, 92:12 | Cite as

Nonlinear stability and thermomechanical analysis of hydromagnetic Falkner–Skan Casson conjugate fluid flow over an angular–geometric surface based on Buongiorno’s model using homotopy analysis method and its extension

  • Emran Khoshrouye Ghiasi
  • Reza SalehEmail author


This paper aims to provide stability and thermomechanical analysis of hydromagnetic Falkner–Skan Casson conjugate fluid flow over an angular–geometric wedge-shaped surface. Based on the Buongiorno’s model, the governing boundary-layer equations are derived and solved iteratively using the homotopy analysis method (HAM). Furthermore, the HAM-series solution is optimised by minimising its squared residual errors. It is shown that the proposed approach can serve as an efficient criterion for accurately solving nonlinear problems.


Casson Falkner–Skan fluid flow Buongiorno’s model homotopy analysis method convergence velocity profile 




  1. 1.
    V M Falkner and S W Skan, Philos. Mag. 12, 865 (1931)CrossRefGoogle Scholar
  2. 2.
    H Schlichting, Boundary-layer theory, 7th edn (McGraw-Hill, New York, 1978)zbMATHGoogle Scholar
  3. 3.
    J Buongiorno, ASME J. Heat Transfer 128, 240 (2006)CrossRefGoogle Scholar
  4. 4.
    T Hussain, S A Shehzad, A Alsaedi, T Hayat and M Ramzan, J. Cent. South Univ. 22, 1132 (2015)CrossRefGoogle Scholar
  5. 5.
    C S K Raju, M M Hoque and T Sivasankar, Adv. Powder Technol. 28, 575 (2017)CrossRefGoogle Scholar
  6. 6.
    G Kumaran and N Sandeep, J. Mol. Liq. 233, 262 (2017)CrossRefGoogle Scholar
  7. 7.
    N S Akbar, J. Magn. Magn. Mater. 378, 463 (2015)ADSCrossRefGoogle Scholar
  8. 8.
    K U Rehman, A Qaiser, M Y Malik and U Ali, Chin. J. Phys. 55, 1605 (2017)CrossRefGoogle Scholar
  9. 9.
    G S Seth, R Tripathi and M K Mishra, Appl. Math. Mech. 38, 1613 (2017)CrossRefGoogle Scholar
  10. 10.
    M S Abel, J Tawade and M M Nandeppanavar, Int. J. Nonlinear Mech. 44, 990 (2009)ADSCrossRefGoogle Scholar
  11. 11.
    N Casson, Rheology of dispersed systems (C.C. Mills, New York, 1959)Google Scholar
  12. 12.
    M Nakamura and T Sawada, J. Non-Newton. Fluid 22, 191 (1987)CrossRefGoogle Scholar
  13. 13.
    M Nakamura and T Sawada, J. Biomech. Eng. Trans. ASME 110, 137 (1988)CrossRefGoogle Scholar
  14. 14.
    E C Bingham, Fluidity and plasticity (McGraw-Hill, New York, 1922)Google Scholar
  15. 15.
    F M White, Viscous fluid flow, 2nd edn (McGraw-Hill, New York, 1991)Google Scholar
  16. 16.
    K Ahmad, Z Hanouf and A Ishak, Eur. Phys. J. Plus 132, 87 (2017)CrossRefGoogle Scholar
  17. 17.
    S J Liao, The proposed homotopy analysis technique for the solution of nonlinear problems, Ph.D. thesis (Shanghai Jiao Tong University, Shanghai, 1992)Google Scholar
  18. 18.
    S J Liao, Beyond perturbation: Introduction to the homotopy analysis method (Chapman & Hall\(/\)CRC Press, Boca Raton, 2003)Google Scholar
  19. 19.
    S J Liao, Commun. Nonlinear Sci. Numer. Simul. 14, 983 (2009)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    S J Liao, Appl. Math. Mech. 19, 957 (1998)CrossRefGoogle Scholar
  21. 21.
    S J Liao, Appl. Math. Comput. 147, 499 (2004)MathSciNetGoogle Scholar
  22. 22.
    B Yao and J Chen, Appl. Math. Comput. 208, 156 (2009)MathSciNetGoogle Scholar
  23. 23.
    E Khoshrouye Ghiasi and R Saleh, Results Phys. 11, 65 (2018)Google Scholar
  24. 24.
    J Cheng, S J Liao, R N Mohapatra and K Vajravelu, J. Math. Anal. Appl. 343, 233 (2008)MathSciNetCrossRefGoogle Scholar
  25. 25.
    M N Tufail, A S Butt and A Ali, J. Appl. Mech. Tech. Phys. 57, 900 (2016)ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    M S Hashmi, N Khan, T Mahmood and S A Shehzad, Int. J. Therm. Sci. 111, 463 (2017)CrossRefGoogle Scholar
  27. 27.
    S J Liao, Commun. Nonlinear Sci. Numer. Simul. 15, 2003 (2010)ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    K Yabushita, M Yamashita and K Tsuboi, J. Phys. A 40, 8403 (2007)ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    V Marinca and N Herişanu, Int. Commun. Heat Mass 35, 710 (2008)CrossRefGoogle Scholar
  30. 30.
    V Marinca, N Herişanu, C Bota and B Marinca, Appl. Math. Lett. 22, 245 (2009)MathSciNetCrossRefGoogle Scholar
  31. 31.
    D Pal and H Mondal, Appl. Math. Comput. 212, 194 (2009)MathSciNetGoogle Scholar
  32. 32.
    S Mukhopadhyay, I C Mondal and A J Chamkha, Heat Trans. Asian Res. 42, 665 (2013)CrossRefGoogle Scholar
  33. 33.
    B L Kuo, Acta Mech. 164, 161 (2003)CrossRefGoogle Scholar
  34. 34.
    A H Craven and L A Peletier, Mathematika 19, 135 (1972)MathSciNetCrossRefGoogle Scholar
  35. 35.
    B Oskam and A E P Veldman, J. Eng. Math. 16, 295 (1982)CrossRefGoogle Scholar
  36. 36.
    M Z Salleh, R Nazar and I Pop, Chem. Eng. Commun. 196, 987 (2009)CrossRefGoogle Scholar
  37. 37.
    M Z Salleh, R Nazar and I Pop, Acta Appl. Math. 112, 263 (2010)MathSciNetCrossRefGoogle Scholar
  38. 38.
    L Fusi, A Farina and F Rosso, Int. J. Nonlinear Mech. 64, 33 (2014)ADSCrossRefGoogle Scholar
  39. 39.
    E Moreno, A Larese and M Cervera, J. Non-Newton. Fluid 228, 1 (2016)CrossRefGoogle Scholar
  40. 40.
    P K Swamee and N Aggarwal, J. Petrol. Sci. Eng. 76, 178 (2011)CrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 2018

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, College of Engineering, Mashhad BranchIslamic Azad UniversityMashhadIran

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