Skip to main content
SpringerLink
Log in

Soret And Dufour effects on an unsteady MHD mixed convective flow past an infinite vertical plate with Ohmic dissipation and heat source

  • Published:
Afrika Matematika Aims and scope Submit manuscript

Abstract

Thermal-diffusion and diffusion-thermo effects on unsteady MHD mixed convection flow past an infinite vertical porous plate in the presence of chemical reaction, heat source and Joule effect have been studied numerically. A uniform magnetic field acts perpendicular to the porous surface. The governing non-linear partial differential equations have been transformed in to linear partial differential equations, which are solved numerically by applying explicit finite difference method. The effects of various parameters on the velocity, temperature, concentration, Nusselt number, Sherwood number and skin friction coefficient have been examined with the help of graphs and tables.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29

Similar content being viewed by others

Abbreviations

Gr:

Grashof number

Gm:

Mass Grashof number

M:

Magnetic field parameter

Pr:

Prandtl number

Sc:

Schmidt number

Ec:

Eckert number

S:

Heat source parameter

K:

Chemical reaction parameter

Sr:

Soret number

Du:

Dufour number

Nu:

Nusselt number

Sh:

Sherwood number

Sf:

Skin friction

U:

Velocity

T:

Temperature

C:

Concentration

t:

Time

Y(or)y:

Position of the plate

\(\beta \) :

Coefficient of volumetric thermal expansion of the fluid

\(\beta ^{*}\) :

Volumetric Coefficient of expansion with concentration

\(\sigma \) :

Electrical conductivity of the fluid

\(\rho \) :

Density

\(\mu \) :

Dynamic viscosity

\(\nu \) :

Kinematic viscosity

References

  1. Baehr, H.D., Stephan, K.: Combined Heat and Mass Transfer. Springer, Berlin (1998)

    Book  Google Scholar 

  2. Helmy, K.A.: MHD unsteady free convection flow past a vertical porous plate. ZAMM 98, 255–270 (1998)

    Article  MathSciNet  Google Scholar 

  3. Chaudhary, R.C., Sharma, B.K.: Combined heat and mass transfer by laminar mixed convection flow from a vertical surface with induced magnetic field. J. Appl. Phys. 99, 34901–34910 (2006)

    Article  Google Scholar 

  4. Sharma, B.K., Chaudhary, R.C.: Hydromagnetic unsteady mixed convection and mass transfer flow past a vertical porous plate immersed in a porous medium with Hall effect. Eng. Trans. 56(1), 3–23 (2008)

    MATH  MathSciNet  Google Scholar 

  5. El-Amin, M.F.: Magnetohydrodynamic free convection and mass transfer flow in micropolar fluid with constant suction. J. Magn. Mater. 234, 567–574 (2001)

    Article  Google Scholar 

  6. Makinde, O.D.: Computational modelling of MHD unsteady Flow and heat transfer over a flat plate with Navier slip and Newtonian heating. Braz. J. Chem. Eng. 29(1), 159–166 (2012)

    Article  Google Scholar 

  7. Cussler, E.L.: Diffusion mass transfer in fluid systems, 2nd edn. Cambridge University Press, Cambridge (1998)

    Google Scholar 

  8. Das, U.N., Deka, R.K., Soundalgekar, V.M.: Effects of mass transfer on flow past an impulsively started infinite vertical plate with constant heat flux and chemical reaction. Forsch. Engenieurwesen Eng. Res. 60(10), 284–287 (1994)

    Google Scholar 

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

    Article  Google Scholar 

  10. Muthucumarswamy, R.: Effects of a chemical reaction on moving isothermal vertical surface with suction. Acta. Mech. 155, 65–70 (2002)

    Article  Google Scholar 

  11. Periasamy, R.K.: Prashu Sivagnana, K.K.: Effects of chemical reaction, heat and mass transfer along wedge with heat source and concentration in the presence of suction or injection. Int. J. Heat Mass Transf. 48, 1388–1394 (2005)

    Article  MATH  Google Scholar 

  12. Chaudhary, R.C., Sharma, B.K., Jha, A.K.: Radiation effect with simultaneous thermal and mass diffusion in MHD mixed convection flow from a vertical surface with Ohmic heating. Rom. J. Phys. 51(7–8), 715–727 (2006)

    Google Scholar 

  13. Sharma, B.K., Agarwal, M., Chaudhary, R.C.: MHD fluctuating free convective flow with radiation embedded in porous medium having variable permeability and heat source/sink. J. Techn. Phys. 47(1), 47–58 (2006)

    MATH  Google Scholar 

  14. Chamkha, A.J.: Unsteady MHD convective Heat and Mass transfer past a semi infinite vertical permeable moving plate with heat absorptio, Int. J. Eng. Sci. 42, 217–230 (2004)

    Google Scholar 

  15. Sharma, B.K., Chaudhary, R.C., Agarwal, M.: Radiation effect on temperature distribution in three-dimensional Couette flow with injection or suction. Appl. Math. Mech. 28(3), 309–316 (2007)

    Article  MATH  Google Scholar 

  16. Sharma, B.K., Chaudhary, R.C., Agarwal, M.: Radiation effect on steady free convective flow along a uniform moving porous vertical plate in presence of heat source/sink and transverse Magnetic Field. Bull. Cal. Math. Soc. 100, 529–538 (2008)

    MATH  MathSciNet  Google Scholar 

  17. Ogulu, A., Makinde, O.D.: Unsteady hydromagnetic free convection flow of a dissipative and radiating fluid past a vertical plate with constant heat flux. Chem. Eng. Commun. 196(4), 454–462 (2009)

    Google Scholar 

  18. Makinde, O.D.: Chemically reacting hydromagnetic unsteady flow of a radiating fluid past a vertical plate with constant heat flux. Z. Nat. 67a, 239–247 (2012)

    Google Scholar 

  19. Dursunkaya, Z., Worek, W.M.: Diffusion-thermo and thermal-diffusion effects in transient and steady natural convection from vertical surface. Int. J. Heat Mass Transf. 35(8), 2060–2065 (1992)

    Article  Google Scholar 

  20. Anghel, M., Takhar, H. S. and Pop, I.: Dufour and Soret effects on free- convection boundary layer over a vertical surface embedded in a porous medium. Stud. Univ. Babes-Bolyai Math. XLV(4), 11–21 (2000)

  21. Postelnicu, A.: Influence of a magnetic field on heat and mass transfer by natural convection from vertical surfaces in porous media considering Soret and Dufour effects. Int. J. Heat Mass Transf. 47(6–7), 1467–1472 (2004)

    Article  MATH  Google Scholar 

  22. Sparrow, E.M., Minkowycz, W.J., Eckert, E.R.G.: Transpiration induced buoyancy and thermal diffusion-diffusion thermo in a helium-air free convection boundary layer. J. Heat Mass Trans. 64, 508–513 (1964)

    Google Scholar 

  23. Dursunkaya, Z., Worek, Z.W.: Diffusion thermo and thermal diffusion effects in transient and steady natural convection from a vertical surface. Int. J. Heat Mass Transf. 35, 2060–2065 (1992)

    Article  Google Scholar 

  24. Alam, M.S., Rahman, M.M.: Dufour and Soret effects on MHD free convective heat and mass transfer flow past a vertical flat plate embedded in a porous medium. J. Naval Arch. Marine Eng. 2(1), 55–65 (2005)

    Google Scholar 

  25. Olanrewaju, P.O., Makinde, O.D.: Effects of thermal diffusion and diffusion thermo on chemically reacting MHD boundary layer flow of heat and mass transfer past a moving vertical plate with suction/injection. Arab. J. Sci. Eng. 36, 1607–1619 (2011)

    Article  Google Scholar 

  26. Makinde, O.D.: On MHD mixed convection with Soret and Dufour effects past a vertical plate embedded in a porous medium. Lat. Am. Appl. Res. 41, 63–68 (2011)

    Google Scholar 

  27. Sharma, B.K., Yadav, K., Mishra, N.K., Chaudhary, R.C.: Soret and Dufour effects on unsteady MHD mixed convection flow past a radiative vertical porous plate embedded in a porous medium with chemical reaction. Appl. Math. 3, 717–723 (2012). doi:10.4236/am.2012.37105

    Article  Google Scholar 

  28. Hoffman, J.D.: Numerical Methods for Engineers and Scientists. McGraw-Hill, New York (1992)

    MATH  Google Scholar 

  29. Ambethkar, V.: Numerical solutions of heat and mass transfer effects of an unsteady MHD free convective flow past an infinite vertical plate with constant suction and heat source or sink. Int. J. Appl. Math. Mech. 5(3), 96–115 (2009)

    Google Scholar 

Download references

Acknowledgments

The authors are extremely thankful to reviewer, for improving the depth of the paper.

Author information

Authors and Affiliations

  1. Department of Mathematics, Birla Institute of Technology and Science, Pilani, Rajasthan, India

    Bhupendra K. Sharma

  2. Department of Chemical Engineering, Birla Institute of Technology and Science, Pilani, Rajasthan, India

    Suresh Gupta, V. Vamsi Krishna & R. J. Bhargavi

Authors
  1. Bhupendra K. Sharma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Suresh Gupta
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. Vamsi Krishna
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. R. J. Bhargavi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bhupendra K. Sharma.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sharma, B.K., Gupta, S., Krishna, V.V. et al. Soret And Dufour effects on an unsteady MHD mixed convective flow past an infinite vertical plate with Ohmic dissipation and heat source. Afr. Mat. 25, 799–821 (2014). https://doi.org/10.1007/s13370-013-0154-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13370-013-0154-6

Keywords

Mathematics Subject Classification (2000)

Search

Navigation