Entropy generation of von Karman's radiative flow with Al2O3 and Cu nanoparticles between two coaxial rotating disks: A finite-element analysis

  • R. KumarEmail author
  • G. S. Seth
  • A. Bhattacharyya
Regular Article


This article explores the entropy generation of von Karman's radiative hydromagnetic nanofluid flow i.e. alumina (Al2O3) and copper (Cu) nanoparticles and water as base fluid between two co-axial rotating porous disks. The governing boundary layer equations of a magnetohydrodynamic (MHD) laminar flow between two stretchable rotating disks are formulated under the influence of a magnetic field. Using the von Karman transformation, the governing equations for fluid flow, heat and mass transfer are converted into a number of coupled differential equations. The calculations are performed by the hp-Galerkin finite-element analysis (FEA). The physical clarification of fluid velocity, temperature and concentration for several regulatory flow parameters which characterize the physics of the flow, are discussed graphically, while the physical parameters such as skin friction coefficient, the rate of heat and mass transfers in the lower and upper disks, are presented through tables. The minimal percentage errors are calculated between the previous published result and current result. The thermal radiation, nanoparticle volume fraction, magnetic field and Brinkmann number have an important influence on the irreversibility of thermal energy in terms of Bejan number. This study has numerous applications in thermal transformation mechanisms for nuclear propulsion devices and spacecraft.



  1. 1.
    T. von Karman, Z. Angew. Math. Mech. 1, 233 (1921)CrossRefGoogle Scholar
  2. 2.
    W.G. Cochran, Math. Proc. Camb. Philos. Soc. 30, 365 (1934)ADSCrossRefGoogle Scholar
  3. 3.
    G.L. Mellor, P.J. Chapple, V.K. Stokes, J. Fluid Mech. 31, 95 (1968)ADSCrossRefGoogle Scholar
  4. 4.
    R.C. Arora, V.K. Stokes, Int. J. Heat Mass Transfer 15, 2119 (1972)CrossRefGoogle Scholar
  5. 5.
    M. Turkyilmazoglu, Phys. Fluids 28, 043601 (2016)ADSCrossRefGoogle Scholar
  6. 6.
    M.M. Rashidi, T. Hayat, E. Erfani, S.A.M. Pour, A.A. Hendi, Commun. Nonlinear Sci. Numer. Simul. 16, 4303 (2011)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    T. Hayat, H. Khalid, M. Waqas, A. Alsaedi, Comput. Methods Appl. Mech. Eng. 341, 397 (2018)ADSCrossRefGoogle Scholar
  8. 8.
    H. Masuda, A. Ebata, K. Teramae, Netsu Bussei 7, 227 (1993)CrossRefGoogle Scholar
  9. 9.
    M. Turkyilmazoglu, Comput. Fluids 94, 139 (2014)MathSciNetCrossRefGoogle Scholar
  10. 10.
    D. Yadav, J. Lee, Eur. Phys. J. Plus 130, 162 (2015)CrossRefGoogle Scholar
  11. 11.
    C. Yin, L. Zheng, C. Zhang, X. Zhang, Propuls. Power Res. 6, 25 (2017)CrossRefGoogle Scholar
  12. 12.
    M. Hassan, M. Marin, R. Ellahi, S.Z. Alamri, Heat Transf. Res. 49, 18 (2018)CrossRefGoogle Scholar
  13. 13.
    R. Ellahi, Appl. Math. Modell. 37, 1451 (2013)MathSciNetCrossRefGoogle Scholar
  14. 14.
    A. Asadollahi, S. Rashidi, J. Esfahani, R. Ellahi, Eur. Phys. J. Plus 133, 306 (2018)CrossRefGoogle Scholar
  15. 15.
    S.Z. Alamri, R. Ellahi, N. Shehzad, A. Zeeshan, J. Mol. Liq. 273, 292 (2019)CrossRefGoogle Scholar
  16. 16.
    M. Hassan, M. Marin, A. Alsharif, R. Ellahi, Phys. Lett. A 382, 2749 (2018)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    H.A. Attia, A.L. Aboul-Hassan, Appl. Math. Modell. 28, 1007 (2004)CrossRefGoogle Scholar
  18. 18.
    M. Sheikholeslami, D. Ganji, M. Gorji-Bandpy, S. Soleimani, J. Taiwan Inst. Chem. Eng. 45, 795 (2014)CrossRefGoogle Scholar
  19. 19.
    T. Hayat, M. Rashid, M.I. Khan, A. Alsaedi, Results Phys. 9, 1618 (2018)ADSCrossRefGoogle Scholar
  20. 20.
    R. Ellahi, M.H. Tariq, M. Hassan, K. Vafai, J. Mol. Liq. 229, 339 (2017)CrossRefGoogle Scholar
  21. 21.
    M. Turkyilmazoglu, Phys. Fluids 21, 106104 (2009)ADSCrossRefGoogle Scholar
  22. 22.
    M.M. Rashidi, N. Kavyani, S. Abelman, Int. J. Heat Mass Transfer 70, 892 (2014)CrossRefGoogle Scholar
  23. 23.
    A. Zeeshan, R. Ellahi, M. Hassan, Eur. Phys. J. Plus 129, 261 (2014)CrossRefGoogle Scholar
  24. 24.
    S.P. Devi, R.U. Devi, J. Appl. Fluid Mech. 5, 2 (2012)Google Scholar
  25. 25.
    M. Sheikholeslami, D.D. Ganji, M.Y. Javed, R. Ellahi, J. Magn. & Magn. Mater. 374, 36 (2015)ADSCrossRefGoogle Scholar
  26. 26.
    M. Hassan, C. Fetecau, A. Majeed, A. Zeeshan, J. Magn. & Magn. Mater. 465, 531 (2018)ADSCrossRefGoogle Scholar
  27. 27.
    K. Jyothi, P.S. Reddy, M.S. Reddy, Powder Technol. 331, 326 (2018)CrossRefGoogle Scholar
  28. 28.
    M. Sheikholeslami, D.D. Ganji, Physica A 417, 273 (2015)ADSCrossRefGoogle Scholar
  29. 29.
    A. Bejan, Entropy Generation Through Heat and Fluid Flow (Wiley, 1982)Google Scholar
  30. 30.
    A. Bejan, Entropy Generation Minimization: The Method of Thermodynamic Optimization of Finite-Size Systems and Finite-Time Processes (CRC Press, 2013)Google Scholar
  31. 31.
    M.M. Rashidi, S. Abelman, N.F. Mehr, Int. J. Heat Mass Transfer 62, 515 (2013)CrossRefGoogle Scholar
  32. 32.
    G.S. Seth, A. Bhattacharyya, R. Kumar, A.J. Chamkha, Phys. Fluids 30, 122003 (2018)ADSCrossRefGoogle Scholar
  33. 33.
    T. Hayat, M.I. Khan, S. Qayyum, A. Alsaedi, Colloids Surf. A 539, 335 (2018)CrossRefGoogle Scholar
  34. 34.
    M.I. Khan, S. Qayyum, T. Hayat, A. Alsaedi, Chin. J. Phys. 56, 1525 (2018)CrossRefGoogle Scholar
  35. 35.
    G. Seth, R. Kumar, A. Bhattacharyya, J. Mol. Liq. 268, 637 (2018)CrossRefGoogle Scholar
  36. 36.
    N. Shehzad, A. Zeeshan, R. Ellahi, S. Rashidi, Entropy 20, 851 (2018)ADSCrossRefGoogle Scholar
  37. 37.
    S. Rashidi, S. Akar, M. Bovand, R. Ellahi, Renew. Energ. 115, 400 (2018)CrossRefGoogle Scholar
  38. 38.
    G.S. Seth, R. Kumar, R. Tripathi, A. Bhattacharyya, Int. J. Heat Technol. 36, 1517 (2018)CrossRefGoogle Scholar
  39. 39.
    M.A. Yousif, H.F. Ismael, T. Abbas, R. Ellahi, Heat Transf. Res. 50, 7 (2019)CrossRefGoogle Scholar
  40. 40.
    A. Zeeshan, N. Shehzad, T. Abbas, R. Ellahi, Entropy 21, 236 (2019)ADSCrossRefGoogle Scholar
  41. 41.
    K.U. Rehman, M.Y. Malik, M. Zahri, M. Tahir, Results Phys. 8, 744 (2018)ADSCrossRefGoogle Scholar
  42. 42.
    P.S. Reddy, P. Sreedevi, A.J. Chamkha, Powder Technol. 307, 46 (2017)CrossRefGoogle Scholar
  43. 43.
    R.K. Tiwari, M.K. Das, Int. J. Heat Mass Transfer 50, 2002 (2007)CrossRefGoogle Scholar
  44. 44.
    J.N. Reddy, An Introduction to the Finite Element Method, Vol. 2 (McGraw-hill New York, 1993)Google Scholar
  45. 45.
    P. Rana, R. Bhargava, O.A. Bég, A. Kadir, Int. J. Appl. Comput. Math. 3, 1421 (2017)MathSciNetCrossRefGoogle Scholar
  46. 46.
    T. Hayat, M.W.A. Khan, M.I. Khan, M. Waqas, A. Alsaedi, Physica B 538, 138 (2018)ADSCrossRefGoogle Scholar
  47. 47.
    M. Sheikholeslami, M. Rashidi, T. Hayat, D. Ganji, J. Mol. Liq. 218, 393 (2016)CrossRefGoogle Scholar
  48. 48.
    H.F. Oztop, E. Abu-Nada, Int. J. Heat Fluid Flow 29, 1326 (2008)CrossRefGoogle Scholar
  49. 49.
    I. Babuška, B. Guo, Adv. Eng. Softw. 15, 159 (1992)CrossRefGoogle Scholar
  50. 50.
    J.M. Melenk, in hp-Finite Element Methods for Singular Perturbations (Springer, 2002) pp. 1--20Google Scholar
  51. 51.
    G.N. Lance, M.H. Rogers, Proc. R. Soc. London A 266, 109 (1962)ADSCrossRefGoogle Scholar

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© Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Applied MathematicsIndian Institute of Technology (Indian School of Mines) DhanbadJharkhandIndia

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