Effect of Thermal Conductivity on Mhd Heat and Mass Transfer: Flow Past an Infinite Vertical Plate with Soret and Dufour Effects

Halima Usman; Ime Jimmy Uwanta

doi:doi:10.11648/j.ajam.20130103.11

| Peer-Reviewed

Effect of Thermal Conductivity on Mhd Heat and Mass Transfer: Flow Past an Infinite Vertical Plate with Soret and Dufour Effects

Halima Usman, Ime Jimmy Uwanta

Published in American Journal of Applied Mathematics (Volume 1, Issue 3)

Received: 22 July 2013 Published: 30 August 2013

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

This paper investigates the study of the effect of thermal conductivity on MHD flow past an infinite vertical plate with Soret and Dufour effects. The governing non-linear Partial Differential Equations are solved numerically by implicit finite difference scheme of Crank-Nicolson. Computations are performed for a wide range of the governing flow parameters such as thermal Grashof number, solutal Grashof number, magnetic field parameter, Prandtl number, Dufour number, Soret number, thermal conductivity and Schmidt number. The effects of these flow parameters on the velocity, temperature and concentration are shown graphically. It is observed that the velocity increases with the increase in Gr, Gc, Du, Ec, k and and it decreases with the increase in M, Sr and b. Temperature decreases with an increase in and Pr and concentration decreases with the increase in Sr and . Finally, the effects of various parameters on the skin friction coefficient, Nusselt number and Sherwood number are shown on Tables.

Published in	American Journal of Applied Mathematics (Volume 1, Issue 3)
DOI	10.11648/j.ajam.20130103.11
Page(s)	28-38
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2013. Published by Science Publishing Group

Keywords

Thermal Conductivity, MHD, Soret and Dufour Effects

References

[1]	Abdulraheem, M. A., Mansour, M. A. and Chamkha, A. J., (2011). Effects of Soret and Dufour numbers on free convection over Isothermal and Adiabatic stretching surfaces embedded in porous media. Journal of porous media, DOI: 10, 1615/ Journal Porous Media, 14(1), pp. 67-72.
[2]	Adrian P., (2007). Influence of chemical reaction on heat and mass transfer by natural convection from vertical surfaces in porous media considering Soret and Dufour effects. Heat Mass Transfer, 43: pp. 595-602.
[3]	Afif A., (2006). Effects of Thermal diffusion and diffusion Thermo on non-Darcy MHD free convective flow and mass transfer past a vertical isothermal isothermal surface embedded in a porous medium with thermal dispersion and temperature dependent viscosity. Applied Math Model.
[4]	Afify, A.A., (2009). Similarity solution in MHD: Effects of thermal-diffusion and diffusion-thermo on free convective heat and mass transfer over a stretching surface considering suction or injection. Communication in Non-Linear Science Numerical Simulation, 14: pp. 2202-2214.
[5]	Ajali, D. S. P., and Uma, D. R. (2010). Soret and Dufour effects on MHD slip flow with thermal radiation over a porous rotating infinite disk. Communications in Non Linear Science and Numerical Simulation, 16(4), pp. 1917-1930.
[6]	Alam, M. S., and Rahman, M. M., (2006). Dufour and Soret effects on mixed convection flow past a vertical porous plate with variable porous with variable suction. Non-linear Analysis: Modeling and control, 11(10), pp. 3-12.
[7]	Alam, M.S., Ferdows, M., Ota, M., and Maleque, M.A. (2006). Dufour and Soret effects on Steady Free Convection and Mass transfer Flow past a semi-infinite Vertical Porous Plate in a Porous Medium. International Journal of Applied Mechanics and Engineering, 11(3), pp.535-545.
[8]	Alam, M. S. and Rahman, M. M. (1992). Dufour and Soret effects on MHD free convective and mass transfer flow past a vertical flat plate embedded in a porous medium. Journal of Naval Architecture and Marine Engineering. 2(1): pp. 369-374.
[9]	Anghel, M., Takher, H. S. and Pop, I., (2000). Dufour and Soret effects on free convection boundary layer over a vertical surface embedded in a porous medium. Studia Universitatis Basas-BolyalMathematica, XLV (4), pp. 11-21.
[10]	Anwar, B.O., Bakier, A.Y.,and Prasad V.R., (2009). Numerical study of free convection magneto hydrodynamic heat and mass transfer from a stretching surface to a saturated porous medium with Soret and Dufour effects. Computational Material Science 46, pp. 57-65.
[11]	Bejan, A., Dincer, I., Lorente, S., Miguel, A. F. and Reis, A. H. (2004). Porous and Complex Flow Structures in Modern Technologies.Springer. New York, NY.
[12]	Bhupendra, K. S., Kailash, Y.Nidhish, K., Mishra, R. C., and Chaudhary, R. C. (2012). Soret and Dufour Effects on Unsteady MHD Mixed Convection Flow past a Radiative Vertical Porous Plate Embedded in a Porous Medium with Chemical Reaction. Applied Mathematics, 3, pp. 717-723 doi: 10.4236/am.
[13]	Emmanuel, O, Jonathan, S, .and Robert, H., (2011). Thermal-diffusion and diffusion-thermo effects on combined Heat and Mass transfer of a steady MHD hydro convective and slip flow due to a rotating disk with viscous dissipation and ohmic heating. Global Journal of Science Frontier Research, International Communications in Heat and Mass Transfer, 35: pp. 908-915.
[14]	Gbadeyan, J. A., Idowu, A. S., Ogunsola, A. W., Agbola, O. O., and Olanrewaju, P. O. (2011). Heat and Mass transfer for Soret and Dufour’s effect on mixed convection boundary layer flow over a stretching vertical surface in a porous medium filled with a visco elastic fluid in the presence of a magnetic field. Global Journal of Science Frontier Research. 11(8), pp. 97-114.
[15]	Hayat, T., Mustafa, M. and Pop, I., (2010). Heat and Mass transfer for Soret and Dufour’s effect on mixed convection boundary layer flow over a stretching vertical surface in a porous medium filled with a visco elastic fluid. Communications in Non Linear Science and Numerical Simulation. 15, pp.1183-1196.
[16]	Ingham, D. B. and Pop, I., (1998). Transport phenomena in porous media. Vol. II. Pergamon: Oxford, UK.
[17]	Kafousiasis, N. G., and Williams, E. M. (1995). Thermal-diffusion and diffusion-Thermo effects on mixed free-forced convective and Mass transfer boundary layer flow with temperature dependent Viscosity. International Journal of Engineering Science, 33, pp. 1369-1384.
[18]	Carnahan, H., Luther, H. A., and Wilkes, J.O., (1969). Applied Numerical Methoda, John Willey, newYork.
[19]	Nield, D. A. and Bejan, A., (1998). Convection in Porous media, Second edition, Springer, New York.
[20]	Olarenwaju, P. O., and Gbadeyan, J.A. (2011). Effects of Soret, Dufour, and Chemical reaction, Thermal Radiation and Volumetric Heat Generation / Absorption on mixed convection stagnation point flow on an Isothermal Vertical plate in porous media. Pacific Journal of Science and Technology. 12(2): pp. 234-245.
[21]	Olanrewaju, P. O., (2010). Dufour and Soret Effects of a Transient free convective flow with Radiative heat transfer past a flat plate moving through a binary mixture. Pacific Journal of Science and Technology, 11(1): pp. 673-685.
[22]	Postelnica, A. (2007). Influence of a magnetic field on Heat and Mass transfer by natural convection from vertical surfaces in porous media considering Soret and Dufour effects. International Journal of Heat Mass transfer, 43, pp. 595-602.
[23]	Vafai, K. (2000). Hand book of porous media, second edition. Taylor and Francis: New York.
[24]	Vafai, K. (2005). Hand book of porous media, second edition. Taylor and Francis: New York.

Cite This Article

Plain Text BibTeX RIS

APA Style

Halima Usman, Ime Jimmy Uwanta. (2013). Effect of Thermal Conductivity on Mhd Heat and Mass Transfer: Flow Past an Infinite Vertical Plate with Soret and Dufour Effects. American Journal of Applied Mathematics, 1(3), 28-38. https://doi.org/10.11648/j.ajam.20130103.11

Copy | Download

ACS Style

Halima Usman; Ime Jimmy Uwanta. Effect of Thermal Conductivity on Mhd Heat and Mass Transfer: Flow Past an Infinite Vertical Plate with Soret and Dufour Effects. Am. J. Appl. Math. 2013, 1(3), 28-38. doi: 10.11648/j.ajam.20130103.11

Copy | Download

AMA Style

Halima Usman, Ime Jimmy Uwanta. Effect of Thermal Conductivity on Mhd Heat and Mass Transfer: Flow Past an Infinite Vertical Plate with Soret and Dufour Effects. Am J Appl Math. 2013;1(3):28-38. doi: 10.11648/j.ajam.20130103.11

Copy | Download

@article{10.11648/j.ajam.20130103.11,
  author = {Halima Usman and Ime Jimmy Uwanta},
  title = {Effect of Thermal Conductivity on Mhd Heat and Mass Transfer: Flow Past an Infinite Vertical Plate with Soret and Dufour Effects},
  journal = {American Journal of Applied Mathematics},
  volume = {1},
  number = {3},
  pages = {28-38},
  doi = {10.11648/j.ajam.20130103.11},
  url = {https://doi.org/10.11648/j.ajam.20130103.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20130103.11},
  abstract = {This paper investigates the study of the effect of thermal conductivity on MHD flow past an infinite vertical plate with Soret and Dufour effects. The governing non-linear Partial Differential Equations are solved numerically by implicit finite difference scheme of Crank-Nicolson. Computations are performed for a wide range of the governing flow parameters such as thermal Grashof number, solutal Grashof number, magnetic field parameter, Prandtl number, Dufour number, Soret number, thermal conductivity and Schmidt number. The effects of these flow parameters on the velocity, temperature and concentration are shown graphically. It is observed that the velocity increases with the increase in Gr, Gc, Du, Ec, k and and it decreases with the increase in M, Sr and b. Temperature decreases with an increase in   and Pr and concentration decreases with the increase in Sr and  . Finally, the effects of various parameters on the skin friction coefficient, Nusselt number and Sherwood number are shown on Tables.},
 year = {2013}
}

Copy | Download

TY  - JOUR
T1  - Effect of Thermal Conductivity on Mhd Heat and Mass Transfer: Flow Past an Infinite Vertical Plate with Soret and Dufour Effects
AU  - Halima Usman
AU  - Ime Jimmy Uwanta
Y1  - 2013/08/30
PY  - 2013
N1  - https://doi.org/10.11648/j.ajam.20130103.11
DO  - 10.11648/j.ajam.20130103.11
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 28
EP  - 38
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20130103.11
AB  - This paper investigates the study of the effect of thermal conductivity on MHD flow past an infinite vertical plate with Soret and Dufour effects. The governing non-linear Partial Differential Equations are solved numerically by implicit finite difference scheme of Crank-Nicolson. Computations are performed for a wide range of the governing flow parameters such as thermal Grashof number, solutal Grashof number, magnetic field parameter, Prandtl number, Dufour number, Soret number, thermal conductivity and Schmidt number. The effects of these flow parameters on the velocity, temperature and concentration are shown graphically. It is observed that the velocity increases with the increase in Gr, Gc, Du, Ec, k and and it decreases with the increase in M, Sr and b. Temperature decreases with an increase in   and Pr and concentration decreases with the increase in Sr and  . Finally, the effects of various parameters on the skin friction coefficient, Nusselt number and Sherwood number are shown on Tables.
VL  - 1
IS  - 3
ER  -

Copy | Download

Author Information

Halima Usman

Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria
Ime Jimmy Uwanta

Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Halima Usman, Ime Jimmy Uwanta. (2013). Effect of Thermal Conductivity on Mhd Heat and Mass Transfer: Flow Past an Infinite Vertical Plate with Soret and Dufour Effects. American Journal of Applied Mathematics, 1(3), 28-38. https://doi.org/10.11648/j.ajam.20130103.11

Copy | Download

ACS Style

Halima Usman; Ime Jimmy Uwanta. Effect of Thermal Conductivity on Mhd Heat and Mass Transfer: Flow Past an Infinite Vertical Plate with Soret and Dufour Effects. Am. J. Appl. Math. 2013, 1(3), 28-38. doi: 10.11648/j.ajam.20130103.11

Copy | Download

AMA Style

Halima Usman, Ime Jimmy Uwanta. Effect of Thermal Conductivity on Mhd Heat and Mass Transfer: Flow Past an Infinite Vertical Plate with Soret and Dufour Effects. Am J Appl Math. 2013;1(3):28-38. doi: 10.11648/j.ajam.20130103.11

Copy | Download

@article{10.11648/j.ajam.20130103.11,
  author = {Halima Usman and Ime Jimmy Uwanta},
  title = {Effect of Thermal Conductivity on Mhd Heat and Mass Transfer: Flow Past an Infinite Vertical Plate with Soret and Dufour Effects},
  journal = {American Journal of Applied Mathematics},
  volume = {1},
  number = {3},
  pages = {28-38},
  doi = {10.11648/j.ajam.20130103.11},
  url = {https://doi.org/10.11648/j.ajam.20130103.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20130103.11},
  abstract = {This paper investigates the study of the effect of thermal conductivity on MHD flow past an infinite vertical plate with Soret and Dufour effects. The governing non-linear Partial Differential Equations are solved numerically by implicit finite difference scheme of Crank-Nicolson. Computations are performed for a wide range of the governing flow parameters such as thermal Grashof number, solutal Grashof number, magnetic field parameter, Prandtl number, Dufour number, Soret number, thermal conductivity and Schmidt number. The effects of these flow parameters on the velocity, temperature and concentration are shown graphically. It is observed that the velocity increases with the increase in Gr, Gc, Du, Ec, k and and it decreases with the increase in M, Sr and b. Temperature decreases with an increase in   and Pr and concentration decreases with the increase in Sr and  . Finally, the effects of various parameters on the skin friction coefficient, Nusselt number and Sherwood number are shown on Tables.},
 year = {2013}
}

Copy | Download

TY  - JOUR
T1  - Effect of Thermal Conductivity on Mhd Heat and Mass Transfer: Flow Past an Infinite Vertical Plate with Soret and Dufour Effects
AU  - Halima Usman
AU  - Ime Jimmy Uwanta
Y1  - 2013/08/30
PY  - 2013
N1  - https://doi.org/10.11648/j.ajam.20130103.11
DO  - 10.11648/j.ajam.20130103.11
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 28
EP  - 38
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20130103.11
AB  - This paper investigates the study of the effect of thermal conductivity on MHD flow past an infinite vertical plate with Soret and Dufour effects. The governing non-linear Partial Differential Equations are solved numerically by implicit finite difference scheme of Crank-Nicolson. Computations are performed for a wide range of the governing flow parameters such as thermal Grashof number, solutal Grashof number, magnetic field parameter, Prandtl number, Dufour number, Soret number, thermal conductivity and Schmidt number. The effects of these flow parameters on the velocity, temperature and concentration are shown graphically. It is observed that the velocity increases with the increase in Gr, Gc, Du, Ec, k and and it decreases with the increase in M, Sr and b. Temperature decreases with an increase in   and Pr and concentration decreases with the increase in Sr and  . Finally, the effects of various parameters on the skin friction coefficient, Nusselt number and Sherwood number are shown on Tables.
VL  - 1
IS  - 3
ER  -

Copy | Download