Entropy generation effects in a hydromagnetic free convection flow past a vertical oscillating plate



An unsteady free convective flow of a viscous fluid past an oscillating plate is considered, and the effects of entropy generation are investigated. The governing partial differential equations are normalized by using suitable transformations, and an exact solution of the problem is obtained by using the Laplace transformation technique. The expressions for the velocity and temperature are then used to compute the skin friction, Nusselt number, local entropy generation number, and Bejan number.


entropy free convection oscillating plate magnetic field 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    H. Schlichting and K. Gersten, Boundary Layer Theory (Springer, Berlin, 2000).CrossRefMATHGoogle Scholar
  2. 2.
    M. J. Lighthill, “The Response of Skin Friction and Heat Transfer to Fluctuations in the Stream Velocity,” Proc. Roy. Soc. London, Ser. A, 224, 1–23 (1954).ADSMathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    J. T. Stuart, “A Solution of the Navier–Stokes and Energy Equations Illustrating the Response of Skin Friction and Temperature of an Infinite Plate Thermometer to Fluctuations in the Stream Velocity,” Proc. Roy. Soc. London, Ser. A 231, 116–130 (1955).ADSMathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    R. S. Ong and J. A. Nicholls, “Flow of a Magnetic Field near an Infinite Oscillating Flat Wall,” J. Aerospace Sci. 26 313–314 (1959).MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    R. S. Nanda and V. P. Sharma, “Free Convection Boundary Layers in Oscillatory Flow,” J. Fluid Mech. 15 419–428 ( 1963).Google Scholar
  6. 6.
    R. Penton, “The Transient for Stokes Oscillating Plane: A Solution in Terms of Tabulated Functions,” J. Fluid Mech. 31, 819–825 (1968).ADSCrossRefGoogle Scholar
  7. 7.
    V. M. Soundalgekar, “Free Convection Effects on the Flow Past an Infinite Vertical Oscillating Plate,” Astrophys. Space Sci. 89, 241–254 (1983).ADSCrossRefMATHGoogle Scholar
  8. 8.
    V. M. Soundalgekar and S. P. Akolkar, “Effect of Free Convection Currents and Mass Transfer on Flow Past a Vertical Oscillating Plate,” Astrophys. Space Sci. 64, 165–171 (1979).ADSCrossRefMATHGoogle Scholar
  9. 9.
    R. C. Choudhary, “Hydromagnetic Flow near an Oscillating Porous Flat Plate,” Proc. Indian Acad. Sci. 86A (6), 531–535 (1977).ADSMATHGoogle Scholar
  10. 10.
    P. Puri and P. K. Kythe, “Thermal Effect in Stokes Second Problem,” Acta Mech. 112, 44–50 (1998).Google Scholar
  11. 11.
    M. E. Erdogan, “A Note on an Unsteady Flow of a Viscous Fluid Due to an Oscillating Plane Wall,” J. Non-Linear Mech. 35, 1–6 (2000).MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    K. Vajravelu and J. Rivera, “Hydromagnetic Flow at an Oscillating Plate,” Int. J. Non-Linear Mech. 38, 305–312 (2003).ADSCrossRefMATHGoogle Scholar
  13. 13.
    C. M. Liu, H. H. Hwung, and C. H. Kong, “The Unsteady Viscous Flow Generated by an Oscillating Porous Plate,” J. Mech. 24 (2), 145–152 (2008).CrossRefGoogle Scholar
  14. 14.
    I. Khan, K. Fakhar, and S. Shafie, “Magnetohydrodynamic Free Convection Flow Past an Oscillating Plate Embedded in a Porous Medium,” J. Phys. Soc. Jpn. 80, 104401–104410 (2011).ADSCrossRefGoogle Scholar
  15. 15.
    I. Khan, A. Hussanan, M. Imran, et al., “Natural Convection Flow Past an Oscillating Plate with Newtonian Heating,” Heat Trans. Res. 42 (2), 119–135 (2014); DOI: 10.1615/HeatTransRes.2013006385.Google Scholar
  16. 16.
    A. Bejan, “A Study of Entropy Generation in Fundamental Convective Heat Transfer,” J. Heat Transfer 101, 718–725 (1979).CrossRefGoogle Scholar
  17. 17.
    M. Q. A. Odat, R. A. Damseh, and M. A. A. Nimr, “Effect of Magnetic Field on Entropy Generation Due to Laminar Forced Convection Past a Horizontal Flat Plate,” Entropy 4, 293–303 (2004).CrossRefMATHGoogle Scholar
  18. 18.
    O. D. Makinde and E. Osalusi, “Entropy Generation in a Liquid Film Falling along an Inclined Porous Heated Plate,” Mech. Res. Comm. 33(5), 692–698 (2006).CrossRefMATHGoogle Scholar
  19. 19.
    O. D. Makinde, Irreversibility Analysis for a Gravity Driven Non-Newtonian Liquid Film along an Inclined Isothermal Plate, Phys. Scripta. 74, 642–645 (2006).ADSCrossRefMATHGoogle Scholar
  20. 20.
    A. Reveillere and A. C. Baytas, “Minimum Entropy Generation for Laminar Boundary Layer Flow over a Permeable Plate,” Int. J. Exergy. 7 (2), 164–177 (2010).CrossRefGoogle Scholar
  21. 21.
    O. D. Makinde, “Thermodynamic Second Law Analysis for a Gravity Driven Variable Viscosity Liquid Film along an Inclined Heated Plate with Convective Cooling,” J. Mech. Sci. Tech. 24 (4), 899–908 (2010).CrossRefGoogle Scholar
  22. 22.
    O. D. Makinde “Entropy Analysis for MHD Boundary Layer Flow and Heat Transfer over a Flat Plate with a Convective Surface Boundary Condition,” Int. J. Exergy 10 (2) 142–154 2012.CrossRefGoogle Scholar
  23. 23.
    O. D. Makinde, “Second Law Analysis for Variable Viscosity Hydromagnetic Boundary Layer Flow with Thermal Radiation and Newtonian Heating,” Entropy 13, 1446–1464 (2011).ADSCrossRefMATHGoogle Scholar
  24. 24.
    A. S. Butt, S. Munawar, A. Ali, and A. Mehmood, “Entropy Generation in the Blasius Flow under Thermal Radiation,” Phys. Scripta 85, 035008 (2012); DOI: 10.1088/0031-8949/85/03/035008.ADSCrossRefMATHGoogle Scholar
  25. 25.
    A. S. Butt, S. Munawar, A. Ali, and A. Mehmood, “Entropy Generation in Hydrodynamic Slip Flow over a Vertical Plate with Convective Boundary,” J. Mech. Sci. Tech. 26 (9), 2977–2984 (2012).CrossRefGoogle Scholar
  26. 26.
    A. S. Butt and A. Ali, “Entropy Effects in Hydromagnetic Free Convection Flow Past a Vertical Plate Embedded in a Porous Medium in the Presence of Thermal Radiation,” Eur. Phys. J. Plus. 128 (5), 1–15 (2013); DOI: 10.1140/epjp/i2013-13051-y.CrossRefGoogle Scholar
  27. 27.
    B. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1970).MATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Department of MathematicsQuaid-i-Azam UniversityIslamabadPakistan

Personalised recommendations