, 90:64 | Cite as

Numerical study of entropy generation and melting heat transfer on MHD generalised non-Newtonian fluid (GNF): Application to optimal energy

  • Z Iqbal
  • Zaffar Mehmood
  • Bilal Ahmad


This paper concerns an application to optimal energy by incorporating thermal equilibrium on MHD-generalised non-Newtonian fluid model with melting heat effect. Highly nonlinear system of partial differential equations is simplified to a nonlinear system using boundary layer approach and similarity transformations. Numerical solutions of velocity and temperature profile are obtained by using shooting method. The contribution of entropy generation is appraised on thermal and fluid velocities. Physical features of relevant parameters have been discussed by plotting graphs and tables. Some noteworthy findings are: Prandtl number, power law index and Weissenberg number contribute in lowering mass boundary layer thickness and entropy effect and enlarging thermal boundary layer thickness. However, an increasing mass boundary layer effect is only due to melting heat parameter. Moreover, thermal boundary layers have same trend for all parameters, i.e., temperature enhances with increase in values of significant parameters. Similarly, Hartman and Weissenberg numbers enhance Bejan number.


Tangent hyperbolic fluid numerical solutions melting heat transfer entropy generation optimal energy 


44.25.+f 47.50.−d 


  1. 1.
    L Ai and K Vafai, Num. Heat Transfer 47, 955 (2005)CrossRefGoogle Scholar
  2. 2.
    A J Friedman, S J Dyke and B M Phillips, Smart Mater. Struct. 22, 045001 (2013)ADSCrossRefGoogle Scholar
  3. 3.
    B C Sakiadis, AIChE J. 7, 26 (1961)CrossRefGoogle Scholar
  4. 4.
    L J Crane, Z. Angew. Math. Phys. 21, 645 (1970)Google Scholar
  5. 5.
    P S Gupta and A S Gupta, Can. J. Chem. Engg. 55, 744 (1977)CrossRefGoogle Scholar
  6. 6.
    T Hayat, Z Abbas and M Sajid, Chaos Solitons Fractals 29, 840 (2009)ADSCrossRefGoogle Scholar
  7. 7.
    S Nadeem, A Hussain and M Khan, Commun. Non-Linear Sci. Numer. Simulat. 15, 475 (2010)ADSCrossRefGoogle Scholar
  8. 8.
    V I Vishnyakov and K B Pavlov, Magnetohydro-dynamics 8, 174 (1972)Google Scholar
  9. 9.
    R Moreau, Magnetohydrodynamics (Kluwer Academic Publishers, Dordrecht, 1990)CrossRefzbMATHGoogle Scholar
  10. 10.
    P Singh and C B Gupta, Indian J. Theor. Phys. 53, 111 (2005)Google Scholar
  11. 11.
    A Bejan, Adv. Heat Transfer 15, 1 (1982)ADSCrossRefGoogle Scholar
  12. 12.
    A Bejan, J. Appl. Phys. 79, 1191 (1996)ADSCrossRefGoogle Scholar
  13. 13.
    A Bejan, J. Heat Transfer 101, 718 (1979)CrossRefGoogle Scholar
  14. 14.
    A Z Sahin, J. Heat Transfer 120, 76 (1998)MathSciNetCrossRefGoogle Scholar
  15. 15.
    A Falahat, IJMSE 2, 44 (2011)Google Scholar
  16. 16.
    A Z Sahin, Heat Mass Transfer 35, 499 (1999)ADSCrossRefGoogle Scholar
  17. 17.
    S Mahmud and R A Fraser, Int. J. Therm. Sci. 42, 177 (2003)CrossRefGoogle Scholar
  18. 18.
    S Mahmud and R A Fraser, Exergy 2, 140 (2002)CrossRefGoogle Scholar
  19. 19.
    S Saouli and S A Saouli, Int. Comm. Heat Mass Transfer 31, 879 (2004)CrossRefGoogle Scholar
  20. 20.
    N C Peddisetty, Pramana – J. Phys. 87: 62 (2016)ADSCrossRefGoogle Scholar
  21. 21.
    M M Bhatti, A Zeeshan and R Ellahi, Pramana – J. Phys. 89: 48 (2017)ADSCrossRefGoogle Scholar
  22. 22.
    N S Akbar, S Nadeem, R Ul Haq and Z H Khan, Indian J. Phys. 87, 1121 (2013)ADSCrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 2018

Authors and Affiliations

  1. 1.Department of MathematicsHITEC UniversityTaxilaPakistan

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