Finite element computation of multi-physical micropolar transport phenomena from an inclined moving plate in porous media

  • MD. Shamshuddin
  • O. Anwar Bég
  • M. Sunder Ram
  • A. Kadir
Original Paper


Non-Newtonian flows arise in numerous industrial transport processes including materials fabrication systems. Micropolar theory offers an excellent mechanism for exploring the fluid dynamics of new non-Newtonian materials which possess internal microstructure. Magnetic fields may also be used for controlling electrically-conducting polymeric flows. To explore numerical simulation of transport in rheological materials processing, in the current paper, a finite element computational solution is presented for magnetohydrodynamic, incompressible, dissipative, radiative and chemically-reacting micropolar fluid flow, heat and mass transfer adjacent to an inclined porous plate embedded in a saturated homogenous porous medium. Heat generation/absorption effects are included. Rosseland’s diffusion approximation is used to describe the radiative heat flux in the energy equation. A Darcy model is employed to simulate drag effects in the porous medium. The governing transport equations are rendered into non-dimensional form under the assumption of low Reynolds number and also low magnetic Reynolds number. Using a Galerkin formulation with a weighted residual scheme, finite element solutions are presented to the boundary value problem. The influence of plate inclination, Eringen coupling number, radiation-conduction number, heat absorption/generation parameter, chemical reaction parameter, plate moving velocity parameter, magnetic parameter, thermal Grashof number, species (solutal) Grashof number, permeability parameter, Eckert number on linear velocity, micro-rotation, temperature and concentration profiles. Furthermore, the influence of selected thermo-physical parameters on friction factor, surface heat transfer and mass transfer rate is also tabulated. The finite element solutions are verified with solutions from several limiting cases in the literature. Interesting features in the flow are identified and interpreted.


Heat source/sink Chemical reaction Inclined porous plate Micropolar fluid FEM Radiative heat transfer Thermal convection Viscous heating Materials processing 


47.11. +j 44.30. +v 


  1. [1]
    A C Eringen J. Appl. Math. Mech. 16 1 (1996)Google Scholar
  2. [2]
    A C Eringen J. Math. Anal. Appl. 38 480 (1972)CrossRefGoogle Scholar
  3. [3]
    A C Eringen Micro-continuum Field Theories II Fluent Media (New York: Springer) (2001)MATHGoogle Scholar
  4. [4]
    G Lukaszewicz Micropolar Fluids, Modelling and Simulation (Boston: Birkhauser Boston) (1999)CrossRefMATHGoogle Scholar
  5. [5]
    T Ariman, M A Turk and N D Sylvester Int. J. Eng. Sci. 11 905 (1973)CrossRefGoogle Scholar
  6. [6]
    T Ariman, M A Turk and N D Sylvester Int. J. Eng. Sci. 12 273 (1974)CrossRefGoogle Scholar
  7. [7]
    G Swapna, L Kumar, O Anwar Bég and Bani Singh Heat Transf. Asian Res. 1 (2014). doi:10.1002/htj.21134
  8. [8]
    S Jangili and J.V. Murthy Front. Heat Mass Transf. 6(1) 1 (2015)CrossRefGoogle Scholar
  9. [9]
    S Rawat, R Bhargava, R Bhargava and O Anwar Bég Proc. IMechE Part C J. Mech. Eng. Sci. 223 2341 (2009)CrossRefGoogle Scholar
  10. [10]
    O Anwar Bég, J Zueco and T B Chang Chem. Eng. Commun. 198(3) 312 (2010)CrossRefGoogle Scholar
  11. [11]
    O Anwar Bég, J Zueco, M Norouzi, M Davoodi, A A Joneidi and A F Elsayed Comput. Biol. Med. 44 44 (2014)CrossRefGoogle Scholar
  12. [12]
    F M Abo-Eldahab and A F Ghonaim Appl. Math. Comput. 169(1) 500 (2005)MathSciNetGoogle Scholar
  13. [13]
    M Ferdows, P Nag, A Postelnicu and K Vajravelu J. Appl.Fluid Mech. 6(2) 285 (2013)Google Scholar
  14. [14]
    B I Olajuwon and J I Oahimire Int. J. Pure Appl. Math. 84 015 (2013)CrossRefGoogle Scholar
  15. [15]
    P K Kundu, K Das and S Jana Bull. Malays. Math. Sci. Soc. 38 1185 (2015)MathSciNetCrossRefGoogle Scholar
  16. [16]
    M M Rahman and Y Sultana Nonlinear Anal. Model. Control 13 71 (2008)Google Scholar
  17. [17]
    P Cheng Int. J. Heat Mass Transf. 20 807 (1977)CrossRefGoogle Scholar
  18. [18]
    P K Singh Int. J. Sci. Eng. Research 3 2229 (2012)Google Scholar
  19. [19]
    M Sudheer Babu, J Girish Kumar and T Shankar reddy Int. J. Appl. Math. Mech. 9(6) 48 (2013)Google Scholar
  20. [20]
    P Roja, T Shankar Reddy and N Bhaskar Reddy Int. J. Sci. Res. Publ. 3 (2013) Issue 6 Google Scholar
  21. [21]
    C H Chen Acta Mech. 172 219 (2004)CrossRefGoogle Scholar
  22. [22]
    Aurangzaib, A R M Kasim, N F Mohammad and S Shafie Heat Transf. Asian Res. 42(2) 89 (2013). doi:10.1002/htj.21034 CrossRefGoogle Scholar
  23. [23]
    J Srinivas, J V Ramana Murthy and A J Chamkha Int.J. Numer. Methods Heat Fluid Flow 26(3) 1027 (2016). doi:10.1108/HFF-09-2015-0354 CrossRefGoogle Scholar
  24. [24]
    S K Bhaumik and R Behera, ICCHMT, Procedia Eng. 127 155 (2015). doi:10.1016/j.proeng.201.11.318
  25. [25]
    M K Nayak and G C Dash Model. Meas. Control B 84(2) 1 (2015)Google Scholar
  26. [26]
    M E M Khedr, A J Chamkha and M Bayomi Nonlinear Anal. Model. Control 14 27 (2009)Google Scholar
  27. [27]
    E Magyari and A J Chamkha Int. J. Therm. Sci. 49 1821 (2010)CrossRefGoogle Scholar
  28. [28]
    A J Chamkha and A R A Khaled Heat Mass Transf. 37 117 (2001)ADSCrossRefGoogle Scholar
  29. [29]
    M M Rahman, M J Uddin and A Aziz Int. J. Therm. Sci. 48(3) 2331 (2009)CrossRefGoogle Scholar
  30. [30]
    D Srinivasacharya and M Upender Turk. J. Eng. Environ. Sci. 38 184 (2015)Google Scholar
  31. [31]
    S Siva Reddy and M D Shamshuddin, ICCHMT, Procedia Eng. 127 885 (2015)Google Scholar
  32. [32]
    S Siva Reddy and M D Shamshuddin Theor. Appl. Mech. 43 117 (2016)ADSCrossRefGoogle Scholar
  33. [33]
    S Rawat, S Kapoor, R Bhargava and O Anwar Bég Int. J. Comput. Appl. 44 40 (2012)Google Scholar
  34. [34]
    K Das Int. J. Numer. Methods Fluids 70(1) 96 (2012)ADSCrossRefGoogle Scholar
  35. [35]
    D Pal and B Talukdar Central Eur. J. Phys. 10 1150 (2012)ADSGoogle Scholar
  36. [36]
    D Srinivasacharya and M Upender Chem. Ind. Chem. Eng. Q 20(2) 183 (2014)CrossRefGoogle Scholar
  37. [37]
    T G Cowling Magnetohydrodynamics (New York: Wiley inter Science) (1957)MATHGoogle Scholar
  38. [38]
    O Anwar Bég New Developments in Hydrodynamics Research Ch1. 1 (eds.) Maximiano J Ibragimov and A Anisimov (New York: Nova Science) (2012)Google Scholar
  39. [39]
    T Adunson and B Gebhart J. Fluid Mech. 52 57 (1972)ADSCrossRefGoogle Scholar
  40. [40]
    A Rapits and C Perdikis ZAMP 78 277 (1998)Google Scholar
  41. [41]
    R Cortell Chin. Phys. Lett. 25 1340 (2008)CrossRefGoogle Scholar
  42. [42]
    S R Rao The Finite Element Method in Engineering, 2nd edn. (Exeter USA: BPCC Wheatons Ltd.) (1989)MATHGoogle Scholar
  43. [43]
    J N Reddy An Introduction to the Finite Element Method (New York: McGraw-Hill) (1985)MATHGoogle Scholar
  44. [44]
    O Anwar Bég, M M Rashidi and R Bhargava Numerical Simulation in Micropolar Fluid Dynamics Lambert: 288 pp, Germany: Sarbrucken (2011)Google Scholar
  45. [45]
    D Gupta, L Kumar, O Anwar Bég and B Singh Comput. Therm. Sci. 6 (2) 155 (2014)CrossRefGoogle Scholar
  46. [46]
    O Anwar Bég, S Rawat, J Zueco, L Osmond and R S R Gorla Theor. Appl. Mech. 41(1) 1 (2014)CrossRefGoogle Scholar
  47. [47]
    R Bhargava, S Sharma, P Bhargava, O Anwar Bég and A Kadir Int. J. Appl. Comput. Math. (2016). DOI: 10.1007/s40819-106-0180-9 (13 pages)
  48. [48]
    J Zueco, O Anwar Bég and H S Takhar Comput. Mater. Sci. 46(4) 1028 (2009)CrossRefGoogle Scholar
  49. [49]
    A Mohammadein, M A El-Hakiem, S M M El-Kabeir and M A Mansour Int. J. Appl. Mech. Eng. 2 187 (1997)Google Scholar

Copyright information

© Indian Association for the Cultivation of Science 2017

Authors and Affiliations

  1. 1.Department of MathematicsVaagdevi College of Engineering (Autonomous)WarangalIndia
  2. 2.Fluid Mechanics, Aeronautical and Mechanical Engineering, School of Computing, Science and Engineering, Newton BuildingThe CrescentSalfordEngland, UK
  3. 3.Department of MathematicsChaitanya Degree College (Autonomous)WarangalIndia
  4. 4.Corrosion and Materials, Petroleum and Gas Engineering, School of Computing, Science and Engineering, Newton BuildingThe CrescentSalfordEngland, UK

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