THERMAL SCIENCE

International Scientific Journal

Mohammad Reza Mohaghegh

,

Javad Abolfazli Esfahani

ENTROPY GENERATION ANALYSIS OF FREE CONVECTION FROM A CONSTANT TEMPERATURE VERTICAL PLATE USING SIMILARITY SOLUTION

ABSTRACT
This paper presents a similarity solution analysis of entropy generation due to heat transfer and fluid flow which has been carried out for laminar free convection from a constant temperature vertical plate in an infinite quiescent fluid. The governing partial differential equations are transformed into a set of ordinary differential equations using similarity variables. So an analytical expression, in terms of entropy generation, entropy generation number, Bejan number and irreversibility distribution ratio are derived using velocity and temperature similarity (exact) solution. The rate of entropy generation is investigated and discussed in details. The results presented by the similarity solution are compared with integral method results. The similarity solution presents more appropriate and correct distribution of entropy generation in boundary layer because more accuracy than integral method. It shows true position of maximum entropy generation and value of it. Also, the result shows that the exact solution minimizes the rate of total entropy generation in the boundary layer compared to integral solution. By introducing group parameter (GP number) which is the ratio of friction entropy to thermal entropy generation, one can recognize that one of the thermal entropy and friction entropy generation is dominated in the boundary layer.
KEYWORDS
entropy generation, laminar free convection, similarity solution, integral method, GP number
PAPER SUBMITTED: 2014-01-03
PAPER REVISED: 2014-07-16
PAPER ACCEPTED: 2014-07-19
PUBLISHED ONLINE: 2014-08-03
DOI REFERENCE: https://doi.org/10.2298/TSCI140103092M
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2016, VOLUME 20, ISSUE Issue 6, PAGES [1855 - 1866]
REFERENCES
  1. Bejan, A., Second law analysis in heat transfer. Energy, 1980. 5: p. 721-732.
  2. Bejan, A., Entropy Generation Through Heat and Fluid Flow. 1982, New York, USA John Wiley & Sons. chapter 2 and 5.
  3. Bejan, A., Thermodynamic of an isothermal flow: The two dimensional turbulent jet. Int. J. Heat and Mass Transfer, 1991. 34: p. 407-413.
  4. Esfahani, J.A. and M. Malek Jafarian, Entropy Generation Analysis of a Flat Plate Boundary Layer with Various Solution Methods. Scientia Iranica, 2005. 12(2): p. 233-240.
  5. Esfahani, J.A. and S. Koohi-Fayegh, Entropy Generation Analysis In Error Estimation Of An Approximate Solution: A Constant Surface Temperature Semi-Infinite Conductive Problem. Thermal Science, 2009. 13 (2): p. 133-140.
  6. Andreozzi, A., A. Auletta, and O. Manca, Entropy generation in natural convection in a symmetrically and uniformly heated vertical channel. International Journal of Heat and Mass Transfer, 2006. 49(17-18): p. 3221-3228.
  7. Ozkol, I., G. Komurgoz, and A. Arıkoglu, Entropy generation in laminar natural convection from a constant temperature vertical plate in an infinite fluid. Proc. IMechE, Part A: J. Power and Energy, 2007. 221: p. 609-616.
  8. Weigand, B. and A. Birkefeld, Similarity solutions of the entropy transport equation. International Journal of Thermal Sciences, 2009. 48(10): p. 1863-1869.
  9. Mukhopadhyay, A., Analysis of entropy generation due to natural convection in square enclosures with multiple discrete heat sources. International Communications in Heat and Mass Transfer, 2010. 37: p. 867-872.
  10. Sun, H., et al., Optimal plate spacing for mixed convection from an array of vertical isothermal plates. International Journal of Thermal Sciences, 2012. 55: p. 16-30.
  11. Ibáñez, G., et al., Optimum slip flow based on the minimization of entropy generation in parallel plate microchannels. Energy, 2013. 50: p. 143-149.
  12. Esfahani, J.A., M. Modirkhazeni, and S. Mohammadi, Accuracy analysis of predicted velocity profiles of laminar duct flow with entropy generation method. Applied Mathematics and Mechanics, 2013. 34(8): p. 971-984.
  13. Amani, E. and M.R.H. Nobari, A numerical investigation of entropy generation in the entrance region of curved pipes at constant wall temperature. Energy, 2011. 36(8): p. 4909-4918.
  14. Chen, C.o.-K., H.-Y. Lai, and C.-C. Liu, Numerical analysis of entropy generation in mixed convection flow with viscous dissipation effects in vertical channel. International Communications in Heat and Mass Transfer, 2011. 38(3): p. 285-290.
  15. Atashafrooz, M., S.A. Gandjalikhan Nassab, and A.B. Ansari, Numerical investigation of entropy generation in laminar forced convection flow over inclined backward and forward facing steps in a duct under bleeding condition. Thermal Science, 2014. 18(2): p. 479-492.
  16. Oztop, H.F. and K. Al-Salem, A review on entropy generation in natural and mixed convection heat transfer for energy systems. Renewable and Sustainable Energy Reviews, 2012. 16(1): p. 911-920.
  17. Abolfazli Esfahani, J. and M. Modirkhazeni, Entropy generation of forced convection film condensation on a horizontal elliptical tube. Comptes Rendus Mأ©canique, 2012. 340(7): p. 543-551.
  18. Mahian, O., et al., Design of a vertical annulus with MHD flow using entropy generation analysis. Thermal Science, 2013. 17(4): p. 1013-1022.
  19. Kargaran, M., et al., The second law analysis of natural gas behaviour within a vortex tube. Thermal Science, 2013. 17(4): p. 1079-1092.
  20. Mwesigye, A., T. Bello-Ochende, and J.P. Meyer, Minimum entropy generation due to heat transfer and fluid friction in a parabolic trough receiver with non-uniform heat flux at different rim angles and concentration ratios. Energy, 2014(0).
  21. Ghasemi, E., et al., Effects of adverse and favorable pressure gradients on entropy generation in a transitional boundary layer region under the influence of freestream turbulence. International Journal of Heat and Mass Transfer, 2014. 77(0): p. 475-488.
  22. El-Maghlany, W.M., K.M. Saqr, and M.A. Teamah, Numerical simulations of the effect of an isotropic heat field on the entropy generation due to natural convection in a square cavity. Energy Conversion and Management, 2014. 85(0): p. 333-342.
  23. Bejan, A., Convection Heat Transfer. 2nd ed. 1993: John Wiley & Sons.
  24. Bejan, A., Entropy generation minimization. 1996: Boca Raton: CRC Press.
  25. Von Karman, T., Z. Angew. Math. Mech. 1921. 1(233).
  26. Squire, H.B., In Modern Developments in Fluid Dynamics, ed. S. Goldstein. 1938, New York: Oxford University Press.
  27. Gebhart, B., et al., Buoyancy -Induced Flows and Transport. Reference ed. 1988, New York: Hemisphere Publishing Corporation.
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Entropy generation analysis of free convection from a constant temperature vertical plate using similarity solution

© 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