THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

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Michele Trancossi

,

Jose Pascoa

DIFFUSIVE BEJAN NUMBER AND SECOND LAW OF THERMODYNAMICS TOWARD A NEW DIMENSIONLESS FORMULATION OF FLUID DYNAMICS LAWS

ABSTRACT
In a recent paper, Liversage and Trancossi have defined a new formulation of drag as a function of the dimensionless Bejan and Reynolds numbers. Further analysis of this hypothesis has permitted to obtain a new dimensionless formulation of the fundamental equations of fluid dynamics in their integral form. The resulting equations have been deeply discussed for the thermodynamic definition of Bejan number evidencing that the proposed formulation allows solving fluid dynamic problems in terms of entropy generation, allowing an effective optimization of design in terms of the second law of thermodynamics. Some samples are discussed evidencing how the new formulation can support the generation of an optimized configuration of fluidic devices and that the optimized configurations allow minimizing the entropy generation.
KEYWORDS
fluid dynamic, conservation laws, Bejan number, drag, friction coefficient, entropy, exergy
PAPER SUBMITTED: 2019-07-26
PAPER REVISED: 2019-08-15
PAPER ACCEPTED: 2019-09-01
PUBLISHED ONLINE: 2019-09-15
DOI REFERENCE: https://doi.org/10.2298/TSCI190726340T
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Issue 6, PAGES [4005 - 4022]
REFERENCES
  1. Liversage P., and Trancossi M., "Analysis of triangular sharkskin profiles according to the second law." IIETA Modelling, Measurement and Control B (MMC_B), Vol. 87, No. 3, September, pp. 188-196, 2018. doi.org/10.18280/mmc_b.870311.
  2. Bhattacharjee, S., Grosshandler, W. L., "The formation of a wall jet near a high-temperature wall under microgravity environment." In: ASME 1988 National Heat Transfer Conference, 1:711-716, 1988. adsabs.harvard.edu/abs/1988nht.....1..711B.
  3. Mahmud, S., and Fraser, R. A. "Thermodynamic analysis of flow and heat transfer inside channel with two parallel plates." Exergy an International Journal, 2(3):140-146, 2002. doi.org/10.1016/S1164-0235(02)00062-6.
  4. Mahmud, S., and Fraser, R. A. (2002). "The second law analysis in fundamental convective heat transfer problems." Intl. J. of Th. Sci., 42(2):177-186, 2002. doi.org/10.1016/S1290-0729(02)00017-0
  5. Awad, M.M. and Lage, J. L. (2013). "Extending the Bejan number to a general form." Thermal Science. 17(2):631. doi.org/10.2298/TSCI130211032A.
  6. Awad, M. M., 2012, "A New Definition of Bejan Number", Thermal Science, Volume 16, Issue 4, pp. 1251-1253. doi: : 10.2298/TSCI12041251A
  7. Awad, M. M., 2014, "An Alternative Form of the Darcy Equation", Thermal Science, Volume 18, Supplement 2, pp S617-S619, doi: 10.2298/TSCI131213042A
  8. Trancossi, M. and Sharma, S., "Numerical and Experimental Second Law Analysis of a Low Thickness High Chamber Wing Profile." SAE Technical Paper 2018-01-1955, 2018. doi.org/10.4271/2018-01-1955.
  9. Trancossi M. and Pascoa J., "A new dimensionless approach to general fluid dynamics problems that accounts both the first and the second law of thermodynamics." Mathematical Modelling of Engineering Problems, Vol. 5, No. 4, December, pp. 331-340, 2018. doi.org/10.18280/mmep.050409.
  10. Awad, M. M., "Hagen number versus Bejan number". Thermal Science. 17 (4): 1245, 2013. doi.org/10.2298/TSCI1304245A.
  11. Sciubba, E., "A minimum entropy generation procedure for the discrete pseudo-optimization of finned-tube heat exchangers." Revue générale de thermique, 35(416):517-525, 1996. doi.org/10.1016/S0035-3159(99)80079-8.
  12. Awad, M. M. "The science and the history of the two Bejan numbers." International Journal of Heat and Mass Transfer 94: 101-103, 2016. doi.org/10.1016/j.ijheatmasstransfer.2015.11.073
  13. Klein, R. J., Lorenzini, G., Zinani, F. S., & Rocha, L. A. (2017). "Dimensionless pressure drop number for non-newtonian fluids applied to constructal design of heat exchangers." International Journal of Heat and Mass Transfer, 115, 910-914. doi.org/10.1016/j.ijheatmasstransfer.2017.07.122
  14. Bejan, A., "General criterion for rating heat-exchanger performance." International Journal of Heat and Mass Transfer, 21(5), 655-658, 1992. doi.org/10.1016/0017-9310(78)90064-9.
  15. Xie, G., Song, Y., Asadi, M., and Lorenzini, G., "Optimization of pin-fins for a heat exchanger by entropy generation minimization and constructal law." Journal of Heat Transfer, 137.6: 061901, 2015. doi.org/10.1115/1.4029851.
  16. Bejan, A., & Sciubba, E., "The optimal spacing of parallel plates cooled by forced convection." International Journal of Heat and Mass Transfer, 35(12), 3259-3264. doi.org/10.1016/0017-9310(92)90213-C
  17. Herwig, H., and Schmandt, B. "How to determine losses in a flow field: A paradigm shift towards the second law analysis." Entropy 16.6 (2014): 2959-2989. dx.doi.org/10.3390/e16062959
  18. Borisov, A. V., Kuznetsov, S. P., Mamaev, I. S., and Tenenev, V. A. "Describing the motion of a body with an elliptical cross section in a viscous uncompressible fluid by model equations reconstructed from data processing." Technical Physics Letters, 42(9):886-890, 2016. doi.org/10.1134/S1063785016090042.
  19. Chernov, N. N., Palii, A. V., Saenko, A. V., and Maevskii, A. M. "A Method of Body Shape Optimization for Decreasing the Aerodynamic Drag Force in Gas Flow." Technical Physics Letters, 44(4):328-330, 2018. doi.org/10.1134/S106378501804017X
  20. Rastan, M. R., Foshat, S., and Sekhavat, S. "High-Reynolds number flow around coated symmetrical hydrofoil: effect of streamwise slip on drag force and vortex structures." Journal of Marine Science and Technology, 1-12, 2018. doi.org/10.1007/s00773-018-0570-2
  21. Czyż, Z., Karpiński, P., Gęca, M., and Diaz, J. U. "The air flow influence on the drag force of a sports car." Advances in Science and Technology. Research Journal, 12(2), 2018. doi.org/10.12913/22998624/86213
  22. Giese, M., Reimann, T., Bailly‐Comte, V., Maréchal, J. C., Sauter, M., and Geyer, T. "Turbulent and Laminar Flow in Karst Conduits Under Unsteady Flow Conditions: Interpretation of Pumping Tests by Discrete Conduit‐Continuum Modeling." Water Resources Research, 54(3): 1918-1933, 2018. doi.org/10.1002/2017WR020658
  23. Pimenta, B. D., Robaina, A. D., Peiter, M. X., Mezzomo, W., Kirchner, J. H., and Ben, L. H. "Performance of explicit approximations of the coefficient of head loss for pressurized conduits." Revista Brasileira de Engenharia Agrícola e Ambiental, 22(5):301-307, 2018. dx.doi.org/10.1590/1807-1929/agriambi.v22n5p301-307
  24. Paez, D., Suribabu, C. R., and Filion, Y. "Method for Extended Period Simulation of Water Distribution Networks with Pressure Driven Demands." Water Resources Management, 32(8):2837-2846, 2018. doi.org/10.1007/s11269-018-1961-1
  25. Fontana, N., Giugni, M., Glielmo, L., Marini, G., and Zollo, R. "Hydraulic and Electric Regulation of a Prototype for Real-Time Control of Pressure and Hydropower Generation in a Water Distribution Network." Journal of Water Resources Planning and Management, 144(11):04018072, 2018. doi.org/10.1061/(ASCE)WR.1943-5452.0001004
  26. Drela, M., "Power balance in aerodynamic flows." AIAA journal, 47(7):1761-1771, 2009. doi.org/10.2514/1.42409.
  27. Li, K.W. "Applied thermodynamics: availability method and energy conversion." CRC Press, 1995, ISBN 9781560323495. www.crcpress.com/Applied-Thermodynamics-Availability-Method-And-Energy-Conversion/Li/p/book/9781560323495.
  28. Hayes, D., et al. "Entropy Generation Minimisation and Exergy analysis approaches for aerospace applications-A review." 54th AIAA Aerospace Sciences Meeting. 2016. doi.org/10.2514/6.2016-0866
  29. Tuck, A. F. "Proposed empirical entropy and Gibbs energy based on observations of scale invariance in open nonequilibrium systems." The Journal of Physical Chemistry A, 121.35: 6620-6629, 2017. doi.org/10.1021/acs.jpca.7b03112
  30. Ward-Smith, A. J., "Internal Fluid Flow-The fluid dynamics of flow in pipes and ducts." Nasa Sti/recon Technical Report A, 81, 1980. adsabs.harvard.edu/abs/1980STIA...8138505W
  31. Johnson, R. W., "Handbook of fluid dynamics." Crc Press, 2016. ISBN13: 978-1-4398-4957-6 www.crcpress.com/Handbook-of-Fluid-Dynamics/Johnson/p/book/9781439849552
  32. Trancossi, M., Pascoa, J., & Cannistraro, G., "Safety Analysis of an Airship Which Loses Lifting Gas from the Hull." SAE Technical Paper No. 2018-01-1954, 2018. doi.org/10.4271/2018-01-1954
  33. Driver, R. D., "Torricelli's law - an ideal example of an elementary ODE." The American mathematical monthly, Vol. 105, n. 5, pp. 453-455, 1998. doi.org/10.2307/3109809
  34. Shin, J. H., "Computational study on dynamic pressure in a swash-plate axial piston pump connected to a hydraulic line with an end resistance." Journal of Mechanical Science and Technology, Vol. 29, No. 6, pp. 2381-2390, 2015. doi.org/10.1007/s12206-015-0531-1
  35. Naterer, G. F., and Camberos, J. A., "Entropy based design and analysis of fluids engineering systems." CRC press, 2008. www.taylorfrancis.com/books/9781420006919
  36. Arntz, A., O. Atinault, and D. Destarac. "Numerical Airframe Aerodynamic Performance Prediction: An Exergy Point of View." 49th International Symposium of Applied Aerodynamics. 2014. hal-onera.archives-ouvertes.fr/hal-01059075/document
  37. Arntz, A., Atinault O., and Merlen A., "Exergy-based formulation for aircraft aeropropulsive performance assessment: theoretical development." AIAA Journal Vol. 53 No.6 pp:1627-1639, 2014. doi.org/10.2514/1.J053467
  38. Bejan, A., & Lorente, S. (2011). "The constructal law and the evolution of design in nature." Physics of life Reviews, 8(3), 209-240. doi.org/10.1016/j.plrev.2011.05.010
  39. Bejan, A., and S. Lorente. "The constructal law and the thermodynamics of flow systems with configuration." International journal of heat and mass transfer Vol. 47. No. 14-16 pp. 3203-3214. 2004. doi.org/10.1016/j.ijheatmasstransfer.2004.02.007
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Diffusive Bejan number and second law of thermodynamics toward a new dimensionless formulation of fluid dynamics laws

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence