heat transfer, pressure drop, and flow visualization for arrays of block-like electronic components. Int J Heat Mass Transf 26:689–699CrossRefGoogle Scholar
  98. Srinivasan K, Katte SS (2004) Analysis of grooved space radiator. In: Proceedings of the 17th national and 6th ISHMT-ASME heat and mass transfer confence, Kalpakkam, vol 12Google Scholar
  99. Sunden B, Svantesson J (1992) Correlation of j-and f-factors for multilouvered heat transfer surfaces. In: Proc. 3rd UK national conference on heat transfer, pp 805–811Google Scholar
  100. Taghilou M, Ghadimi B, Seyyedvalilu MH (2014) Optimization of double pipe fin pin heat exchanger using entropy generation minimization. IJE Trans C Aspects 27(9):1445–1454Google Scholar
  101. Torii K, Yanagihara JI (1997) A review on heat transfer enhancement by longitudinal vortices. J HTSJ 36(142):73–86Google Scholar
  102. Torikoshi K (1994) Flow and heat transfer performance of a plate-fin and tube heat exchanger. Heat Transf 4:411–416Google Scholar
  103. Turk AY, Junkhan GH (1986) Heat transfer enhancement downstream of vortex generators on a flat plate. In: Tien CL, Carey VP, Ferrell JK (eds) Heat transfer, vol 6. Hemisphere, Washington, pp 2903–2908Google Scholar
  104. Wang C-C, Chi K-Y (2000) Heat transfer and friction characteristics of plain fin-and-tube heat exchangers, part I: new experimental data. Int J Heat Mass Transf 43:2681–2691CrossRefGoogle Scholar
  105. Wang C-C, Chen P-Y, Jang J-Y (1996) Heat transfer and friction characteristics of convex-louver fin-and-tube heat exchangers. Exp Heat Transf 9:61–78CrossRefGoogle Scholar
  106. Wang C-C, Chi K-Y, Chang C-J (2000) Heat transfer and friction characteristics of plain fin-and-tube heat exchangers, part II: correlation. Int J Heat Mass Transf 43:2693–2700CrossRefGoogle Scholar
  107. Wang QW, Lin M, Zeng M (2008a) Effect of blocked core-tube diameter on heat transfer performance of internally finned tubes. Heat Transf Eng 29(1):107–115CrossRefGoogle Scholar
  108. Wang QW, Lin M, Zeng M, Tian L (2008b) Computational analysis of heat transfer and pressure drop performance for internally finned tubes with three different longitudinal wavy fins. Heat Mass Transf 45:147–156CrossRefGoogle Scholar
  109. Wang QW, Lin M, Zeng M, Tian L (2008c) Investigation of turbulent flow and heat transfer in periodic wavy channel of internally finned tube with blocked core tube. ASME J Heat Transf 130(6). Article No.: 061801CrossRefGoogle Scholar
  110. Webb RL, Kim NY (2005) Principles of enhanced heat transfer. Taylor & Francis, New YorkGoogle Scholar
  111. Wilkins JE Jr (1960) Minimizing the mass of thin radiating fins. J Aerospace Sci 27:145–146Google Scholar
  112. Xi GN, Torikoshi K (1996) Computation and visualizationof flow and heat transfer in finned tube heat exchangers. In: International symposium on heat transfer, Tsinhua University, Beijing China (7.10–11.10), pp 632–637Google Scholar
  113. Yan W-M, Sheen P-J (2000) Heat transfer and friction characteristics of finand-tube heat exchangers. Int J Heat Mass Transf 43:1651–1659CrossRefGoogle Scholar
  114. Yang YT, Peng HS (2009) Investigation of planted pin fins for heat transfer enhancement in plate fin heat sink. Microelectron Reliab 49(2):163–169CrossRefGoogle Scholar
  115. Yang Y, Li Y, Si B, Zheng J (2017) Heat transfer performances of cryogenic fluids in offset strip fin-channels considering the effect of fin efficiency. Int J Heat Mass Transf 114:1114–1125CrossRefGoogle Scholar
  116. Yazicioğlu B, Yüncü H (2007) Optimum fin spacing of rectangular fins on a vertical base in free convection heat transfer. Heat Mass Transf 44(1):11–21CrossRefGoogle Scholar
  117. Youn B (1997) Internal report. Samsung Electric CorpGoogle Scholar
  118. Yu B, Tao WQ (2004) Pressure drop and heat transfer characteristics of turbulent flow in annular tubes with internal wave-like longitudinal fins. Heat Mass Transf 40:643–651CrossRefGoogle Scholar
  119. Yu B, Nie JH, Wang QW, Tao WQ (1999) Experimental study on the pressure drop and heat transfer characteristics of tubes with internal wave-like longitudinal fins. Heat Mass Transf 35:65–73CrossRefGoogle Scholar
  120. Yu X, Feng J, Feng Q, Wang Q (2005) Development of a plate-pin fin heat sink and its performance comparisons with a plate fin heat sink. Appl Therm Eng 25(2):173–182CrossRefGoogle Scholar
  121. Zaretabar M, Asadian H, Ganji D (2018) Numerical simulation of heat sink cooling in the mainboard chip of a computer with temperature dependent thermal conductivity. Appl Therm Eng 130:1450–1459CrossRefGoogle Scholar
  122. Zeitoun O, Hegazy AS (2004) Heat transfer for laminar flow in internally finned pipes with different fin heights and uniform wall temperature. Heat Mass Transf 40:253–259CrossRefGoogle Scholar
  123. Zhang J (2005) Numerical simulations of steady low-Reynolds-number flows and enhanced heat transfer in wavy plate-fin passages. Ph.D. thesis, University of CincinnatiGoogle Scholar
  124. Zhang J, Muley A, Borghess JB, Manglik RM (2003) Computational and experimental study of enhanced laminar flow heat transfer in three dimensional sinusoidal wavy-plate-fin channels. In: Proceedings of the 2003 ASME summer heat transfer conference, Nevada, USA, HT2003-47148Google Scholar
  125. Zhang J, Kundu J, Manglik RM (2004) Effect of fin waviness and spacing on the lateral vortex structure and laminar heat transfer in wavy-plate-fin cores. Int J Heat Mass Trans 47:1719–1730CrossRefGoogle Scholar
  126. Zukauskas A (1972) Heat transfer from tubes in crossflow. In: Hartnett JP, Irvine TF (eds) Advances in heat transfer, vol 8. Academic Press, New York, pp 93–160Google Scholar

Copyright information

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Sujoy Kumar Saha
    • 1
  • Hrishiraj Ranjan
    • 1
  • Madhu Sruthi Emani
    • 1
  • Anand Kumar Bharti
    • 1
  1. 1.Mechanical Engineering DepartmentIndian Institute of Engineering, Science and Technology, ShibpurHowrahIndia

Personalised recommendations