The Friction Factor of Turbulent Flow of the Base Fluid and Nanofluid in the Statistical Approach

علوم کاربردی و محاسباتی در مکانیک

Article 8, Volume 31, Issue 1 - Serial Number 21, February 2020, Pages 105-122   

Document Type: Original Article

DOI: 10.22067/fum-mech.v31i1.81926

Author

Farhad Vahidinia

Abstract

In this paper, the presented correlations in scientific literature for friction factor of turbulent flow in the base fluid and nanofluid has been analyzed statistically. In order to perform the statistical analysis and select the best probability distribution function for the friction factor, from 48 probability distribution functions and 3 statistic of Kolmogorov-Smirnov, Anderson-Darling and chi squared has been used. The results show that, based on all three statistics, the probability distribution function of the friction factor in the base fluid and nanofluid is the Johnson SB probability distribution function. Furthermore, it was observed that the probability distribution function of the friction factor of the base fluid and nanofluid is wider than the normal distribution function. On the other side, the probability distribution function of Johnson SB has a right skewness.

Keywords

Friction factor; Johnson SB Probability Distribution Function; Turbulent Flow; The Statistics of Kolmogorov-Smirnov; Anderson-Darling and Chi Squared

Supplementary Files

EA8-vahidinia-Nahayi.pdf

References

1. Syam Sundar, L. and Singh, M.K., "Convective Heat Transfer and Friction Factor Correlations of Nanofluid in a Tube and with Inserts: A Review", Renewable and Sustainable Energy Reviews, Vol. 20, pp. 23-35, (2013).

2. Khoshvaght-Aliabadi, M. and Sahamiyan, M., "Performance of Nanofluid Flow in Corrugated Minichannels Heat Sink (Cmchs)", Energy Conversion and Management, Vol. 108, pp. 297-308, (2016).

3. Ghazvini, M. and Shokouhmand, H., "Investigation of a Nanofluid-Cooled Microchannel Heat Sink Using Fin and Porous Media Approaches", Energy Conversion and Management, Vol. 50, No. 9, pp. 2373-80, (2009).

4. Duangthongsuk, W. and Wongwises, S., "An Experimental Study on the Heat Transfer Performance and Pressure Drop of TiO2-Water Nanofluids Flowing under a Turbulent Flow Regime" International Journal of Heat and Mass Transfer, Vol. 53, No. 1-3, pp. 334-44, (2010).

5. Sajid, M. U. and Hafiz M. A., "Recent Advances in Application of Nanofluids in Heat Transfer Devices: A Critical Review", Renewable and Sustainable Energy Reviews, Vol. 103, pp. 556-92, (2019).

6. Hamzah, M. H., Sidik, N. A. C., Ken, T. L., Mamat, R. and Najafi, G., "Factors Affecting the Performance of Hybrid Nanofluids: A Comprehensive Review", International Journal of Heat and Mass Transfer, Vol. 115, pp. 630-46, (2017).

7. Ambreen, T. and Kim, M. H., "Heat Transfer and Pressure Drop Correlations of Nanofluids: A State of Art Review", Renewable and Sustainable Energy Reviews, Vol. 91, pp. 564-83, (2018).

8. Sharma, K. V., Syam Sundar, L. and Sarma, P. K., "Estimation of Heat Transfer Coefficient and Friction Factor in the Transition Flow with Low Volume Concentration of Al2O3 Nanofluid Flowing in a Circular Tube and with Twisted Tape Insert", International Communications in Heat and Mass Transfer, Vol. 36, No. 5, pp. 503-07, (2009).

9. Akhavan-Behabadi, M. A., Shahidi, M. and Aligoodarz, M. R., "An Experimental Study on Heat Transfer and Pressure Drop of Mwcnt–Water Nano-Fluid inside Horizontal Coiled Wire Inserted Tube", International Communications in Heat and Mass Transfer, Vol. 63, pp. 62-72, (2015).

10. Vahidinia, F., Keshtegar, B. and Miri, M., "Statistical Analysis of the Effect of Nanoparticles Volume Fraction on Turbulent Forced Convective Heat Transfer Coefficient of Nanofluid in a Circular Tube", Ciência e Natura, Vol. 37, pp. 141-52, (2015).

11. وحیدی نیا، فرهاد، میری، محدثه و کشته گر، بهروز، "مطالعۀ تولید آنتروپی و ارزیابی خواص آماری انتقال حرارت در جریان مغشوش"، مجله علوم کاربردی و محاسباتی در مکانیک، سال 29، شماره 1، ص 68-63، (1396).

12. Blasius, H., Grenzschichten in Flüssigkeiten Mit Kleiner Reibung, Druck von BG Teubner, (1907).

13. Petukhov, B. S., "Heat Transfer and Friction in Turbulent Pipe Flow with Variable Physical Properties", In Advances in Heat Transfer, Vol. 6, pp. 503-64, (1970).

14. Naphon, P., Nuchjapo, M. and Kurujareon, J., "Tube Side Heat Transfer Coefficient and Friction Factor Characteristics of Horizontal Tubes with Helical Rib", Energy Conversion and Management, Vol. 47, No. 18-19, pp. 3031-44, (2006).

15. Li, M., Khan, T. S., Al-Hajri, E. and Ayub, Z. H., "Single Phase Heat Transfer and Pressure Drop Analysis of a Dimpled Enhanced Tube", Applied Thermal Engineering, Vol. 101, pp. 38-46, (2016).

16. Vajjha, R. S., Das, D. K. and Kulkarni, D. P., "Development of New Correlations for Convective Heat Transfer and Friction Factor in Turbulent Regime for Nanofluids", International Journal of Heat and Mass Transfer, Vol. 53, No. 21-22, pp. 4607-18, (2010).

17. Hejazian, M., Keshavarz Moraveji, M. and Beheshti, A., "Comparative Numerical Investigation on TiO2/Water Nanofluid Turbulent Flow by Implementation of Single Phase and Two Phase Approaches", Numerical Heat Transfer, Part A: Applications, Vol. 66, No. 3, pp. 330-48, (2014).

18. Hejazian, M., Keshavarz Moraveji M. and Beheshti A., "Comparative Study of Euler and Mixture Models for Turbulent Flow of Al2O3 Nanofluid inside a Horizontal Tube", International Communications in Heat and Mass Transfer, Vol. 52, pp. 152-58, (2014).

19. Keshavarz Moraveji, M. and Hejazian M., "Modeling of Turbulent Forced Convective Heat Transfer and Friction Factor in a Tube for Fe3O4 Magnetic Nanofluid with Computational Fluid Dynamics", International Communications in Heat and Mass Transfer, Vol. 39, No. 8, pp. 1293-96, (2012).

20. Keshavarz Moraveji, M., Ardehali, R. M. and Ijam A., "CFD Investigation of Nanofluid Effects (Cooling Performance and Pressure Drop) in Mini-Channel Heat Sink", International Communications in Heat and Mass Transfer, Vol. 40, pp. 58-66, (2013).

21. Nabil, M. F., Azmi W. H., Hamid, K. A. and Mamat R., "Experimental Investigation of Heat Transfer and Friction Factor of TiO2-SiO2 Nanofluids in Water: Ethylene Glycol Mixture", International Journal of Heat and Mass Transfer, pp. 124, pp. 1361-69, (2018).

22. Naik, M. T., Janardana, G. R. and Syam Sundar, L., "Experimental Investigation of Heat Transfer and Friction Factor with Water–Propylene Glycol Based Cuo Nanofluid in a Tube with Twisted Tape Inserts", International Communications in Heat and Mass Transfer, Vol. 46, pp. 13-21, (2013).

23. Yarmand, H. Gharehkhani, S., Ahmadi, G., Seyed Shirazi, S. F., Baradaran, S., Montazer, E., Mohd Zubir, M. N., Alehashem, M. S., Kazi, S. N. and Dahari, M., "Graphene Nanoplatelets–Silver Hybrid Nanofluids for Enhanced Heat Transfer", Energy Conversion and Management, Vol. 100, pp. 419-28, (2015).

24. Ravi Kumar, N. T., Bhramara, P., Addis, B. M., Syam Sundar, L., Singh, M. K. and Sousa, A. C. M., "Heat Transfer, Friction Factor and Effectiveness Analysis of Fe3O4/Water Nanofluid Flow in a Double Pipe Heat Exchanger with Return Bend", International Communications in Heat and Mass Transfer, Vol. 81, pp. 155-63, (2017).

25. Syam Sundar, L., Singh, M.K. and Sousa, A.C.M., "Turbulent Heat Transfer and Friction Factor of Nanodiamond-Nickel Hybrid Nanofluids Flow in a Tube: An Experimental Study", International Journal of Heat and Mass Transfer, Vol. 117, pp. 223-34, (2018).

26. Syam Sundar, L. Singh, M.K., Bidkin, I. and Sousa, A.C.M., "Experimental Investigations in Heat Transfer and Friction Factor of Magnetic Ni Nanofluid Flowing in a Tube", International Journal of Heat and Mass Transfer, Vol. 70, pp. 224-34, (2014).

27. Durga Prasad, P.V., Gupta, A.V.S.S.K.S., Sreeramulu, M., Syam Sundar, L., Singh, M.K. and Sousa, A.C.M., "Experimental Study of Heat Transfer and Friction Factor of Al2O3 Nanofluid in U-Tube Heat Exchanger with Helical Tape Inserts", Experimental Thermal and Fluid Science, Vol. 62, pp. 141-50, (2015).

28. Abdul Hamid, K., Azmi, W. H., Nabil, M. F. and Mamat, R. "Experimental Investigation of Nanoparticle Mixture Ratios on TiO2–SiO2 Nanofluids Heat Transfer Performance under Turbulent Flow", International Journal of Heat and Mass Transfer, Vol. 118, pp. 617-27, (2018).

29. Ravi Kumar, N. T., Bhramara, P., Syam Sundar, L., Singh, M. K. and Sousa, A. C. M., "Heat Transfer, Friction Factor and Effectiveness of Fe3O4 Nanofluid Flow in an Inner Tube of Double Pipe U-Bend Heat Exchanger with and without Longitudinal Strip Inserts", Experimental Thermal and Fluid Science, Vol. 85, pp. 331-43, (2017).

30. Syam Sundar, L., Otero-Irurueta, G., Singh, M. K. and Sousa, A. C. M., "Heat Transfer and Friction Factor of Multi-Walled Carbon Nanotubes–Fe3O4 Nanocomposite Nanofluids Flow in a Tube with/without Longitudinal Strip Inserts." International Journal of Heat and Mass Transfer, Vol. 100, pp. 691-703, (2016).

31. Syam Sundar, L., Singh, M.K. and Sousa, A.C.M., "Heat Transfer and Friction Factor of Nanodiamond-Nickel Hybrid Nanofluids Flow in a Tube with Longitudinal Strip Inserts", International Journal of Heat and Mass Transfer, Vol. 121, pp. 390-401, (2018).

32. Abbasian Arani, A.A. and Amani, J., "Experimental Investigation of Diameter Effect on Heat Transfer Performance and Pressure Drop of TiO2–Water Nanofluid", Experimental Thermal and Fluid Science, Vol. 44, pp. 520-33, (2013).

33. Syam Sundar, L. and Sharma, K.V., "Heat Transfer Enhancements of Low Volume Concentration Al2O3 Nanofluid and with Longitudinal Strip Inserts in a Circular Tube", International Journal of Heat and Mass Transfer, Vol. 53, No. 19-20, pp. 4280-86, (2010).