Effect of viscosity on entropy generation for laminar flow in helical pipes

Abstract

Entropy generation for fully developed laminar flow in a helical pipe carrying high viscous fluid under constant temperature boundary conditions is investigated analytically. This work focuses on geometrical, fluid, and thermal aspects and their influence on irreversibilities in helical coils. The effect of viscosity on the irreversibilities and its influence on the operating parameters of the helical coil are studied with the second law of thermodynamics. The most commonly used relationships for estimating viscosity change due to temperature are selected for analysis. The entropy generation and avoidable exergy destruction in each case are presented. Bejan number is plotted for varying viscosities under different wall temperatures for both heat transfer to and from the fluid. The thermodynamic potential of improvement based on avoidable and unavoidable exergy destruction concepts showed that the potential of improvement for heating and the cooling condition is considerable for a given operating condition in helical tubes. The selected model for estimating viscosity influences the optimum operating wall temperature, thereby giving an insight into a selection of a proper viscosity model. The optimum helical number is not affected by fluid properties and wall temperature. The heat transfer to pumping ratio is evaluated and it is found that the optimal value is influenced by the change in viscosity.

Keywords

• Laminar flow
• Viscosity
• Helical pipe
• Entropy
• Exergy

References

1. [1] Naphon, P., Wongwises, S. A review of flow and heat transfer characteristics in curved tubes. Renewable and Sustainable Energy Reviews 2006;10: 463-90. https://doi.org/10.1016/j.rser.2004.09.014.
2. [2] Prasad, B.V., Das, D.H., Prabhakar, A.K. Pressure drop, heat transfer and performance of a helical coil tubular exchanger. Heat Recovery Systems and CHP 1989;9: 249-56. https://doi.org/10.1016/0890-4332(89)90008-2.
3. [3] Goering, D.J., Humphrey, J.A.C., Greif, R. The dual influence of curvature and buoyancy in fully developed tube flow. Int. J. Heat Mass Transfer 1997;40: 2187-99. https://doi.org/10.1016/S0017-9310(96)00248-7.
4. [4] Ciofalo, M., Arini, A., Liberto, M.D. On the influence of gravitational and centrifugal buoyancy on laminar flow and heat transfer in curved pipes and coils. Int. J. Heat Mass Transfer 2015;82: 123-34. https://doi.org/10.1016/j.ijheatmasstransfer.2014.10.074.
5. [5] Manlapaz, E., Churchill, S.W. Fully developed laminar convection from a helical coil. Chem Eng Commun 1981;9: 185-200. https://doi.org/10.1080/00986448108911023.
6. [6] Kumar, V., Gupta, P., Nigam, K.D.P. Fluid flow and heat transfer in curved tubes with temperature-dependent properties. Ind. Eng. Chem. Res. 2007;46: 3226-36. https://doi.org/10.1021/ie0608399.
7. [7] Bejan, A. Second-law analysis in heat transfer and thermal design. Adv. Heat Transfer 1982;15: 1-58. https://doi.org/10.1016/S0065-2717(08)70172-2.
8. [8] Şahin, A. Z. A second law comparison for optimum shape of duct subjected to constant wall temperature and laminar flow. Heat and Mass Transfer 1998;33: 425-30. https://doi.org/10.1007/s002310050210.

9. [9] Chamkha, A.J. Unsteady laminar hydromagnetic fluid particle flow and heat transfer in channels and circular pipes. International Journal of Heat and Fluid Flow 2000;21: 740-746. https://doi.org/10.1016/S0142-727X(00)00031-X.
10. [10] Ko, T.H. A numerical study on entropy generation and optimization for laminar forced convection in a rectangular curved duct with longitudinal ribs. International Journal of Thermal Sciences 2006;45: 1113-25. https://doi.org/10.1016/j.ijthermalsci.2006.03.003.
11. [11] Sanchez, M., Henderson, A.W., Papavassiliou, D.V., Lemley, E.C. Entropy generation in laminar flow junctions. In: ASME 2012 Fluids Engineering Division Summer Meeting collocated with the ASME 2012 Heat Transfer Summer Conference and the ASME 2012 10th International Conference on Nanochannels, Microchannels, and Minichannels, pp. 325-30. Fluids Engineering Division, ASME. https://doi.org/10.1115/FEDSM2012-72334.
12. [12] Pendyala, S., Narla,V. K., Prattipati, R. Second law analysis for turbulent flow in helical pipes subject to variable viscosity. AIP Conference Proceedings. 2020;2246: 020038. https://doi.org/10.1063/5.0014559.
13. [13] Mehryan, S., Izadi, M., Chamkha, A.J., Sheremet, M.A. Natural convection and entropy generation of a ferrouid in a square enclosure under the effect of a horizontal periodic magnetic field. Journal of Molecular Liquids 2018;263: 510-25. https://doi.org/10.1016/j.molliq.2018.04.119.
14. [14] Tsatsaronis, G., Park, M.H. On avoidable and unavoidable exergy destructions and investment costs in thermal systems. Energy Conversion and Management 2002;43: 1259-70. https://doi.org/10.1016/S0196-8904(02)00012-2.
15. [15] Cziesla, F., Tsatsaronis, G., Gao, Z. Avoidable thermodynamic inefficiencies and costs in an externally fired combined cycle power plant. Energy 2006;31: 1472-89. https://doi.org/10.1016/j.energy.2005.08.001.
16. [16] Bahiraei, F., Saray, R.K., Salehzadeh, A. Investigation of potential of improvement of helical coils based on avoidable and unavoidable exergy destruction concepts. Energy 2011; 36:3113-9. https://doi.org/10.1016/ j.energy.2011.02.057.
17. [17] Shokouhmand, H., Salimpour, M.R. Entropy generation analysis of fully developed laminar forced convection in a helical tube with uniform wall temperature. Heat Mass Transfer 2007;44: 213-20. https://doi.org/10.1007/s00231-007-0235-x.
18. [18] Shokouhmand, H., Salimpour, M.R. Optimal Reynolds number of laminar forced convection in a helical tube subjected to uniform wall temperature. Int Comm Heat Mass Transf. 2007;34:753-61. https://doi.org/10.1016/j.icheatmasstransfer.2007.02.010.
19. [19] Wang, C., Liu, S., Wu, J., Li, Z. Effects of temperature-dependent viscosity on fluid flow and heat transfer in a helical rectangular duct with a finite pitch. Brazilian Journal of Chemical Engineering 2014;3: 787-97. https://doi.org/10.1590/0104-6632.20140313s00002676.
20. [20] Şahin, A.Z. Thermodynamics of laminar viscous flow through a duct subjected to constant heat flux. Energy 1996;21: 1179-89. https://doi.org/10.1016/0360-5442(96)00062-X
21. [21] Şahin, A.Z. Thermodynamic design optimization of a heat recuperator. Int. Comm. Heat Mass Transfer 1997;24: 1029-38. https://doi.org/10.1016/S0735-1933(97)00088-2.
22. [22] Şahin, A.Z. Effect of viscosity on effectiveness of parallel flow heat exchanger. Energy Convers. Mgmt 1998;39: 1233-8. https://doi.org/10.1016/S0196-8904(98)00013-2.
23. [23] Şahin, A.Z. Second law analysis of laminar viscous flow through a duct subjected to constant wall temperature. ASME Journal of Heat Transfer 1998;120: 76-83. https://doi.org/10.1115/1.2830068.
24. [24] Şahin, A.Z. Entropy generation in turbulent liquid flow through a smooth duct subjected to constant wall temperature. Int. J. Heat Mass Transfer 2000;43: 1469-78. https://doi.org/10.1016/S0017-9310(99)00216-1.
25. [25] Chamkha, A. J. On laminar hydromagnetic mixed convection flow in a vertical channel with symmetric and asymmetric wall heating conditions, International Journal of Heat and Mass Transfer 2002;45: 2509-25. https://doi.org/10.1016/S0017-9310(01)00342-8.
26. [26] Chamkha, A. Unsteady laminar hydromagnetic flow and heat transfer in porous channels with temperature‐dependent properties, International Journal of Numerical Methods for Heat & Fluid Flow 2001;11: 430-48. https://doi.org/10.1108/EUM0000000005529.
27. [27] Chamkha, A. J., Grosan T., Pop I. Fully developed free convection of a micropolar fluid in a vertical channel, International Communications in Heat and Mass Transfer, 2002; 29: 1119-27. https://doi.org/10.1016/S0735-1933(02)00440-2.
28. [28] Chamkha, A. J., Grosan T., Pop I. Fully Developed Mixed Convection of a Micropolar Fluid in a Vertical Channel, International Journal of Fluid Mechanics Research 2003;30: 251-63. DOI: 10.1615/InterJFluidMechRes.v30.i3.10.
29. [29] Chamkha, A. J. Flow of Two-Immiscible Fluids in Porous and Nonporous Channels. ASME. J. Fluids Eng. March 2000; 122: 117–24. https://doi.org/10.1115/1.483233.
30. [30] Mansoor, S. Entropy generation rate in a microscale thin film. Journal of Thermal Engineering 2019;5: 405-13.
31. [31] Kurtulmuş N., Bilgili M., Şahin B. Energy and Exergy analysis of a vapor absorption refrigeration system in an intercity bus application. Journal of Thermal Engineering 2019;5: 355-71. https://doi.org/10.18186/thermal.583316.
32. [32] Kaşka, Ö., Bor, O., Tokgöz, N., Aksoy, M. First and second law evaluation of combined Brayton-Organic Rankine power cycle. Journal of Thermal Engineering 2020;6: 577-91. https://doi.org/10.18186/thermal.764299.
33. [33] Sherman, F.S. Viscous Flow. McGraw-Hill Co., New York; 1990.
34. [34] Bejan, A.: Entropy generation minimization: the new thermodynamics of finite size devices and finite-time processes. Applied Physics Reviews 1996;79: 1191-218. https://doi.org/10.1063/1.362674.
35. [35] Prattipati, R., Narla, V.K., Pendyala, S., Prasad, B. Performance comparison of straight and helical pipes subjected to constant heat flux. In: Proceedings of the 6th International and 43rd National Conference on Fluid Mechanics and Fluid Power. 2016, MN NITA, MNNIT, Allahabad, India.
36. [36] Srinivasan, P.S., Nandapurkar, S.S., Holland, F.A. Pressure drop and heat transfer in coils. Chem. Res. 1968;218: 113-9.
37. [37] Paoletti, S., Rispoli, F., Sciubba, E. Calculation of exergetic losses in compact heat exchanger passages. ASME AES 1989;10: 21-9.
38. [38] Dincer, I., Rosen, M.A. Energy, Environment And Sustainable Development. Elsevier, Kidlington, UK; 2013.