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Simple power-type heat transfer correlations for turbulent pipe flow in tubes

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Abstract

  • Heat transfer in the turbulent flow of fluid in a pipe is analyzed.

  • Nusselt number as a function of the Reynolds and Prandtl number is given.

  • Power-type correlations were proposed within a wide range of Reynolds and Prandtl number.

  • Relationships for the Nusselt number compare well with experimental data.

The paper presents three power-type correlations of a simple form, which are valid for Reynolds numbers range from 3·103 ≤ Re ≤ 106, and for three different ranges of Prandtl number: 0.1 ≤ Pr ≤ 1.0, 1.0 < Pr ≤ 3.0, and 3.0 <Pr ≤ 103. Heat transfer correlations developed in the paper were compared with experimental results available in the literature. The comparisons performed in the paper confirm the good accuracy of the proposed correlations. They are also much simpler compared with the relationship of Gnielinski, which is also widely used in the heat transfer calculations.

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References

  1. S. Kakaç, H. Liu, A. Pramuanjaroenkij, Heat exchangers. Selection, rating, and thermal design. 3rd edition, CRC Press-Taylor & Francis Group, Boca Raton 2012.

    MATH  Google Scholar 

  2. S. G. Penoncello, Thermal energy systems. CRC Press-Taylor and Francis Group, Boca Raton 2015.

    Google Scholar 

  3. D. Taler, Mathematical modelling and control of plate fin and tube heat. Energ Convers Manage 96 (2015), 452–462.

    Article  Google Scholar 

  4. M. Trojan, D. Taler, Thermal simulation of superheaters taking into account the processes occurring on the side of the steam and flue gas. Fuel 150 (2015), 75–87.

    Article  Google Scholar 

  5. D. Taler, K. Kaczmarski, Mathematical modelling of the transient response of pipeline. J of Therm Sci 25 (2016) 549–557.

    Article  Google Scholar 

  6. J. Taler, P. Dzierwa, D. Taler, M. Jaremkiewicz, M. Trojan, Monitoring of thermal stresses and heating optimization including industrial applications. Nova Publishers, New York 2016.

    Google Scholar 

  7. P. Dzierwa, Optimum heating of pressure components of steam boilers with regard to thermal stresses. J Therm Stresses 39 (2016), pp. 874–886.

    Article  Google Scholar 

  8. P. Dzierwa, M. Trojan, D. Taler, K. Kamińska, J. Taler, Optimum heating of thick-walled pressure components assuming a quasi-steady state of temperature distribution. J Therm Sci 25 (2016), pp. 380–388.

    Article  Google Scholar 

  9. J. Taler, P. Dzierwa, D. Taler, P. Harchut, Optimization of the boiler start-up taking into account thermal stresses, Energy 92 (2015), 160–170.

    Article  Google Scholar 

  10. F. W. Dittus, L. M. K. Boelter, Heat transfer in automobile radiators of the tubular type. The University of California Publications on Engineering 2 (1930) 443–461, Reprinted in Int. Commun. Heat Mass 12 (1985) 3–22.

    MATH  Google Scholar 

  11. R. H. S., Winterton, Where did the Dittus and Boelter equation come from?. Int. J. Heat Mass Tran. 41 (1998) 809–810.

    Article  Google Scholar 

  12. W. H. McAdams, Heat Transmission. 3rd edn., McGraw-Hill, New York 1954.

    Google Scholar 

  13. A. P. Colburn, A method of correlating forced convectin heat transfer data and a comparison with fluid friction. Trans. AIChE 29 (1933) 174–210.

    Google Scholar 

  14. E. N. Sieder, E. C. Tate, Heat transfer and pressure drop of liquids in tubes. Ind. Eng. Chem. 28 (1936) 1429–1436.

    Article  Google Scholar 

  15. R. L. Webb, A critical evaluation of analytical solutions and Reynolds analogy equations for turbulent heat and mass transfer in smooth tubes. Warme Stoffubertrag. 4 (1971) 197–204.

    Article  ADS  Google Scholar 

  16. R. W. Allen, E. R. G. Eckert, Friction and heat-transfer measurements to turbulent pipe flow of water (Pr = 7 and 8) at uniform wall heat flux. J. Heat Trans-T. ASME 86 (1964) 301–310.

    Article  Google Scholar 

  17. F. Kreith, R. M. Manglik, M. S. Bohn, Principles of heat transfer. 7th edition, Cengage Learning, Stamford 2011.

    Google Scholar 

  18. D. R. Mirth, S. Ramadhyani, D. C. Hittle, Thermal performance of chilled-water cooling coils operating at low water velocities. ASHRAE Transactions, Part 1, 99 (1993) 43–53.

    Google Scholar 

  19. V. Gnielinski, Neue Gleichungen für den Wärme-und den Stoffübergang in turbulent durchströmten Rohren und Kanälen. Forsch. Ingenieurwes. (Engineering Research) 41 (1975) 8–16.

    Article  Google Scholar 

  20. V. Gnielinski, New equations for heat and mass transfer in the turbulent pipe and channel flow. Int. Chem. Eng. 16 (1976) 359–368.

    Google Scholar 

  21. G. K., Filonienko, Friction factor for turbulent pipe flow. Teploenergetika 1 (1954), no. 4, 40–44 (in Russian).

    Google Scholar 

  22. B. S. Petukhov, Heat transfer and friction in turbulent pipe flow with variable physical properties, in Advances in Heat Transfer, Vol. 6, 1970, pp. 503–564, Edited by J. P. Hartnett and T. F. Irvine, Academic Press, New York 1970.

    Article  Google Scholar 

  23. S. Kakaç, Y. Yener, A. Pramuanjaroenkij, Convective heat transfer. 3rd Edition, CRC Press–Taylor & Francis, Boca Raton 2014.

    MATH  Google Scholar 

  24. M. Li, T. S. Khan, E. Al-Hajri, Z. H. Ayub, Single phase heat transfer and pressure drop analysis of a dimpled enhanced tube. Appl. Therm. Eng. 101 (2016) 38–46.

    Article  Google Scholar 

  25. E. Martinez, W. Vicente, G. Soto, M. Salinas, Comparative analysis of heat transfer and pressure drop in helically segmented finned tube heat exchangers. Appl. Therm. Eng. 30 (2010) 1470–1476.

    Article  Google Scholar 

  26. L. Prandtl, Führer durch die Strömungslehre. Vieweg und Sohn, Braunschweig 1949 (Translation into English: L. Prandtl, Essentials of fluid dynamics, Blackie & Son, London, 1969, 117).

    MATH  Google Scholar 

  27. W. Yoo, S. Jeon, C. Son, J. Yang, D. Ahn, S. Kim, K. Hwang, S. Ha, Full surface heat transfer characteristics of rotor ventilation duct of a turbine generator. Appl. Therm. Eng. 94 (2016) 385–394.

    Article  Google Scholar 

  28. E. P. B. Filho, J. M. S. Jabardo, Experimental study of the thermal hydraulic performance of sub-cooled refrigerants flowing in smooth, micro-fin and herringbone tubes. Appl. Therm. Eng. 62 (2014) 461–469.

    Article  Google Scholar 

  29. Q. Li, Y. Xuan, Convective heat transfer and flow characteristics of Cu-water nanofluid. Sci. China Ser. E: Technol. Sci. 45 (2002) 408–416.

    Google Scholar 

  30. W. H. Azmi, K. Abdul Hamid, R. Mamat, K. V. Sharma, M. S. Mohamad, Effects of working temperature on thermo-physical properties and forced convection heat transfer of TiO2 nanofluids in water-Ethylene glycol mixture. Appl. Therm. Eng. 106 (2016) 1190–1199.

    Article  Google Scholar 

  31. Y.-L. He, Z.-J. Zheng, B.-C. Du, K. Wang, Y. Qiu, Experimental investigation on turbulent heat transfer characteristics of molten salt in a shell-and-tube heat exchanger. Appl. Therm. Eng. 108 (2016) 1206–1213.

    Article  Google Scholar 

  32. Y. T. Wu, B. Liu, C. F. Ma, H. Guo, Convective heat transfer in the laminar-turbulent transition region with molten salt in a circular tube. Exp. Thermal Fluid Sci. 33 (2009) 1128–1132.

    Article  Google Scholar 

  33. Y. S. Chen, Y. Wang, J. H. Zhang, X. F. Yuan, J. Tian, Z. F. Tang, H. H. Zhu, Y. Fu, N. X. Wang, Convective heat transfer characteristics in the turbulent region of molten salt in concentric tube. Appl. Therm. Eng. 98 (2016) 213–219.

    Article  ADS  Google Scholar 

  34. J. Qian, Q. Kong, H. Zhang, W. Huang, W. Li, Performance of a gas cooled molten salt heat exchanger. Appl. Therm. Eng. 108 (2016) 1429–1435.

    Article  Google Scholar 

  35. J. Lu, S. He, J. Liang, J. Ding, J. Yang, Convective heat transfer in the laminar-turbulent transition region of molten salt in annular passage. Exp. Thermal Fluid Sci. 51 (2013) 71–76.

    Article  Google Scholar 

  36. E. E. Wilson, A basis for rational design of heat transfer apparatus. Trans. ASME, 37 (1915) 47–82.

    Google Scholar 

  37. J. W. Rose, Heat-transfer coefficients, Wilson plots and accuracy of thermal measurements. Exp. Therm. Fluid Sci. 28 (2004) 77–86.

    Article  Google Scholar 

  38. D. Taler, A new heat transfer correlation for transition and turbulent fluid flow in tubes. Int. J. Therm. Sci. 108 (2016) 108–122.

    Article  Google Scholar 

  39. H. Reichardt, Vollständige Darstellung der turbulenten Geschwindigkeitsverteilung in glatten Leitungen. Z. Angew. Math. Mech. 31 (1951) no. 7, 208–219.

    Article  MATH  Google Scholar 

  40. H. Reichardt, The principles of turbulent heat transfer, Transl. by P. A. Scheck in Recent advances in heat and mass transfer. ed. by J. P. Hartnett, McGraw-Hill, Boston 1961, 223–252.

    Google Scholar 

  41. Bevington P. R., Data reduction and error analysis for the physical sciences. McGraw-Hill, New York 1969.

    Google Scholar 

  42. G. A. F Seber, C. J. Wild, Nonlinear regression. Wiley, New York 1989.

    Book  MATH  Google Scholar 

  43. D. Taler, Experimental determination of correlations for average heat transfer coefficients in heat exchangers on both fluid sides. Heat and Mass Transfer 49 (2013) 1125–1139.

    Article  ADS  Google Scholar 

  44. S. Lau, Effect of plenum length and diameter on turbulent heat transfer in a downstream tube and on plenum-related pressure loss. Ph. D. Thesis, University of Minnesota, 1981.

    Google Scholar 

  45. A. Black III, The effect of circumferentially-varying boundary conditions on turbulent heat transfer in a tube. Ph. D. Thesis, University of Minnesota, 1966.

    Google Scholar 

  46. R. Kemink, Heat transfer in a downstream tube of a fluid withdrawal branch. Ph. D. Thesis, University of Minnesota, 1977.

    Google Scholar 

  47. D. Wesley, Heat transfer in pipe downstream of a Tee. Ph. D. Thesis, University of Minnesota, 1976.

    Google Scholar 

  48. J. P. Abraham, E. M. Sparrow, W. J. Minkowycz, Internal-flow Nusselt numbers for the low-Reynoldsnumber end of the laminar-to-turbulent transition regime. Int. J. Heat Mass Tran. 54 (2011), 584–588.

    Article  MATH  Google Scholar 

  49. S. Eiamsa-ard, P. Promvonge, Thermal characteristics in round tube fitted with serrated twisted tape. Appl. Therm. Eng. 30 (2010) 1673–1682.

    Google Scholar 

  50. X. W. Li, J. A. Meng, Z. X. Li, Roughness enhanced mechanism for turbulent convective heat transfer. Int. J. Heat Mass Tran. 54 (2011) 1775–1781.

    Article  MATH  Google Scholar 

  51. J. A. Olivier, J. P. Meyer, Single-phase heat transfer and pressure drop of the cooling water inside smooth tubes for transitional flow with different inlet geometries. HVAC&R Research, 16 (2010) 471–496.

    Article  Google Scholar 

  52. M. Everts, S. R. Ayres, F. A. M. Houver, C. P. Vanderwagen, N. M. Kotze, J. P. Meyer, The influence of surface roughness on heat transfer in the transitional flow regime. Proceedings of the 15th International Heat Transfer Conference, IHTC-15, August 10-15, 2014, Kyoto, Japan

    Book  Google Scholar 

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Authors and Affiliations

  1. Institute of Heat Engineering and Air Protection, Faculty of Environmental Engineering, Cracow University of Technology, Al. Jana Pawła II 37, 31-864, Cracow, Poland

    Dawid Taler

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Taler, D. Simple power-type heat transfer correlations for turbulent pipe flow in tubes. J. Therm. Sci. 26, 339–348 (2017). https://doi.org/10.1007/s11630-017-0947-2

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  • DOI: https://doi.org/10.1007/s11630-017-0947-2

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