Design of spiral heat exchanger from economic and thermal point of view using a tuned wind-driven optimizer

  • Emerson Hochsteiner de Vasconcelos Segundo
  • Viviana Cocco Mariani
  • Leandro dos Santos Coelho
Technical Paper


This paper presents an optimization of spiral heat exchangers by wind-driven optimization and a novel variant of this algorithm by the insertion of a statistic distribution to self-adapting of the evolution parameters of the algorithm. Spiral heat exchangers are the ideal type for cooling slurries and fluids that presents high viscosity and is very common in food and petrochemical industries. The variables used for the optimization were the spacing channels for hot and cold streams, the length, the width and the thickness of the heat exchanger. Two case studies were presented where the minimization of the cost and the maximization of the overall heat transfer coefficient were implemented. Reductions about 4.46 and 23% were obtained for the cost and increases about 18.8 and 16.4% were reached for the overall heat transfer coefficient for each case study in comparison to previous works. The proposed technique reached better results in all the simulations, in some cases with GA, but performed better accuracy among all the simulations.


Spiral heat exchanger Wind-driven optimization Minimization of total cost Maximization of overall heat transfer coefficient Optimization 


List of symbols


Numerical constant (€)


Numerical constant (€ m−2)


Heat exchanger surface area (m2)


Width of spiral heat exchanger (m)


Core diameter (m)


Energy cost (€ W−1 h−1)


Capital investment (€)


Annual operating cost (€ year−1)


Total discounted operating cost (€)


Specific heat (J kg−1 K−1)


Total cost (€)


Hydraulic diameter (m)


Spiral outer diameter (m)


Amount of hours of work (h year−1)


Convective coefficient (W m−2K−1)


Annual discount rate (%)


Thermal conductivity (W m−1K−1)


Thermal conductivity of the wall (W m−1K−1)


Tube of spiral heat exchanger (m)

\(\Delta T_{\text{LM}}\)

Logarithmic mean temperature difference (K)


Mass flow rate (kg s−1)


Nusselt number


Equipment life (yr)


Prandtl number


Heat duty (W)


Spiral mean diameter (m)

\(R_{ \hbox{min} }\)

Spiral minimum diameter (m)

\(R_{ \hbox{max} }\)

Spiral maximum diameter (m)


Reynolds number


Fouling resistance (m2 K W−1)


Channel spacing (m)


Temperature (K)


Overall heat transfer coefficient (W m−2 K−1)


Fluid velocity (m s−1)

\(\Delta P\)

Pressure drop (kPa)

\(\Delta P_{ \hbox{max} }\)

Maximum pressure drop (kPa)

Greek letters


Numerical constants


Viscosity (Pa s)


Consistency viscosity (cP)


Yield stress (Pa)


Density (kg m−3)


Pumping efficiency



Cold stream


Hot stream







The authors would like to thank the National Council of Scientific and Technologic Development of Brazil-CNPq (projects: 303906/2015-4-PQ and 303908/2015-7-PQ) and Paraná Association of Culture-APC for the scholarship financial support of this work.


  1. 1.
    Turgut OE, Çoban MT (2017) Thermal design of spiral heat exchangers and heat pipes through global best algorithm. Heat Mass Transfer 53:899–916CrossRefGoogle Scholar
  2. 2.
    Vahdat A, Amidpour M (2011) Economic optimization of shell-and-tube heat exchanger based on constructal theory. Energy 36:1087–1096CrossRefGoogle Scholar
  3. 3.
    Wilhelmson B (2005) Consider spiral heat exchangers for fouling application. Hydrocarb Process 84:81–83Google Scholar
  4. 4.
    Trom L (1995) Use spiral plate exchangers for various applications. Hydrocarb Process 74:73–81Google Scholar
  5. 5.
    Bes T, Roetzel W (1992) Distribution of heat flux density in spiral heat exchangers. Int J Heat Mass Transf 35:1331–1347CrossRefGoogle Scholar
  6. 6.
    Egner MW, Burmeister LC (2005) Heat transfer for laminar flow in spiral ducts of rectangular cross section. J Heat Transfer 127:352–356CrossRefGoogle Scholar
  7. 7.
    Wu SY, Yuan XF, Li YR, Xiao L (2007) Exergy transfer effectiveness on heat exchanger for finite pressure drop. Energy 32:2110–2120CrossRefGoogle Scholar
  8. 8.
    Picon-Núnez M, Canizalez-Davalos L, Martínez-Rodríguez G, Polley GT (2007) Shortcut design approach for spiral heat exchangers. Food Bioprod Process 85:322–327CrossRefGoogle Scholar
  9. 9.
    Picon-Núnez M, Canizalez-Davalos L, Medina-Flores JM (2009) Alternative sizing methodology for compact heat exchangers of spiral type. Heat Transfer Eng 30:744–750CrossRefGoogle Scholar
  10. 10.
    Naphon P, Wongwises S (2002) An experimental study on the in-tube convective heat transfer coefficient in a spiral coil heat exchanger. Int Commun Heat Mass Transfer 29:797–809CrossRefGoogle Scholar
  11. 11.
    Caputo AC, Pelagagge PM, Salini P (2008) Heat exchanger design based on economic optimization. Appl Therm Eng 28:1151–1159CrossRefGoogle Scholar
  12. 12.
    Bidabadi M, Sadaghiani AK, Vadhat Azad A (2013) Spiral heat exchanger optimization using genetic algorithm. Sci Iran B 20:1445–1454Google Scholar
  13. 13.
    Abdous MA, Saffari H, Avval HB, Khoshzat M (2015) Investigation of entropy generation in a helically coiled tube in flow boiling condition under a constant heat flux. Int J Refrig 60:217–233CrossRefGoogle Scholar
  14. 14.
    Nabil BH, Bechir C, Slimane G (2014) Global modeling of heat and mass transfers in spiral tubular absorver of a water-lithium bromide absorption chiller. Int J Refrig 38:323–332CrossRefGoogle Scholar
  15. 15.
    Eldeeb R, Aute V, Radermacher R (2016) A survey of correlations for heat transfer and pressure drop for evaporation and condensation in plate heat exchangers. Int J Refrig 65:12–26CrossRefGoogle Scholar
  16. 16.
    Selbas R, Kizilkan O, Reppich M (2006) A new design approach for shell-and-tube heat exchangers using genetic algorithms from economic point of view. Chem Eng Process 45:268–275CrossRefGoogle Scholar
  17. 17.
    Mishra M, Das PK, Sarangi S (2009) Second law based optimisation of crossflow plate-fin heat exchanger design using genetic algorithm. Appl Therm Eng 29:2983–2989CrossRefGoogle Scholar
  18. 18.
    Hajabdollahi H, Ahmadi P, Dincer I (2011) Thermoeconomic optimization of a shell-and-tube condenser using both genetic algorithm and particle swarm. Int J Refrig 34:1066–1076CrossRefGoogle Scholar
  19. 19.
    Amini M, Bazargan M (2014) Two objective optimization in shell-and-tube heat exchangers using genetic algorithm. Appl Therm Eng 69:278–285CrossRefGoogle Scholar
  20. 20.
    Babu BV, Munawar SA (2007) Differential evolution strategies for optimal design of shell-and-tube heat exchangers. Chem Eng Sci 62:3720–3739CrossRefGoogle Scholar
  21. 21.
    Vasconcelos Segundo EH, Amoroso AL, Mariani VC, Coelho LS (2017) Economic optimization design for shell-and-tube heat exchangers by a Tsallis differential evolution. Appl Therm Eng 111:143–151CrossRefGoogle Scholar
  22. 22.
    Vasconcelos Segundo EH, Amoroso AL, Mariani VC, Coelho LS (2017) Thermodynamic optimization design of plate-fin heat exchangers by Tsallis JADE. Int J Therm Sci 113:136–144CrossRefGoogle Scholar
  23. 23.
    Patel VK, Rao RV (2010) Design optimization of shell-and-tube heat exchanger using particle swarm optimization technique. Appl Therm Eng 30:1417–1425CrossRefGoogle Scholar
  24. 24.
    Rao RV, Patel VK (2010) Thermodynamic optimization of cross flow plate-fin heat exchangers using a particle swarm optimization. Int J Therm Sci 49:1712–1721CrossRefGoogle Scholar
  25. 25.
    Moretta AA (2010) Spiral plate heat exchangers: sizing units for cooling non-newtonian slurries. Chem Eng 117:44–49Google Scholar
  26. 26.
    Minton PE (1970) Designing spiral plate heat exchangers. Chem Eng 77:103–112Google Scholar
  27. 27.
    Morimoto E, Hotta K (1988) Study of the geometric structure and heat transfer characteristics of a spiral plate heat exchanger. Heat Transfer Japanese Res 17:53–71Google Scholar
  28. 28.
    Perry JH (1997) Chemical Engineers Handbook, 7th edn. McGraw-Hill, New YorkGoogle Scholar
  29. 29.
    Holland JH (1992) Adaptation in natural and artificial systems, 2nd edn. MIT Press, CambridgeGoogle Scholar
  30. 30.
    McClorke DS, Bryden KM, Carmichael CG (2003) A new methodology for evolutionary optimization of energy systems. Comput Methods Appl Mech Eng 192:5021–5036CrossRefzbMATHGoogle Scholar
  31. 31.
    Ponce-Ortega JM, Serna-González M, Jiménez-Gutiérrez A (2008) Synthesis of multipass heat exchangers networks using genetic algorithms. Comput Chem Eng 32:2320–2332CrossRefGoogle Scholar
  32. 32.
    Harris SD, Elliott L, Ingham DB, Pourkahanian M, Wilson CW (2000) The optimisation of reaction rate parameters for chemical kinetic modelling of combustion using genetic algorithms. Comput Methods Appl Mech Eng 190:1065–1090CrossRefzbMATHGoogle Scholar
  33. 33.
    Gholizadeh S, Salajegheh E (2009) Optimal design of structures subjected to time history loading by swarm intelligence and an advanced metamodel. Comput Methods Appl Mech Eng 198:2936–2949CrossRefzbMATHGoogle Scholar
  34. 34.
    Shokrian M, High KA (2014) Application of a multi objective multi-leader swarm optimization algorithm on NLP and MINLP problems. Comput Chem Eng 60:57–75CrossRefGoogle Scholar
  35. 35.
    Kennedy J, Eberhart R (1995) Particle Swarm Optimization. In: Proceedings of the IEEE International Conference on Neural Networks, Perth, Australia, 1942–1948Google Scholar
  36. 36.
    Bayraktar Z, Komurcu M, Werner DH (2010) Wind driven optimization (WDO): A novel nature-inspired optimization algorithm and its application to electromagnetic. In: Proceedings of the IEEE International Symposium on Antennas and Propagation and CNC/USNC/URSI Radio Science Meeting, Toronto, Canada, 1-4Google Scholar
  37. 37.
    Bayraktar Z, Komurcu M, Bossard JA, Werner DH (2013) The wind driven optimization technique and its application in electromagnetics. IEEE Trans Antennas Propag 61:2745–2757MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    Stull RB (1999) Meteorology for scientists and engineers, 2nd edn. Brooks/Cole, Belmont, USAGoogle Scholar
  39. 39.
    Tsallis C (1988) Possible generalization of Boltzmann-Gibbs statistics. J Stat Phys 52:479–487MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Boulesnane A, Meshoul S (2014) A new multi-region modified wind driven optimization algorithm with collision avoidance for dynamic environments. In: Tan Y, Shi Y, Coello CAC (eds) Advances in swarm intelligence. Lecture notes in computer science, vol 8795. Springer, Cham, pp 412–421Google Scholar
  41. 41.
    Bao Z, Zhou Y, Li L, Ma M (2015) A hybrid global optimization algorithm based on wind driven optimization and differential evolution. Math Probl Eng 2015:1–20Google Scholar
  42. 42.
    Bayraktar Z, Komurcu M (2015) Adaptive Wind Driven Optimization. In: Proceedings of the 9th EAI International Conference on Bio-Inspired Information and Communications Technologies, New York, USA, pp 124–127Google Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  • Emerson Hochsteiner de Vasconcelos Segundo
    • 1
  • Viviana Cocco Mariani
    • 1
    • 3
  • Leandro dos Santos Coelho
    • 2
    • 3
  1. 1.Mechanical Engineering Graduate Program (PPGEM)Pontifical Catholic University of Paraná (PUCPR)CuritibaBrazil
  2. 2.Industrial and Systems Engineering Graduate Program (PPGEPS)Pontifical Catholic University of Paraná (PUCPR)CuritibaBrazil
  3. 3.Department of Electrical EngineeringFederal University of Paraná (UFPR)CuritibaBrazil

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