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MHD free-convective flow of micropolar and Newtonian fluids through porous medium in a vertical channel

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Abstract

We have studied the fully-developed free-convective flow of an electrically conducting fluid in a vertical channel occupied by porous medium under the influence of transverse magnetic field. The internal prefecture of the channel is divided into two regions; one region filled with micropolar fluid and the other region with a Newtonian fluid or both the regions filled by Newtonian fluids. Analytical solutions of the governing equations of fluid flow are found to be in excellent agreement with analytical prediction. Analytical results for the details of the velocity, micro-rotation velocity and temperature fields are shown through graphs for various values of physical parameters. It is noticed that Newtonian fluids prop up the linear velocity of the fluid in contrast to micropolar fluid. Also the skin friction coefficient at both the walls is derived and its numerical values are offered through tables.

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References

  1. Eringen AC (1966) Theory of micropolar fluids. J Math Mech 16:1–18

    MathSciNet  Google Scholar 

  2. Eringen AC (1972) Theory of thermo micro fluids. J Math Anal Appl 38:480–496

    Article  MATH  Google Scholar 

  3. Ericksen JC (1960) Anisotropic fluids. Arch Ration Mech Anal 4:231–237

    Article  MATH  MathSciNet  Google Scholar 

  4. Ericksen JC (1960) Transversely isotropic fluids. Colloid Polym Sci 173:117–122

    Article  Google Scholar 

  5. Hoyt JW, Fabula AG (1964) US Naval Ordinance Test Station Report

  6. Vogel WM, Patterson AM (1964) Pacific Naval Laboratory of the Defense Research Board of Canada, Report. 64-2

  7. Ariman T, Turk MA, Sylvester ND (1973) Microcontinum fluid mechanics—a review. Int J Eng Sci 11:905–930

    Article  MATH  Google Scholar 

  8. Ariman T, Turk MA, Sylvester ND (1974) Application of microcontinum fluid mechanics. Int J Eng Sci 12:273–293

    Article  MATH  Google Scholar 

  9. Lukaszewicz G (1999) Micropolar fluids: theory and application. Birkhäuser, Basel

    MATH  Google Scholar 

  10. Eringen AC (2001) Microcontinum field theories, II: Fluent media. Springer, New York

    Google Scholar 

  11. Ahmadi G (1976) Self-similar solution of incompressible micropolar boundary layer flow over a semi-infinite plate. Int J Eng Sci 14:639–646

    Article  MATH  Google Scholar 

  12. Jena SK, Mathur MN (1982) Free-convection in the laminar boundary layer flow of thermo-micropolar fluid past a non-isothermal vertical flat plate with suction/injection. Acta Mech 42:227–238

    Article  Google Scholar 

  13. Ÿucel A (1989) Mixed convection in micropolar fluid over a horizontal plate with surface mass transfer. Int J Eng Sci 27:1593–1608

    Article  Google Scholar 

  14. Rahman MM, Sattar MA (2006) MHD convective flow of micropolar fluid past a continuously moving vertical porous plate in the presence of heat generation/absorption. Trans ASME J Heat Trans 128-2:142–152

    Article  Google Scholar 

  15. Rahman MM, Sattar MA (2007) Transient convective flow of micropolar fluid past a continuously moving vertical porous plate in the presence of radiation. Int J Appl Mech Eng 12-2:497–513

    Google Scholar 

  16. Rahman MM, Sultana T (2008) Radiative heat transfer flow of micropolar fluid with variable heat flux in a porous medium. Nonlinear Anal: Model Control 13-1:71–87

    Google Scholar 

  17. Rahman MM (2009) Convective flows of micropolar fluids from radiate isothermal porous surfaces with viscous dissipation and Joule heating. Commun Nonlinear Sci Numer Simul 14-7: 3018–3030

    Article  ADS  Google Scholar 

  18. Rahman MM, Eltayeb IA, Mujibur Rahman SM (2009) Thermo-micropolar fluid flow along a vertical permeable plate with uniform surface heat flux in the presence of heat generation. Thermo Sci 13-1:23–36

    Article  Google Scholar 

  19. Mukhopadhyay S, Layek GC (2009) Radiation effect on forced convective flow and heat transfer over a porous plate in a porous medium. Meccanica 44(5):587–597

    Article  MathSciNet  Google Scholar 

  20. Pal D, Mondal H (2009) Radiation effects on combined convection over a vertical flat plate embedded in a porous medium of variable porosity. Meccanica 44(2):133–144

    Article  MathSciNet  Google Scholar 

  21. Elgazery NS, Abd Elazem NY (2009) The effects of variable properties on MHD unsteady natural convection heat and mass transfer over a vertical wavy surface. Meccanica 44(5):573–586

    Article  MathSciNet  Google Scholar 

  22. Sahoo B (2010) Flow and heat transfer of an electrically conducting third grade fluid past an infinite plate with partial slip. Meccanica 45(3):319–330

    Article  MathSciNet  Google Scholar 

  23. Kumar N, Gupta S (2010) Heat and mass transfer in MHD unsteady free convective flow of a micropolar fluid over a vertical moving porous plate embedded in a porous medium in the presence of thermal radiation. In: Proceedings of National Academy of Sciences, India (Section-A). Accepted

  24. Balram M, Sastry VUK (1973) Micropolar free convection flow. Int J Heat Mass Transf 16:437–441

    Article  Google Scholar 

  25. Lein FS, Chen CK (1986) Effects of microstructure on the conjugated mixed forced and free convection-conduction analysis of heat transfer in a vertical plate. Trans ASME J Heat Trans 108:580–584

    Article  Google Scholar 

  26. Lein FS, Chen TM, Chen CK (1990) Analysis of free convection micropolar boundary layer about a horizontal permeable cylinder at a non-uniform thermal condition. Trans ASME J Heat Trans 112:504–506

    Article  Google Scholar 

  27. Ishak A (2010) Thermal boundary layer flow over a stretching sheet in a micropolar fluid with radiation effect. Meccanica 45(3):367–373

    Article  MathSciNet  Google Scholar 

  28. Chamkha AJ, Grosan T, Pop I (2002) Fully developed free convection of a micropolar fluid in a vertical channel. Int Commun Heat Mass Transf 29:1119–1127

    Article  Google Scholar 

  29. Cheng CY (2006) Fully developed natural convection heat and mass transfer of a micropolar fluid in a vertical channel with asymmetric wall temperatures and concentrations. Int Commun Heat Mass Transf 33:627–635

    Article  Google Scholar 

  30. Bhargava R, Rawat S, Takhar HS, Beg OA (2007) Pulsatile magneto-biofluid flow and mass transfer in a non-Darcian porous medium channel. Meccanica 42:247–262

    Article  MATH  MathSciNet  Google Scholar 

  31. Guria M, Das S Jana RN, Ghosh SK (2009) Oscillatory Couette flow in the presence of an inclined magnetic field. Meccanica 44(5):555–564

    Article  MathSciNet  Google Scholar 

  32. Muthuraj R, Srinivas S (2010) Effects of thermal radiation and space porosity on MHD mixed convection flow in a vertical channel using HAM. Commun Nonlinear Sci Numer Simul 15:2098–2108

    Article  MATH  ADS  MathSciNet  Google Scholar 

  33. Sajid M, Pop I, Hayat T (2010) Fully developed mixed convection flow of a viscoelastic fluid between permeable parallel vertical plates. Comput Appl Math 59:493–498

    Article  MATH  MathSciNet  Google Scholar 

  34. Muthuraj R, Srinivas S (2010) Mixed convective heat and mass transfer in a vertical wavy channel with traveling thermal waves and porous medium. Comput Appl Math 59:3516–3528

    Article  MATH  MathSciNet  Google Scholar 

  35. Srinivas S, Gayathri R, Kothandapani M (2010) Mixed convective heat and mass transfer in an asymmetric channel with peristalsis. Comm Nonlinear Sci Numer Simul, In Press

  36. Lohsasbi J, Sahai V (1988) Magnetohydrodynamic heat transfer in two phase flow between two parallel plates. Appl Sci Res 45:53–66

    Article  Google Scholar 

  37. Malashetty MS, Leela V (1992) Magnetohydrodynamic heat transfer in two-phase flow. Int J Eng Sci 30:371–377

    Article  MATH  Google Scholar 

  38. Malashetty MS, Umavathi JC (1997) Two-phase magnetohydrodynamic flow and heat transfer in an inclined channel. Int J Multiph Flow 22:545–560

    Article  Google Scholar 

  39. Malashetty MS, Umavathi JC, Prathap Kumar J (2001) Two-fluid magneto convection flow in an inclined channel. Int J Transp Phenom 2:73–84

    Google Scholar 

  40. Malashetty MS, Umavathi JC, Prathap Kumar J (2001) Convective magnetohydrodynamic two fluids flow and heat transfer in an inclined channel. Heat Mass Transf 37:259–264

    Article  ADS  Google Scholar 

  41. Kumar N, Gupta S (2009) Unsteady MHD and heat transfer of two viscous immiscible fluids through a porous medium in a horizontal channel. J Damghan Univ Basic Sci 2-1:87–98

    Google Scholar 

  42. Ziabakhsh Z, Domairry G (2009) Analytic solution of natural convection flow of a non-Newtonian fluid between two vertical flat plates using HAM. Commun Nonlinear Sci Numer Simul 14:1868–1880

    Article  ADS  Google Scholar 

  43. Prathap Kumar J, Umavathi JC Chamkha AJ, Pop I (2010) Fully-developed free-convective flow of micropolar and viscous fluids in a vertical channel. Appl Math Model 34, 1175–1186

    Article  MATH  MathSciNet  Google Scholar 

  44. Muthuraj R, Srinivas S (2010) Fully developed MHD flow of a micropolar and viscous fluids in a vertical porous space using HAM. Int J Appl Math Mech 6(11):55–78

    MathSciNet  Google Scholar 

  45. Kline KA (1977) A spin-vorticity relation for unidirectional plane flows of micropolar fluids. Int J Eng Sci 15:131–134

    Article  MATH  Google Scholar 

  46. Rees DAS, Bassom AP (1996) The Blasius boundary layer flow of a micropolar fluid. Int J Eng Sci 34:113–124

    Article  MATH  MathSciNet  Google Scholar 

  47. Gorla RSR (1988) Combined forced and free convection in micropolar boundary layer flow on a vertical flat plate. Int J Eng Sci 26:385–391

    Article  MATH  Google Scholar 

  48. Rees DA, Pop I (1998) Free convection boundary layer flow of a micropolar fluid from a vertical flat plate. IMA J Appl Math 61:170–197

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, National Defence Academy, Pune, 23, Maharashtra, India

    Navin Kumar & Sandeep Gupta

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  1. Navin Kumar
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  2. Sandeep Gupta
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Correspondence to Navin Kumar.

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Kumar, N., Gupta, S. MHD free-convective flow of micropolar and Newtonian fluids through porous medium in a vertical channel. Meccanica 47, 277–291 (2012). https://doi.org/10.1007/s11012-011-9435-z

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  • DOI: https://doi.org/10.1007/s11012-011-9435-z

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