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Articles

Heat and Mass Transfer Equations for Turbulent Flow with Wide Ranges of Prandtl and Schmidt Numbers

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References

  • Q. Q. Wang, G. N. Xie, M. Zeng, and L. Q. Luo, “Prediction of heat transfer rates for shell-and-tube heat exchangers by artificial neural networks approach,” J. Therm. Sci., vol. 15, no. 3, pp. 257–262, Sep. 2006. DOI: 10.1007/s11630-006-0257-6.
  • J. P. Meyer and J. A. Olivier, “Heat transfer and pressure drop characteristics of smooth horizontal tubes in the transitional flow regime,” Heat Transf. Eng., vol. 35, no. 14–15, pp. 1246–1253, Oct. 2014. DOI: 10.1080/01457632.2013.876793.
  • W. K. Gao et al., “Heat transfer characteristics of carbon dioxide cross flow over tube bundles at supercritical pressures,” Appl. Therm. Eng., vol. 158, pp. 1137861–11378616, Jul. 2019. DOI: 10.1016/j.applthermaleng.2019.113786.
  • Z. Q. Yang, M. Q. Gong, G. F. Chen, X. Zou, and J. Shen, “Two-phase flow patterns, heat transfer and pressure drop characteristics of R600a during flow boiling inside a horizontal tube,” Appl. Therm. Eng., vol. 120, pp. 654–671, Jun. 2017. DOI: 10.1016/j.applthermaleng.2017.03.124.
  • A. P. Colburn, “A method of correlating forced convection heat-transfer data and a comparison with fluid friction,” Int. J. Heat Mass Transf., vol. 7, no. 12, pp. 1359–1384, Mar. 1964. DOI: 10.1016/0017-9310(64)90125-5.
  • C. M. Chu, “Use of chilton-colburn analogy to estimate effective plume chimney height of a forced draft, air-cooled heat exchanger,” Heat Transf. Eng., vol. 27, no. 9, pp. 81–85, Nov. 2006. DOI: 10.1080/01457630600846315.
  • M. Everts and J. P. Meyer, “Relationship between pressure drop and heat transfer of developing and fully developed flow in smooth horizontal circular tubes in the laminar, transitional, quasi-turbulent and turbulent flow regimes,” Int. J. Heat Mass Transf., vol. 117, pp. 1231–1250, Feb. 2018. DOI: 10.1016/j.ijheatmasstransfer.2017.10.072.
  • M. Kadivar, M. Sharifpur, and J. P. Meyer, “Convection heat transfer, entropy generation analysis and thermodynamic optimization of nanofluid flow in spiral coil tube,” Heat Transf. Eng., vol. 42, no. 18, pp. 1573–1589, 2020. DOI: 10.1080/01457632.2020.1807103.
  • W. R. van Zyl, J. Dirker, and J. P. Meyer, “Single-phase convective heat transfer and pressure drop coefficients in concentric annuli,” Heat Transf. Eng, vol. 34, no. 13, pp. 1112–1123, 2013. Oct 2013. DOI: 10.1080/01457632.2013.763550.
  • R. Wejkowski, “Heat transfer and pressure loss in combined tube banks with triple-finned tubes,” Heat Transf. Eng., vol. 37, no. 1, pp. 45–52, Jan. 2016. DOI: 10.1080/01457632.2015.1042336.
  • Y. L. Liu et al., “Experimental and numerical study on heat and mass transfer of cross-flow liquid desiccant dehumidifier/regenerator,” Heat Transf. Eng., vol. 41, no. 9–10, pp. 867–881, May 2020. DOI: 10.1080/01457632.2019.1576436.
  • V. Gnielinski, “Neue Gleichungen für den Wärme- und den Stoffübergang in turbulent durchströmten Rohren und Kanälen,” Forsch Ing.-Wes., vol. 41, no. 1, pp. 8–16, Jan. 1975. DOI: 10.1007/BF02559682.
  • W. M. Kays and M. E. Crawford, Convective Heat and Mass Transfer, 3rd ed. Hightstown, NJ, USA: MHE, 1993.
  • B. Petukhov, “Heat transfer and friction in turbulent pipe flow with variable physical properties,” Adv. Heat Transf., vol. 6, pp. 503–564, May 1970. DOI: 10.1016/S0065-2717(08)70153-9.
  • V. Gnielinski, “On heat transfer in tubes,” Int. J. Heat Mass Transf., vol. 63, pp. 134–140, Aug. 2013. DOI: 10.1016/j.ijheatmasstransfer.2013.04.015.
  • H. J. Zhao, X. W. Li, and X. X. Wu, “New friction factor and Nusselt number equations for laminar forced convection of liquid with variable properties,” Sci. China Technol. Sci., vol. 61, no. 1, pp. 98–109, Jan. 2018. DOI: 10.1007/s11431-017-9120-5.
  • H. J. Zhao, X. W. Li, and X. X. Wu, “New friction factor and Nusselt number equations for turbulent convection of liquids with variable properties in circular tubes,” Int. J. Heat Mass Transf., vol. 124, pp. 454–462, Sep. 2018. DOI: 10.1016/j.ijheatmasstransfer.2018.03.082.
  • M. Mehrabi, S. Abadi, and J. P. Meyer, “Heat transfer and fluid flow optimization of titanium dioxide-water nanofluids in a turbulent flow regime,” Heat Transf. Eng., vol. 41, no. 1, pp. 36–49, Jan. 2020. DOI: 10.1080/01457632.2018.1513623.
  • M. Bachiri and A. Bouabdallah, “An analytic investigation of the steady-state natural convection boundary layer flow on a vertical plate for a wide range of prandtl numbers,” Heat Transf. Eng., vol. 31, no. 7, pp. 608–616, Jul. 2010. DOI: 10.1080/01457630903425908.
  • B. Kader, “Temperature and concentration profiles in fully turbulent boundary layers,” Int. J. Heat Mass Transf., vol. 24, no. 9, pp. 1541–1544, Feb. 1981. DOI: 10.1016/0017-9310(81)90220-9.
  • R. Gowen and J. Smith, “The effect of the Prandtl number on temperature profiles for heat transfer in turbulent pipe flow,” Chem. Eng. Sci., vol. 22, no. 12, pp. 1701–1711, Jun. 1967. DOI: 10.1016/0009-2509(67)80205-7.
  • F. Schwertfirm and M. Manhart, “DNS of passive scalar transport in turbulent channel flow at high Schmidt numbers,” Int. J. Heat Fluid Flow, vol. 28, no. 6, pp. 1204–1214, Dec. 2007. DOI: 10.1016/j.ijheatfluidflow.2007.05.012.
  • R. G. Deissler, Analysis of Turbulent Heat Transfer, Mass Transfer, and Friction in Smooth Tubes at High Prandtl and Schmidt Numbers. Washington, DC, USA: NACA, 1954.
  • P. K. Sarma et al., “Evaluation of momentum and thermal eddy diffusivities for turbulent flow in tubes,” Int. J. Heat Mass Transf., vol. 53, no. 5–6, pp. 1237–1242, Feb. 2010. DOI: 10.1016/j.ijheatmasstransfer.2009.11.023.
  • C. Rosén and C. Trägardh, “Prediction of turbulent high Schmidt number mass transfer using a low Reynolds number k—ϵ turbulence model,” Chem. Eng. J. Biochem. Eng. J., vol. 59, no. 2, pp. 153–159, Oct. 1995. DOI: 10.1016/0923-0467(94)02921-0.
  • Q. J. Slaiman, M. M. Abu-Khader, and B. O. Hasan, “Prediction of heat transfer coefficient based on eddy diffusivity concept,” Chem. Eng. Res. Des., vol. 85, no. 4, pp. 455–464, Apr. 2007. DOI: 10.1205/cherd06002.
  • S. Aravinth, “Prediction of heat and mass transfer for fully developed turbulent fluid flow through tubes,” Int. J. Heat Mass Transf., vol. 43, no. 8, pp. 1399–1408, Apr. 2000. DOI: 10.1016/S0017-9310(99)00218-5.
  • R. M. C. So and T. P. Sommer, “A near-wall eddy conductivity model for fluids with different Prandtl numbers,” J Heat Transfer, vol. 116, no. 4, pp. 844–854, Nov. 1994. DOI: 10.1115/1.2911457.
  • S. Thakre and J. Joshi, “CFD modeling of heat transfer in turbulent pipe flows,” AIChE J., vol. 46, no. 9, pp. 1798–1812, Apr. 2000. DOI: 10.1002/aic.690460909.
  • J. Kim and P. Moin, “Transport of passive scalars in a turbulent channel flow,” in Turbulent Shear Flows 6, J. C. André, J. Cousteix, F. Durst, B. E. Launder, F. W. Schmidt, and J. H. Whitelaw, Eds. Berlin, Heidelberg: Springer, 1989, pp. 85–96.
  • M. Kozuka, Y. Seki, and H. Kawamura, “DNS of turbulent heat transfer in a channel flow with a high spatial resolution,” Int. J. Heat Fluid Flow, vol. 30, no. 3, pp. 514–524, Jun. 2009. DOI: 10.1016/j.ijheatfluidflow.2009.02.023.
  • Y. Na, D. V. Papavassiliou, and T. J. Hanratty, “Use of direct numerical simulation to study the effect of Prandtl number on temperature fields,” Int. J. Heat Fluid Flow, vol. 20, no. 3, pp. 187–195, Jun. 1999. DOI: 10.1016/S0142-727X(99)00008-9.
  • L. Redjem-Saad, M. Ould-Rouiss, and G. Lauriat, “Direct numerical simulation of turbulent heat transfer in pipe flows: Effect of Prandtl number,” Int. J. Heat Fluid Flow, vol. 28, no. 5, pp. 847–861, Oct. 2007. DOI: 10.1016/j.ijheatfluidflow.2007.02.003.
  • C. Irrenfried and H. Steiner, “DNS based analytical P-function model for RANS with heat transfer at high Prandtl numbers,” Int. J. Heat Fluid Flow, vol. 66, pp. 217–225, Aug. 2017. DOI: 10.1016/j.ijheatfluidflow.2017.06.011.
  • S. Saha, A. S. H. Ooi, and H. M. Blackburn, “Validation criteria for DNS of turbulent heat transfer in pipe flow,” Proc. Eng., vol. 90, pp. 599–604, Jan. 2014. DOI: 10.1016/j.proeng.2014.11.778.
  • W. M. Kays, “Turbulent Prandtl number—Where are we?” J. Heat Transfer, vol. 116, no. 2, pp. 284–295, May 1994. DOI: 10.1115/1.2911398.
  • H. Steiner, C. Irrenfried, and G. Brenn, “Near-wall determination of the turbulent prandtl number based on experiments, numerical simulation and analytical models,” Heat Transf. Eng., vol. 41, no. 1516, pp. 1341–1353, Sep. 2020. DOI: 10.1080/01457632.2019.1628483.
  • J. Grifoll and F. Giralt, “The near wall mixing length formulation revisited,” Int. J. Heat Mass Transf., vol. 43, no. 19, pp. 3743–3746, Nov. 2000. DOI: 10.1016/S0017-9310(00)00009-0.
  • J. Kim, P. Moin, and R. Moser, “Turbulence statistics in fully developed channel flow at low reynolds number,” J. Fluid Mech., vol. 177, pp. 133–166, Apr. 1987. DOI: 10.1017/S0022112087000892.
  • J. G. M. Eggels et al., “Fully developed turbulent pipe flow: A comparison between direct numerical simulation and experiment,” J. Fluid Mech., vol. 268, pp. 175–210, Apr. 1994. DOI: 10.1017/S002211209400131X.
  • H. Kawamura, H. Abe, and Y. Matsuo, “DNS of turbulent heat transfer in channel flow with respect to Reynolds and Prandtl number effects,” Int. J. Heat Fluid Flow, vol. 20, no. 3, pp. 196–207, Jun. 1999. DOI: 10.1016/S0142-727X(99)00014-4.
  • H. Schlichting and G. Klaus, Boundary Layer Theory, 9th ed. Berlin, HD, DE: Springer, 2017.
  • P. Davidson, Turbulence: An Introduction for Scientists and Engineers. New York, NY, USA: Oxford University Press, 2015.
  • L. Prandtl, Recent Results of Turbulence Research. Washington, DC, USA: NACA, 1933.
  • J. Nikuradse, Laws of Flow in Rough Pipes. Washington, DC, USA: NACA, 1950.
  • B. A. Kader and A. M. Yaglom, “Heat and mass transfer laws for fully turbulent wall flows,” Int. J. Heat Mass Transf., vol. 15, no. 12, pp. 2329–2351, Dec. 1972. DOI: 10.1016/0017-9310(72)90131-7.
  • W. C. Williams, “If the Dittus and Boelter equation is really the McAdams equation, then should not the McAdams equation really be the Koo equation?” Int. J. Heat Mass Transf., vol. 54, no. 7–8, pp. 1682–1683, Mar. 2011. DOI: 10.1016/j.ijheatmasstransfer.2010.11.047.
  • J. Grifoll and F. Giralt, “Mixing length equation for high Schmidt number mass transfer at solid boundaries,” Can. J. Chem. Eng., vol. 65, no. 1, pp. 18–22, Feb. 1987. DOI: 0.1002/cjce.5450650104. DOI: 10.1002/cjce.5450650104.
  • E. R. Van Driest, “On turbulent flow near a wall,” J. Aeronaut. Sci., vol. 23, no. 11, pp. 1007–1011, Nov. 1956. DOI: 10.2514/8.3713.
  • D. C. Wilcox, Turbulence Modeling for CFD. La Cañada, CA, USA: DCW, 1993.
  • F. Durst, J. Jovanović, and J. Sender, “LDA measurements in the near-wall region of a turbulent pipe flow,” J. Fluid Mech., vol. 295, no. 1, pp. 305–335, Apr. 1995. DOI: 10.1017/S0022112095001984.
  • M. van Reeuwijk and M. Hadžiabdić, “Modelling high Schmidt number turbulent mass transfer,” Int. J. Heat Fluid Flow, vol. 51, pp. 42–49, Feb. 2015. DOI: 10.1016/j.ijheatfluidflow.2014.10.025.
  • R. Bergant and I. Tiselj, “Near-wall passive scalar transport at high Prandtl numbers,” Phys. Fluids, vol. 19, no. 6, pp. 1185–1194, Jun. 2007. DOI: 10.1063/1.2739402.
  • B. Chaouat and C. Peyret, “Investigation of the wall scalar fluctuations effect on passive scalar turbulent fields at several Prandtl numbers by means of direct numerical simulations,” J Heat Transfer, vol. 141, no. 12, pp. 1220021–1220029, Dec. 2019. DOI: 10.1115/1.4044882.
  • J. C. Neumann, “Transfert de chaleur en régime turbulent pour les grands nombres de Prandtl,” Inform. Aéraul. et Therm., vol. 5, no. 4, pp. 4–20, 1968.
  • R. D. Moser, J. Kim, and N. N. Mansour, “Direct numerical simulation of turbulent channel flow up to Reτ = 590,” Phys. Fluids, vol. 11, no. 4, pp. 943–945, Apr. 1999. DOI: 10.1063/1.869966.
  • D. A. Shaw and T. J. Hanratty, “Turbulent mass transfer rates to a wall for large Schmidt numbers,” AIChE J., vol. 23, no. 1, pp. 28–37, Jan. 1977. DOI: 10.1002/aic.690230106.
  • B. T. Farzad, M. Saied, and A. Masoud, “On the validity of boussinesq approximation in variable property turbulent mixed convection channel flows,” Heat Transf. Eng., vol. 39, no. 5, pp. 473–491, Apr. 2018. DOI: 10.1080/01457632.2017.1312902.
  • K. Janberg, “Etude experimentale de la distribution des temperatures dans le film visqueux, aux grands nombres de Prandtl,” Int. J. Heat Mass Transf., vol. 13, no. 7, pp. 1234–1237, Jul. 1970. DOI: 10.1016/0017-9310(70)90013-X.
  • W. M. Kays and E. Y. Leung, “Heat transfer in annular passages—Hydrodynamically developed turbulent flow with arbitrarily prescribed heat flux,” Int. J. Heat Mass Transf., vol. 6, no. 7, pp. 537–557, Jul. 1963. DOI: 10.1016/0017-9310(63)90012-7.
  • S. Kakac, R. K. Shah, and W. Aung, Handbook of Single-Phase Convective Heat Transfer. New York, NY, USA: Wiley-Interscience, 1987.
  • P. Harriott and R. Hamilton, “Solid-liquid mass transfer in turbulent pipe flow,” Chem. Eng. Sci., vol. 20, no. 12, pp. 1073–1078, Oct. 1965. DOI: 10.1016/0009-2509(65)80110-5.
  • F. P. Berger and K. F. Hau, “Mass transfer in turbulent pipe flow measured by the electrochemical method,” Int. J. Heat Mass Transf., vol. 20, no. 11, pp. 1185–1194, Nov. 1977. DOI: 10.1016/0017-9310(77)90127-2.
  • T. Wei and J. Abraham, “Heat transfer regimes in fully developed circular tube flows, a map of flow regimes,” Int. Commun. Heat Mass Transf., vol. 104, pp. 147–152, May 2019. DOI: 10.1016/j.icheatmasstransfer.2019.02.006.

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