Skip to main content
SpringerLink
Log in

Thermodynamic analysis and optimization of air-cooled heat exchangers

  • Original
  • Published:
Heat and Mass Transfer Aims and scope Submit manuscript

Abstract

In the present study, a thermodynamic second-law analysis was performed to investigate the effects of different geometry and flow parameters on the air-cooled heat exchanger performance. For this purpose, the entropy generation due to heat transfer and pressure loss of internal and external flows of the air-cooled heat exchanger was calculated; and it was observed that the total entropy generation has a minimum at special tube-side Reynolds number. Also, it was seen that the increasing of the tube-side Reynolds number resulted in the rise of the irreversibility of the air-cooled heat exchanger. The results also showed when air-side Reynolds number decreased, the entropy generation rate of the external flow reduced. Finally, based on the computed results, a new correlation was developed to predict the optimum Reynolds number of the tube-side fluid flow.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Abbreviations

A a :

Effective air-side area (m2)

A c :

Free flow area through heat exchanger (m2)

C1…C6 :

Constant of Eq. 43

c p :

Specific heat capacity (J/kg K)

d f :

Fin diameter (m)

d i :

Tube inside diameter (m)

d o :

Tube outside diameter (m)

d r :

Fin root diameter (m)

E( ):

Error function

e x :

Exergy (J)

f :

Friction factor

f D :

Friction factor

G c :

Mass velocity (kg/s m2)

h :

Specific enthalpy (J/kg)

\( \bar{h} \) :

Average heat transfer coefficient (W/m2 K)

k :

Fluid conductivity (W/m K)

L :

Length of finned tube (m)

\( \dot{m} \) :

Mass flow rate (kg/s)

Nu :

Nusselt number

N S :

Entropy generation number

N SΔT :

Heat transfer entropy generation number

N SΔP :

Pressure loss entropy generation number

n r :

Number of tube rows

n tr :

Number of tubes per row

P :

Pressure (Pa)

Pr :

Prandtl number

P d :

Parameter used in Eq. 34, = ((P t /2)2 + P 2 L )0.5

P f :

Fin pitch (m)

P L :

Longitudinal pitch (m)

P t :

Transversal tube pitch (m)

\( \dot{Q} \) :

Heat transfer rate (W)

q ′ :

Heat transfer rate per unit length (W/m)

Re :

Reynolds number

r i :

Tube inside radius (m)

\( \dot{S}_{gen} \) :

Entropy generation rate (W/K)

\( \dot{S}_{gen}^{\prime } \) :

Entropy generation rate per unit length (W/K m)

s :

Specific entropy (J/kg K)

T :

Bulk temperature of process fluid (K)

T 0 :

Ambient temperature (K)

t :

Bulk temperature of air (K)

t f :

Fin thickness (mean) (m)

V :

Volume (m3)

\( \overline{V} \) :

Average velocity (m/s)

β 1 :

Dimensionless parameter, \( = {\frac{{t_{2} kdA_{a} }}{{\delta Qd_{r} }}} \)

β 2 :

Dimensionless parameter, \( = {\frac{{\Updelta \dot{m}_{a} \mu \ln ({{t_{2} } \mathord{\left/ {\vphantom {{t_{2} } {t_{1} }}} \right. \kern-\nulldelimiterspace} {t_{1} }})}}{{\delta Qd_{r}^{2} \rho^{2} n_{r} \omega }}} \)

\( \varepsilon_{R} \) :

Rational effectiveness, \( = 1- {\frac{{T_{0} \dot{S}_{gen} }}{{\dot{m}_{H} (e_{x,in} - e_{x,out} )_{H} }}} \)

\( \varepsilon \) :

Heat exchanger effectiveness

\( \phi \) :

Dimensionless parameter, \( = {\frac{{Ns_{\Updelta P} }}{{Ns_{\Updelta T} }}} \)

η 1 :

Dimensionless parameter, = πkT 2/q ′

η 2 :

Dimensionless parameter, \( = 3 2\dot{m}^{ 2} \rho^{ 2} q^{\prime}/\mu^{ 5} \pi^{ 3} \ln ({{T_{1} } \mathord{\left/ {\vphantom {{T_{1} } {T_{2} }}} \right. \kern-\nulldelimiterspace} {T_{2} }}) \)

η w−s :

Witte and Shamsunder efficiency, \( = 1 - {{T_{0} \dot{S}_{gen} } \mathord{\left/ {\vphantom {{T_{0} \dot{S}_{gen} } {\dot{Q}}}} \right. \kern-\nulldelimiterspace} {\dot{Q}}} \)

ξ 1 :

Dimensionless parameter, = (T 1 − T 2)/T 1

ξ 2 :

Dimensionless parameter, = (t 2 − t 1)/t 1 ω

μ :

Viscosity (kg/m s)

ρ :

Density (kg/m3)

τ :

Dimensionless parameter, = (T p,in − T 0)/T 0

ω :

Thermal capacity ratio, \( = {{(\dot{m}c_{p} )_{\max } } \mathord{\left/ {\vphantom {{(\dot{m}c_{p} )_{\max } } {(\dot{m}c_{p} )_{\min } }}} \right. \kern-\nulldelimiterspace} {(\dot{m}c_{p} )_{\min } }} \)

a:

Air side

C:

Cold stream

i:

Tube side

in:

Inlet

H:

Hot stream

o:

Air side

opt:

Optimal

out:

Outlet

Pi:

Process fluid inlet

1:

Inlet

2:

Outlet

References

  1. Bejan A (1996) Entropy generation minimization. CRC Press, Boca Raton

    MATH  Google Scholar 

  2. Bejan A (1982) Entropy generation through heat and fluid flow. Wiley, New York

    Google Scholar 

  3. Nag P, Naresh K (1989) Second law optimization of convection heat transfer through a duct with constant heat flux. Int J Energy Res 13:537–543

    Article  Google Scholar 

  4. Sahin Z (1998) Irreversibilities in various duct geometries with constant wall heat flux and laminar flow. Energy 23(6):465–473

    Article  Google Scholar 

  5. Sahin Z (2000) Entropy generation in turbulent liquid flow through a smooth duct subjected to constant wall temperature. Int J Heat Mass Transf 43:1469–1478

    Article  MATH  Google Scholar 

  6. Shuja SZ (2002) Optimal fin geometry based on exergoeconomic analysis for a pin-fin array with application to electronics cooling. Exergy Int J 2(4):248–258

    Article  Google Scholar 

  7. Ko TH, Ting K (2005) Entropy generation and thermodynamic optimization of fully developed laminar convection in a helical coil. Int Commun Heat Mass Transf 32:214–223

    Article  Google Scholar 

  8. Ko TH, Ting K (2006) Optimal Reynolds number for the fully developed laminar forced convection in a helical coiled tube. Energy 31:2142–2152

    Article  Google Scholar 

  9. Ko TH (2006) Thermodynamic analysis of optimal curvature ratio for fully developed laminar forced convection in a helical coiled tube with uniform heat flux. Int J Therm Sci 45:729–737

    Article  Google Scholar 

  10. Shokouhmand H, Salimpour MR (2007) Entropy generation analysis of fully developed laminar forced convection in a helical tube with uniform wall temperature. Heat Mass Transf 44(2):213–220

    Article  Google Scholar 

  11. Shokouhmand H, Salimpour MR (2007) Optimal Reynolds number of laminar forced convection in a helical tube subjected to uniform wall temperature. Int Commun Heat Mass Transf 34:753–761

    Article  Google Scholar 

  12. Shokouhmand H, Jam F, Salimpour MR (2009) Optimal porosity in an air heater conduit filled with a porous matrix. Heat Transf Eng 30(5):375–382

    Article  Google Scholar 

  13. Shah RK (1975) Thermal entry length solutions for the circular tube and parallel plates. In: Proceedings of 3rd national heat and mass transfer conference, Indian Institute of Technology, Bombay 1(HMT):11–75

  14. Gnielinski V (1975) Neue Gleichungen für den Wärme- und den Stoffübergang in turbulent durchströmten Rohren und Kanälen. Forschung im Ingenieurwesen 41(1):8–16

    Article  Google Scholar 

  15. Briggs DE, Young EH (1963) Convective heat transfer and pressure drop of air flowing across triangular pitch banks of finned tubes. Chem Eng Progr Symp Ser 59(41):1–10

    Google Scholar 

  16. Ward DJ, Young EH (1959) Heat transfer and pressure drop of air in forced convection across triangular pitch banks of finned tubes. Chem Eng Proger Symp Ser 55(29):37–44

    Google Scholar 

  17. Gianolio E, Cuti F (1981) Heat transfer coefficients and pressure drops for air coolers with different numbers of rows under induced and forced draft. Heat Transf Eng 3(1):38–47

    Article  Google Scholar 

  18. Robinson KK, Briggs DE (1966) Pressure drop of air flowing across triangular pitch banks of finned tubes. Chem Eng Progr Symp Ser 62(64):177–184

    Google Scholar 

  19. Bejan A (1997) Advanced engineering thermodynamics. Wiley, New York

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Isfahan University of Technology, 84156-83111, Isfahan, Iran

    Mohammad Reza Salimpour & Zabihollah Bahrami

Authors
  1. Mohammad Reza Salimpour
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zabihollah Bahrami
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohammad Reza Salimpour.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Salimpour, M.R., Bahrami, Z. Thermodynamic analysis and optimization of air-cooled heat exchangers. Heat Mass Transfer 47, 35–44 (2011). https://doi.org/10.1007/s00231-010-0672-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00231-010-0672-9

Keywords

Search

Navigation