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Entropy analysis for nanofluid flow over a stretching sheet in the presence of heat generation/absorption and partial slip

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Abstract

The boundary layer heat transfer and entropy generation of a nanofluid over an isothermal linear stretching sheet with heat generation/ absorption have been analyzed. In the nanofluid model, the development of nanoparticles concentration gradient due to slip mechanisms, the effects of Brownian motion and thermophoresis, is taken into account. The dependency of the local Nusselt number and entropy generation number on the non-dimensional parameters is numerically investigated. The results show that the increase of heat generation parameter, Brownian motion parameter, or thermophoresis parameter decreases the entropy generation number in the vicinity of the sheet.

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References

  1. E. G. Fisher, Extrusion of plastics, Wiley, New York (1976).

    Google Scholar 

  2. Z. Tadmor and I. Klein, Engineering principles of plasticating extrusion, Van Nostrand Reinhold, New York (1970).

    Google Scholar 

  3. E. M. A. Elbashbeshy and M. A. A. Bazid, Heat transfer over an unsteady stretching surface, Heat and Mass Transfer, 41(1) (2004) 1–4.

    Article  Google Scholar 

  4. A. Tamayol, K. Hooman and M. Bahrami, Thermal analysis of flow in a porous medium over a permeable stretching wall, Transport in Porous Media, 85 (2010) 661–676.

    Article  MathSciNet  Google Scholar 

  5. B. C. Sakiadis, Boundary-layer behavior on continuous solid surface: I. Boundary-layer equations for two-dimensional and axisymmetric flow, J AIChe, 7 (1961) 26–33.

    Article  Google Scholar 

  6. K. Das, Slip flow and convective heat transfer of nanofluids over a permeable stretching surface, Computers & Fluids, 64(15) (2012) 34–42.

    Article  MathSciNet  Google Scholar 

  7. T. Hayat, M. Qasim and S. Mesloub, MHD flow and heat transfer over permeable stretching sheet with slip conditions, Int. J. for Numerical Methods in Fluids, 66(8) (2011) 963–975.

    Article  MathSciNet  MATH  Google Scholar 

  8. O. D. Makinde, Computational modelling of MHD unsteady flow and heat transfer toward a flat plate with Navier slip and Newtonian heating, Braz. J. Chem. Eng, 29(1) (2012) 159–166.

    Article  Google Scholar 

  9. O. D. Makinde and P. Sibanda, Effects of chemical reaction on boundary layer flow past a vertical stretching surface in the presence of internal heat generation, Int. J. of Numerical Methods for Heat & Fluid Flow, 21(6) (2011) 779–792.

    Article  Google Scholar 

  10. A. Mehmood, A. Ali and T. Shah, Heat transfer analysis of unsteady boundary layer flow by homotopy analysis method, Communications in Nonlinear Science and Numerical Simulation, 13(5) (2008) 902–912.

    Article  MathSciNet  MATH  Google Scholar 

  11. S. Kiwan and M. E. Ali, Near-Slit effects on the flow and heat transfer from a stretching plate in a porous medium, Numerical Heat Transfer, Part A: Applications, 54(1) (2008) 93–108.

    Article  Google Scholar 

  12. A. Alsaedi, M. Awais and T. Hayat, Effects of heat generation/absorption on stagnation point flow of nanofluid over a surface with convective boundary conditions, Commun Nonlinear Sci Numer Simulat, 17(11) (2012) 4210–4223.

    Article  MathSciNet  MATH  Google Scholar 

  13. W. A. Khan and I. Pop, Boundary-layer flow of a nanofluid past a stretching sheet, Int. J. of Heat and Mass Transfer, 53(11–12) (2010) 2477–2483.

    Article  MATH  Google Scholar 

  14. A. Noghrehabadi, R. Pourrajab and M. Ghalambaz, Effect of partial slip boundary condition on the flow and heat transfer of nanofluids past stretching sheet prescribed constant wall temperature, Int. J. Thermal Sci., 54 (2012) 253–261.

    Article  Google Scholar 

  15. A. Bejan, Second-law analysis in heat transfer and thermal design, Adv. Heat Transfer, 15 (1982) 1–58.

    Article  Google Scholar 

  16. A. Bejan, Entropy generation minimization, CRC Press, Boca Raton, New York (1996).

    MATH  Google Scholar 

  17. B. Weigand and A. Birkefeld, Similarity solutions of the entropy transport equation, Int. J. Therm. Sci, 48 (2009) 1863–1869.

    Article  Google Scholar 

  18. O. D. Makinde, Second law analysis for variable viscosity hydromagnetic boundary layer flow with thermal radiation and Newtonian heating, Entropy, 13 (2011) 1446–1464.

    Article  Google Scholar 

  19. O. D. Makinde, Thermodynamic second law analysis for a gravity-driven variable viscosity liquid film along an inclined heated plate with convective cooling, Journal of Mechanical Science and Technology, 24(4) (2010) 899–908.

    Article  Google Scholar 

  20. M. Esmaeilpour and M. Abdollahzadeh, Free convection and entropy generation of nanofluid inside an enclosure with different patterns of vertical wavy walls, Int. J. Therm. Sci., 52 (2012) 127–136.

    Article  Google Scholar 

  21. M. Majumder, N. Chopra, R. Andrews and B. J. Hinds, Nanoscale hydrodynamics: Enhanced flow in carbon nanotubes, Nature, 438 (2005).

  22. R. A. Van Gorder, E. Sweet and K. Vajravelu, Nano boundary layers over stretching surfaces, Commun. Nonlinear Sci. Numer. Simulat, 15(6) (2010) 1494–1500.

    Article  MATH  Google Scholar 

  23. C. Y. Wang, Analysis of viscous flow due to a stretching sheet with surface slip and suction, Nonlinear Analysis: Real World Applications, 10(1) (2009) 375–380.

    Article  MathSciNet  MATH  Google Scholar 

  24. O. D. Makinde and A. Aziz, Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition, Int. J. Therm. Sci., 50 (2011) 1326–32.

    Article  Google Scholar 

  25. M. A. A. Hamad and M. Ferdows, Similarity solution of boundary layer stagnation-point flow towards a heated porous stretching sheet saturated with a nanofluid with heat absorption/generation and suction/blowing: A Lie group analysis, Commun. Nonlinear Sci. and Numer. Simulat, 17(1) (2012) 132–40.

    Article  MathSciNet  MATH  Google Scholar 

  26. A. V. Kuznetsov and D. A. Nield, Natural convective boundary-layer flow of a nanofluid past a vertical plate, Int. J. Therm. Sci., 49 (2010) 243–247.

    Article  Google Scholar 

  27. D. A. Nield and A. V. Kuznetsov, The Cheng-Minkowycz problem for natural convective boundary-layer flow in a porous medium saturated by a nanofluid, Int. J. Heat Mass Transfer, 52(25–26) (2009) 5792–5795.

    Article  MATH  Google Scholar 

  28. B. Sahoo and Y. Do, Effects of slip on sheet-driven flow and heat transfer of a third grade fluid past a stretching sheet, Int. Commun. Heat and Mass Transfer, 37(8) (2010) 1064–1071.

    Article  Google Scholar 

  29. C. Y. Wang, Flow due to a stretching boundary with partial slip—an exact solution of the Navier-Stokes equations, Chemical Engineering Science, 57 (2002) 3745–3747.

    Article  Google Scholar 

  30. L. C. Woods, Thermodynamics of fluid systems, Oxford University Press, Oxford (1975).

    Google Scholar 

  31. M. Mourad, A. Hassen, H. Nejib and B. B. Ammar, Second law analysis in convective heat and mass transfer, Entropy, 8 (2006) 1–17.

    Article  Google Scholar 

  32. H. F. Oztop and K. Al-Salem, A review on entropy generation in natural and mixed convection heat transfer for energy systems, Renewable and Sustainable Energy Reviews, 16(1) (2012) 911–920.

    Article  Google Scholar 

  33. K. Ghachem, L. Kolsi, C. Maatki, A. K. Hussein and M. N. Borjini, Numerical simulation of three-dimensional double diffusive free convection flow and irreversibility studies in a solar distiller, Int. Comm. Heat Mass Transfer, 39(6) (2012) 869–876.

    Article  Google Scholar 

  34. E. Fehlberg, Low-order classical Runge-Kutta formulas with step size control and their application to some heat transfer problems, in: Technical Report, NASA (1969).

    Google Scholar 

  35. E. Fehlberg, Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf Warmeleitungsprobleme, Computing Arch. Elektron. Rechnen, 6(1–2) (1970) 61–71.

    MathSciNet  MATH  Google Scholar 

  36. H. I. Andersson, Slip flow past a stretching surface, Acta Mech, 158(1–2) (2002) 121–125.

    Article  MATH  Google Scholar 

  37. I. Pop and D. B. Ingham, Convective heat transfer: mathematical and computational modelling of viscous fluids and porous media, Elsevier Science & Technology Books, 2001.

    Google Scholar 

  38. J. Buongiorno, Convective transport in nanofluids, J. of Heat Transfer, 128(3) (2006) 240–250.

    Article  Google Scholar 

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Correspondence to Aminreza Noghrehabadi.

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Recommended by Associate Editor Dongsik Kim

Aminreza Noghrehabadi is an assistant professor in the department of Mechanical Egineering at Shahid Chamran University of Ahvaz. His research interests are in nanofluid heat and mass transfer, NEMS actuators, and heat transfer in porous media.

Mohammad Reza Saffarian is an assistant professor in the department of Mechanical Engineering, Shahid Chamran University of Ahvaz. His research interests are in non-Newtonian fluid mechanics, settling tanks, gas tTurbines, and heating, ventilating, and air conditioning.

Rashid Pourrajab is a M.Sc. student in the department of mechanical engineering at Shahid Chamran University of Ahvaz. His research has been mainly focused on the development of new heat transfer enhancement fluid called nanofluids. He is working on modeling, production and experiments with nanofluids.

Mohammad Ghalambaz is currently Ph.D. student in the department of mechanical engineering at Shahid Chamran University of Ahvaz. His research interests are on the field of Nanofluid heat and mass transfer, NEMS actuators and Swarm optimization techniques.

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Noghrehabadi, A., Saffarian, M.R., Pourrajab, R. et al. Entropy analysis for nanofluid flow over a stretching sheet in the presence of heat generation/absorption and partial slip. J Mech Sci Technol 27, 927–937 (2013). https://doi.org/10.1007/s12206-013-0104-0

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  • DOI: https://doi.org/10.1007/s12206-013-0104-0

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