Skip to main content
SpringerLink
Log in

Similarity solution of MHD boundary layer flow with diffusion and chemical reaction over a porous flat plate with suction/blowing

  • Brief Notes and Discussions
  • Published:
Meccanica Aims and scope Submit manuscript

Abstract

Similarity analysis of diffusion of chemically reactive solute distribution in MHD boundary layer flow of an electrically conducting incompressible fluid over a porous flat plate is presented. The reaction rate of the solute is considered inversely proportional along the plate. Adopting the similarity transformation technique the governing equations are converted into the self-similar ordinary differential equations which are solved by shooting procedure using Runge-Kutta method. For increase of the Schmidt number the solute boundary layer thickness is reduced. Most importantly, the effects of reaction rate and order of reaction on concentration field are of conflicting natures, due to increasing reaction rate parameter the concentration decreases, but for the increase in order of reaction it increases. In presence of chemical reaction, the concentration profiles attain negative value when Schmidt number is large.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Blasius H (1908) Grenzschichten in Flüssigkeiten mit kleiner Reibung. Z Math Phys 56:1–37

    Google Scholar 

  2. Howarth L (1938) On the solution of the laminar boundary layer equations. Proc R Soc Lond Ser A, Math Phys Sci 164:547–579

    Article  ADS  MATH  Google Scholar 

  3. Rajagopal KR, Gupta AS (1984) An exact solution for the flow of a non-newtonian fluid past an infinite porous plate. Meccanica 19:158–160

    Article  MathSciNet  MATH  Google Scholar 

  4. Gaffuri G (1981) Velocity and temperature fields past a finite flat plate in a slip flow. Meccanica 16:22–26

    Article  ADS  MATH  Google Scholar 

  5. Pozzi A, Tognaccini R (2005) Influence of the Prandtl number on the unsteady thermo-fluid dynamic field around a thick plate. Meccanica 40:251–266

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

  8. Chambre PL, Young JD (1958) On diffusion of a chemically reactive species in a laminar boundary layer flow. Phys Fluids 1:48–54

    Article  ADS  MATH  Google Scholar 

  9. Gebhart B, Pera L (1971) The nature of vertical natural convection flow resulting from the combined buoyancy effects of thermal and mass transfer. Int J Heat Mass Transf 14:2025–2050

    Article  MATH  Google Scholar 

  10. Stan II (1972) On boundary layer flow with chemical surface reaction. Meccanica 7:72

    Article  Google Scholar 

  11. Cheng P (1977) The influence of lateral mass flux on a free convection boundary layers in saturated porous medium. Int J Heat Mass Transf 20:201–206

    Article  Google Scholar 

  12. Soundalgekar VM (1979) Effects of mass transfer and free convective currents on the flow past an impulsively started vertical plate. J Appl Mech 46:757–760

    Article  MATH  Google Scholar 

  13. Soundalgekar VM, Birajdar NS, Darvekar VK (1984) Mass transfer effects on the flow past an impulsively started infinite vertical plate with variable temperature or constant heat flux. J Astrophys Space Sci 100:159–164

    Article  ADS  Google Scholar 

  14. Das UN, Deka R, Soundalgekar VM (1994) Effect of mass transfer on flow past an impulsively started infinite vertical plate with constant heat flux and chemical reaction. Forsch Ingenieurwes 60:284–287

    Article  Google Scholar 

  15. Muthucumaraswamy R, Ganesan P (2000) On impulsive motion of a vertical plate with heat flux and diffusion of chemically reactive species. Forsch Ingenieurwes 66:17–23

    Article  Google Scholar 

  16. Muthucumaraswamy R, Ganesan P (2001) First order chemical reaction on the flow past an impulsively started vertical plate with uniform heat and mass flux. Acta Mech 147:45–57

    Article  MATH  Google Scholar 

  17. Anderson HI, Hansen OR, Holmedal B (1994) Diffusion of a chemically reactive species from a stretching sheet. Int J Heat Mass Transf 37:659–664

    Article  Google Scholar 

  18. Mahmoud MAA (2010) Chemical reaction and variable viscosity effects on flow and mass transfer of a non-Newtonian visco-elastic fluid past a stretching surface embedded in a porous medium. Meccanica 45:835–846

    Article  MathSciNet  Google Scholar 

  19. Fan JR, Shi JM, Xu XZ (1998) Similarity solution of mixed convection with diffusion and chemical reaction over a horizontal moving plate. Acta Mech 126:59–69

    Article  MATH  Google Scholar 

  20. Anjalidavi SP, Kandasamy R (1999) Effected of chemical reaction, heat and mass transfer on laminar flow along a semi infinite horizontal plate. Heat Mass Transf 35:465–467

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  22. Chamkha AJ, Mohamed RA, Ahmed SE (2010) Unsteady MHD natural convection from a heated vertical porous plate in a micropolar fluid with Joule heating, chemical reaction and radiation effects. Meccanica. doi:10.1007/s11012-010-9321-0

    Google Scholar 

  23. Riley N (1984) Magnetohydrodynamic free convection. J Fluid Mech 18:577–586

    Article  MathSciNet  ADS  Google Scholar 

  24. Watanabe T, Pop I (1995) Hall effects on magnetohydrodynamic boundary layer flow over a continuous moving flat plate. Acta Mech 108:35–47

    Article  MATH  Google Scholar 

  25. Anjalidavi SP, Kandasamy R (2000) Effects of chemical reaction, heat and mass transfer on MHD flow past a semi infinite plate. Z Angew Math Mech 80:697–700

    Article  Google Scholar 

  26. Damseh RA, Duwairi HM, Al-Odat M (2006) Similarity analysis of magnetic field and thermal radiation effects on forced convection flow. Turk J Eng Environ Sci 30:83–89

    Google Scholar 

  27. Sharma PR, Singh G (2010) Effects of variable thermal conductivity, viscous dissipation on steady MHD natural convection flow of low Prandtl fluid on an inclined porous plate with Ohmic heating. Meccanica 45:237–247

    Article  MathSciNet  Google Scholar 

  28. Bhattacharyya K, Mukhopadhyay S, Layek GC (2011) Slip effects on boundary layer stagnation-point flow and heat transfer towards a shrinking sheet. Int J Heat Mass Transf 54:308–313

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, The University of Burdwan, Burdwan, 713104, West Bengal, India

    Krishnendu Bhattacharyya & G. C. Layek

Authors
  1. Krishnendu Bhattacharyya
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. C. Layek
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Krishnendu Bhattacharyya.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bhattacharyya, K., Layek, G.C. Similarity solution of MHD boundary layer flow with diffusion and chemical reaction over a porous flat plate with suction/blowing. Meccanica 47, 1043–1048 (2012). https://doi.org/10.1007/s11012-011-9461-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11012-011-9461-x

Keywords

Search

Navigation