Skip to main content
SpringerLink
Log in

Saturated flow boiling heat transfer correlation for carbon dioxide for horizontal smooth tubes

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

Abstract

Literature comprises fewer studies about flow boiling modelling of refrigerants for in tube flows. In addition, researches on two phase flow heat transfer are based on the mathematical models which were derived in a very limited operational condition and correlated for their own measurements. In this study, a new flow boiling model including the superposed effects of nucleate and convective boiling mechanisms is proposed through the minimization of the cumulative error between the proposed mathematical model and actual data by means of artificial cooperative search algorithm and applied to the database of R-744 (carbon dioxide), available from different studies in the literature. Predictions obtained from the proposed model have been compared with those of retained from the literature correlations developed for flow boiling in tubes. The comparison results indicate that the new model outperforms the literature correlations in terms of prediction accuracy. Results of the comparisons reveal that the proposed flow boiling mathematical model has a mean absolute relative error of 14.6% and predicts 76.7% of the experimental data within ±20.0%.

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

Similar content being viewed by others

Abbreviations

A:

Empirical constant

Bo:

Boiling number, \(Bo = \frac{q}{{Gh_{fg} }}\)

Bd:

Bond number, \(Bd = \frac{{g(\rho_{l} - \rho_{g} )D_{h}^{2} }}{\sigma }\)

Co:

Convection number, \(Co = \left( {\frac{1 - x}{x}} \right)^{0.8} \left( {\frac{{\rho_{g} }}{{\rho_{l} }}} \right)^{0.5}\)

Dh :

Hydraulic tube diameter (mm)

f :

Friction factor

F:

Convective two phase multiplier

Fr:

Froude number, \(Fr = \frac{{G^{2} }}{{gD_{h} \rho^{2} }}\)

Ff :

Fluid-specific parameter used in Kandlikar correlation

g:

Gravitational acceleration (m/s2)

G:

Mass flux (kg/m2 s)

h:

Heat transfer coefficient (W/m2 K)

hfg :

Latent heat of the vaporization (kJ/kg)

k:

Thermal conductivity (W/m K)

K:

Empirical constant

M:

Molar mass (kg/kmol)

MARE:

Mean absolute relative error

MRE:

Mean relative error

N:

Number of the experimental data

pr :

Reduced pressure, \(p_{r} = \frac{{p_{sat} }}{{p_{crit} }}\)

Pr:

Prandtl number, \(\Pr = \frac{{\mu C_{p} }}{k}\)

q:

Heat flux (W/m2)

Rel :

Liquid Reynold number, \(\text{Re}_{l} = \frac{{G(1 - x)D_{h} }}{{\mu_{l} }}\)

Relo :

Liquid only Reynold number, \(\text{Re}_{lo} = \frac{{GD_{h} }}{{\mu_{l} }}\)

S:

Supression factor

T:

Temperature (K/°C)

x :

Vapor quality

X tt :

Martinelli parameter

We:

Weber number, \(We = \frac{{G^{2} g}}{\rho \sigma }\)

ɛ:

Surface roughness (μm)

μ:

Dynamic viscosity (Pa s)

ρ:

Density (kg/m3)

σ:

Surface tension (Pa/m)

cb:

Convective boiling

crit:

Critical

exp:

Experimental

g:

Gas

l:

Liquid

lo:

Liquid only

nb:

Nucleate boiling

pred:

Predicted

sat:

Saturated

tp:

Two phase

References

  1. Bertsch SS, Groll EA, Garimella SV (2008) Review and comparative analysis of studies on saturated flow boiling in small channels. Nanosc Microsc Therm 12:187–227

    Article  Google Scholar 

  2. Saitoh S, Daiguji H, Hihara E (2005) Effect of tube diameter on the boiling heat transfer of R134a in horizontal small diameter tubes. Int J Heat Mass Transf 38:4973–4984

    Article  MATH  Google Scholar 

  3. da Silva Lima RJ, Quiben JM, Thome JR (2009) Flow boiling in horizontal smooth tubes: new heat transfer results for R-134a at three saturation temperatures. Appl Therm Eng 29:1289–1298

    Article  Google Scholar 

  4. Docoulombier M, Colasson S, Bonjour J, Haberschill P (2009) Carbon dioxide flow boiling in a single microchannel—part II: heat transfer. Exp Therm Fluid Sci 35:597–611

    Article  Google Scholar 

  5. Grauso S, Mastrullo R, Mauro AW, Thome JR, Vanoli GP (2013) Flow pattern map, heat transfer and pressure drops during evaporation of R-1234ze(E) and R134a in a horizontal, circular smooth tube: experiments and assessment of predictive methods. Int J Refrig 36:478–498

    Article  Google Scholar 

  6. Tran TN, Wambsganss MW, France DM (1996) Small circular- and rectangular-channel boiling with two refrigerants. Int J Multiph Flow 22:485–498

    Article  MATH  Google Scholar 

  7. Hamdar M, Zoughaib A, Clodic D (2010) Flow boiling heat transfer and pressure drop of pure HFC-152a in a horizontal mini-channel. Int J Refrig 33:566–577

    Article  Google Scholar 

  8. Anwar Z (2013) Evaporative heat transfer with R134a in a vertical minichannel. Pak J Eng Appl Sci 13:101–109

    Google Scholar 

  9. Saisorn S, Kaew-On J, Wongwises S (2011) Two phase flow of R-134a refrigerant during flow boiling through a horizontal circular mini-channel. Exp Therm Fluid Sci 35:887–895

    Article  Google Scholar 

  10. Lin S, Kew PA, Cornwell K (2001) Two-phase heat transfer to a refrigerant in a 1 mm diameter tube. Int J Refrig 24:51–56

    Article  Google Scholar 

  11. Agostini B, Bontemps A (2005) Vertical flow boiling of refrigerant R134a in small channels. Int J Heat Fluid Flow 26:296–306

    Article  Google Scholar 

  12. Shiferaw D, Huo X, Karayiannis TG, Kenning DBR (2007) Examination of heat transfer correlations and a model for flow boiling of R134a in small diameter tubes. Int J Heat Mass Transf 50:5177–5193

    Article  MATH  Google Scholar 

  13. Collier JG, Thome JR (1994) Convective boiling and condensation. Clarendon Press, Oxford

    Google Scholar 

  14. Ong CL, Thome JR (2011) Macro-to-microchannel transition in two phase flow: part 2—flow boiling heat transfer and critical heat flux. Exp Therm Fluid Sci 35:873–886

    Article  Google Scholar 

  15. Fang XD, Zhou Z, Li D (2013) Review of correlations of flow boiling heat transfer coefficients for carbon dioxide. Int J Refrig 36:2017–2039

    Article  Google Scholar 

  16. Thome JR, Ribatski G (2005) State-of-the-art of two phase flow and flow boiling heat transfer and pressure drop of CO2 in nacro- and micro-channels. Int J Refrig 28:1149–1168

    Article  Google Scholar 

  17. Mastrullo R, Mauro AW, Rosato A, Vanoli GP (2009) Carbon dioxide local heat transfer coefficients during flow boiling in a horizontal circular smooth tube. Int J Heat Mass Transf 52:4184–4194

    Article  MATH  Google Scholar 

  18. Mastrullo R, Mauro AW, Rosato A, Vanoli GP (2010) Carbon dioxide heat transfer coefficients and pressure drop during flow boiling: assessment of predictive methods. Int J Refrig 33:1068–1085

    Article  MATH  Google Scholar 

  19. Jung DS, McLinden M, Radermacher R, Didion D (1989) A study of flow boiling heat transfer with refrigerant mixtures. Int J Heat Mass Transf 32:1751–1764

    Article  Google Scholar 

  20. Cheng L, Ribatski G, Quiben JM, Thome JR (2008) New prediction methods for CO2 evaporation inside tubes: part I—a two phase flow pattern map and a flow pattern based phenomenological model for two phase flow frictional pressure drops. Int J Heat Mass Transf 51:111–124

    Article  MATH  Google Scholar 

  21. Cheng L, Ribatski G, Thome JR (2008) New prediction methods for CO2 evaporation inside tubes: part—II an updated general flow boiling heat transfer model based on flow patterns. Int J Heat Mass Transf 51:125–135

    Article  MATH  Google Scholar 

  22. Park CY, Hrnjak PS (2007) CO2 and R410A flow boiling heat transfer, pressure drop, and flow pattern at low temperatures in a horizontal smooth tube. Int J Refrig 30:166–178

    Article  Google Scholar 

  23. Wattelet JP, Chato JC, Souza AL, Christoffersen BR (1994) Evaporative characteristics of R-12, R-134a, and mixture at low mass fluxes. ASHRAE Trans 94:603–615

    Google Scholar 

  24. Liu Z, Winterton RHS (1991) A general correlation for saturated and subcooled flow boiling in tubes and annuli based on a nucleate pool boiling equation. Int J Heat Mass Transf 34:2759–2766

    Article  Google Scholar 

  25. Shah MM (1982) Chart correlation for saturated boiling heat transfer: equations and further study. ASHRAE Trans 88:185–196

    Google Scholar 

  26. Gungor KE, Winterton RHS (1986) A general correlation for flow boiling in tubes and annuli. Int J Heat Mass Transf 29:351–358

    Article  MATH  Google Scholar 

  27. Gungor KE, Winterton RHS (1987) Simplified general correlation for saturated flow boiling and comparison with data. Chem Eng Res Des 65:148–156

    Google Scholar 

  28. Thome JR, El-Hajal J (2004) Flow coiling heat transfer to carbon dioxide: general prediction method. Int J Refrig 28:294–301

    Article  Google Scholar 

  29. Yoon SH, Cho ES, Hwang YW, Kim MS, Min K, Kim Y (2004) Characteristics of evaporative heat transfer and pressure drop of carbon dioxide and correlation development. Int J Refrig 27:111–119

    Article  Google Scholar 

  30. Choi KI, Pamitran AS, Oh JT (2007) Two-phase flow heat transfer of CO2 vaporization in smooth horizontal minichannels. Int J Refrig 20:767–777

    Article  Google Scholar 

  31. Fang XD (2013) A new correlation of flow boiling heat transfer coefficients for carbon dioxide. Int J Heat Mass Transf 64:802–807

    Article  Google Scholar 

  32. Shah MM (2014) Evaluation of correlations for predicting heat transfer during boiling of carbon dioxide inside channels. In: Proceedings of the 15th international heat transfer conference (IHTC-15) August 10–15, Kyoto, Japan

  33. Pettersen J (2004) Two phase flow patterns in microchannel vaporization of CO2 at near-critical pressure. Heat Transf Eng 25:52–60

    Article  Google Scholar 

  34. Mastrullo R, Mauro AW, Thome JR, Toto D, Vanoli GP (2012) Flow pattern maps for convective boiling of CO2 and R410A in a horizontal smooth tube: experiments and new correlations analyzing the effect of the reduced pressure. Int J Heat Mass Transf 55:1519–1528

    Article  Google Scholar 

  35. Zhao X, Bansal P (2009) Experimental investigation on flow boiling heat transfer of CO2 at low temperatures. Heat Transf Eng 30:2–11

    Article  Google Scholar 

  36. Zhao X, Bansal P (2010) Subcooled boiling heat transfer of CO2 in a horizontal tube at low temperatures. Heat Transf Eng 31:1015–1022

    Article  Google Scholar 

  37. Pamitran AS, Choi K-I, Oh J-T (2011) Evaporation heat transfer coefficient in single circular small tubes for flow natural refrigerants of C3H8, NH3, and CO2. Int J Multiph Flow 37:794–801

    Article  Google Scholar 

  38. Tanaka S, Daiguji H, Takemuka F, Hihara E (2001) Boiling heat transfer of carbon dioxide in horizontal tubes. In: Proceedings of the 38th national heat transfer symposium of Japan, Saitama, Japan, pp 899–900

  39. Wang J, Ogasawara S, Hihara E (2003) Boiling heat transfer and air coil evaporator of carbon dioxide. In: Proceedings of the 21st IIR international congress of refrigeration, 17–22 August, Washington, DC, USA

  40. Choi KI, Pamitran AS, Oh CY, Oh JT (2007) Boiling heat transfer of R-22, R134a, and CO2 in horizontal mini-channels. Int J Refrig 30:1336–1346

    Article  Google Scholar 

  41. Oh JT, Pamitran AS, Choi KI, Hrnjak P (2011) Experimental investigation on two phase flow boiling heat transfer of five refrigerants in horizontal small tubes of 0.5, 1.5 and 3.0 mm inner diameters. Int J Heat Mass Transf 54:2080–2088

    Article  Google Scholar 

  42. Cho JM, Kim MS (2007) Experimental studies on the evaporative heat transfer and pressure drop of CO2 in smooth and micro-fin tubes of the diameters of 5 and 9.52 mm. Int J Refrig 30:986–994

    Article  Google Scholar 

  43. Grauso S, Mastrullo R, Mauro AW, Vanoli GP (2013) Flow boiling of R410A and CO2 from low to medium reduced pressures in macro channels: experiments and assessment of prediction method. Int J Heat Mass Transf 56:107–118

    Article  Google Scholar 

  44. Kim YJ, Cho JM, Kim MS (2008) Experimental study on the evaporative heat transfer and pressure drop of CO2 flowing upward in vertical smooth and micro-fin tubes with the diameter of 5 mm. Int J Refrig 31:771–779

    Article  Google Scholar 

  45. Mastrullo R, Mauro AW, Rosato A, Vanoli GP (2009) Comparison of R744 and R134a heat transfer coefficients during flow boiling in a horizontal circular smooth tube. In: international conference on renewable energies and power quality (ICERPQ ‘09), 15–17 April, Valencia, Spain

  46. Oh HK, Son CH (2011) Flow boiling heat transfer and pressure drop characteristics of CO2 in a horizontal tube of 4.57 mm inner diameter. Appl Therm Eng 31:163–172

    Article  Google Scholar 

  47. Ono T, Gao L, Honda T (2010) Heat transfer and flow characteristics of flow boiling of CO2–oil mixtures in horizontal smooth and micro-fin tubes. Heat Transf Asian Res 39:195–207

    Google Scholar 

  48. Wu J, Koettig T, Franke CH, Helmer D, Eisel T, Haug F, Bremer J (2011) Investigation of heat transfer and pressure drop of CO2 two-phase flow in a horizontal mini-channel. Int J Heat Mass Transf 54:2154–2162

    Article  Google Scholar 

  49. Huai X, Koyama S, Zhao TS, Shinmura E, Hidehiko K, Masaki M (2004) An experimental study of flow boiling characteristics of carbon dioxide in multiport mini channel. Appl Therm Eng 24:1443–1463

    Article  Google Scholar 

  50. Yun R, Kim YC, Kim MS, Choi YD (2005) Flow boiling heat transfer of carbon dioxide in horizontal mini tubes. Int J Heat Fluid Flow 26:801–809

    Article  Google Scholar 

  51. Yun R, Kim Y, Kim MS (2005) Convective boiling heat transfer characteristics of CO2 in micro-channels. Int J Heat Mass Transf 48:235–242

    Article  Google Scholar 

  52. Kutateladze SS (1961) Boiling heat transfer. Int J Heat Mass Transf 4:3–45

    Article  Google Scholar 

  53. Kim SM, Mudawar I (2013) Universal approach to predicting saturated flow boiling heat transfer in mini/micro-channels—part II, two phase heat transfer coefficient. Int J Heat Mass Transf 64:1239–1256

    Article  Google Scholar 

  54. Steiner D, Taborek J (1992) Flow boiling heat transfer of single components in vertical tubes. Heat Transf Eng 13:43–69

    Article  Google Scholar 

  55. Oh HK, Son CH (2011) Evaporation flow pattern and heat transfer of R-22 and R134a in small diameter tubes. Heat Mass Transf 47:703–717

    Article  Google Scholar 

  56. Schrock VM, Grossmann LM (1962) Forced convection boiling in tubes. Nucl Sci Eng 12:474–481

    Google Scholar 

  57. Cooper MG (1984) Saturation nucleate pool boiling—a simple correlation. In: 1st UK national conference on heat transfer, vol 2, pp 785–793

  58. Mahmoud MM, Karayiannis TG (2013) Heat transfer correlation for flow boiling in small to micro tubes. Int J Heat Mass Transf 66:553–574

    Article  Google Scholar 

  59. Greco A (2008) Convective boiling of pure and mixed refrigerants: an experimental study of the major parameters affecting heat transfer. Int J Heat Mass Transf 51:869–909

    Article  Google Scholar 

  60. Civicioglu P (2013) Artificial cooperative search algorithm for numerical optimization problems. Inf Sci 229:58–76

    Article  MATH  Google Scholar 

  61. Karaboga D (2005) An idea based on honey bee swarm for numerical optimization. Technical report—TR06, Erciyes University, Engineering Faculty, Computer Engineering Department

  62. Yang XS (2010) A new metaheuristic bat—inspired algorithm. In: Gonzalez JR et al (eds) Nature inspired cooperative strategies for optimization (NISCO 2010), vol 284. Studies in computational intelligence. Springer, Berlin, pp 65–74

  63. Sun J, Feng B, Xu W (2004) Particle swarm optimization with particles having quantum behavior. In: Proceedings of the congress on evolutionary computation, Portland, OR, USA, pp 325–331

  64. Sun J, Xu W, Feng B (2004) A global search strategy of quantum behaved particle swarm optimization. In: IEEE conference on cybernetics and intelligent systems, pp 111–116

  65. Oftadeh R, Mahjoob MJ, Shariatpanahi M (2010) A novel metaheuristic optimization algorithm inspired by hunting of animals: hunting search. Comput Math Appl 60:2087–2098

    Article  MATH  Google Scholar 

  66. Erol OK, Eksin I (2006) A new optimization method: big bang–big crunch. Adv Eng Softw 37:106–111

    Article  Google Scholar 

  67. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of the IEEE international conference on neural networks, vol IV, pp 1942–1948

  68. Kandlikar SG (1990) A general correlation for two phase flow boiling heat transfer coefficient inside horizontal and vertical tubes. J Heat Transf Trans ASME 102:219–228

    Article  Google Scholar 

  69. Shah M (1976) New correlation for heat transfer during boiling flow through pipes. ASHRAE Trans 82:66–86

    Google Scholar 

  70. Lazarek GM, Black SH (1982) Evaporative heat transfer pressure drop and critical heat flux in small vertical tube with R-113. Int J Heat Mass Transf 25:945–960

    Article  Google Scholar 

  71. Wattelet JP (1994) Heat transfer flow regimes of refrigerants in a horizontal-tube evaporator. Ph.D. thesis, University of Illinois at Urbana–Champaign

  72. Kenning DBR, Cooper MG (1989) Saturated flow boiling of water in vertical tubes. Int J Heat Mass Transf 32:445–458

    Article  Google Scholar 

  73. Li W, Wu Z (2010) A General correlation for evaporative heat transfer in micro/mini channels. Int J Heat Mass Transf 53:1778–1787

    Article  Google Scholar 

  74. Kew PA, Cornwell K (1997) Correlations for prediction of boiling heat transfer in small-diameter channels. Appl Therm Eng 17:705–715

    Article  Google Scholar 

  75. Sun L, Mishima K (2009) An evaluation of prediction methods for saturated flow boiling heat transfer in mini-channels. Int J Heat Mass Transf 52:5323–5329

    Article  MATH  Google Scholar 

  76. Warrier GR, Dhir VK, Momoda LA (2002) Heat transfer and pressure drop in narrow rectangular channels. Exp Therm Fluid Sci 26:53–64

    Article  Google Scholar 

  77. Mahmoud MM, Karayiannis TG (2012) A statistical correlation for flow boiling heat transfer in micro tubes. In: Proceedings of the third European conference on microfluids–microfluidics, Heidelberg, Germany, pp 3–5

  78. Chisholm D (1967) A theoretical basis for the Lockhart–Martinelli correlation for two-phase flow. Int J Heat Mass Transf 10:1767–1778

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mechanical Engineering Department, Ege University, 35040, Bornova, Izmir, Turkey

    Oguz Emrah Turgut

  2. Mechanical Engineering Department, Adnan Menderes University, Aydın, Turkey

    Mustafa Asker

Authors
  1. Oguz Emrah Turgut
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mustafa Asker
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Oguz Emrah Turgut.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Turgut, O.E., Asker, M. Saturated flow boiling heat transfer correlation for carbon dioxide for horizontal smooth tubes. Heat Mass Transfer 53, 2165–2185 (2017). https://doi.org/10.1007/s00231-017-1975-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00231-017-1975-x

Keywords

Search

Navigation