Heat and Mass Transfer Under the Effects of Soret and Dufour Parameters of Free Convective Flow Past a Vertical Porous Surface in the Presence of Magnetic Field

Deva Kanta Phukan

doi:doi:10.11648/j.ijtam.20251102.12

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Heat and Mass Transfer Under the Effects of Soret and Dufour Parameters of Free Convective Flow Past a Vertical Porous Surface in the Presence of Magnetic Field

Deva Kanta Phukan^*

Published in International Journal of Theoretical and Applied Mathematics (Volume 11, Issue 2)

Received: 28 May 2025 Accepted: 25 June 2025 Published: 5 August 2025

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Abstract

We have considered Soret and Dufour effects on two dimensional free convection flow of an electrically conducting, incompressible, viscous fluid along a semi-vertical permeable moving plate. A uniform transverse magnetic field is applied in the presence of thermal and concentration buoyancy forces. The thermal and concentration boundary layer effects have been considered. By systematically transforming the governing partial differential equations into non-dimensional forms using selected similarity variables and then the non dimensional governing equations converted to coupled non-linear ordinary differential equations by small perturbation technique. The confined similarity equations are solved using a shooting method together with a Runge-Kutta algorithm. A representative set of graphical results for the velocity, temperature and concentration have been plotted within the boundary layer region for various existing flow parameters. The skin friction coefficient is seen to increase with increasing Soret number, Dufour number, thermal Grasohf number, concentration Grashof number but decreases with increasing the magnetic parameter, Prandtl number and Schmidt number. Nussult number decreases with increasing Prandtl and Soret number but decreases with increasing Dufour number. Sherwood number increases with increasing Schmidt and Dufour number but decreases with increasing Soret number. The fluid velocity in the boundary layer become significantly higher with increasing Soret number, Dufour number, thermal Grasohf number, concentration Grashof number but decreases with increasing magnetic parameter, Prandtl number, Schmidt number, suction and permeability parameter. The fluid temperature is become higher in the boundary layer region with increasing Dufour number and become lower with increasing Soret and Prandtl number, but reverse effect is observed in case of concentration.

Published in	International Journal of Theoretical and Applied Mathematics (Volume 11, Issue 2)
DOI	10.11648/j.ijtam.20251102.12
Page(s)	34-44
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), 2025. Published by Science Publishing Group

Keywords

Conducting Fluid, Vertical Porous Plate, Magnetic Field, Heat and Mass Transfer, Soret and Dufour Number

References

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[5]	Hossain, M. A., Unsteady MHD convective transfer past a semi-infinite vertical porous moving plate with variable plate temperature, Int. J. Heat Mass Transfer, 35, 3485 (1992).
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[16]	Veerkrishna, M., Jyothi, K., and Chamkha, A. J., Heat and mass transfer on MHD oscillatory flow of second grade fluid through a porous medium over a semi-infinite vertical stretching sheet, J. Porous Media, 21 (2018).
[17]	Veerkrishna, M., Gangadhara Reddy, M., and Chamkha, A.J., Heat and mass transfer on MHD free convective flow over an infinite non-conducting vertical porous plate, Int. J. Fluid Mech. Res., 45(5), 1-25 (2018).
[18]	Veerkrishna, M., Anand, P. V. S., and Chamkha, A.J., Heat and mass transfer on free convective flow of a micropolar fluid through a porous surface with inclined magnetic field and Hall effects, J. Porous Media, 19(3), 203-223 (2019). https://doi.org/10.1615/SpecialTopicsRevPorousMedia.2018026943
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APA Style

Phukan, D. K. (2025). Heat and Mass Transfer Under the Effects of Soret and Dufour Parameters of Free Convective Flow Past a Vertical Porous Surface in the Presence of Magnetic Field. International Journal of Theoretical and Applied Mathematics, 11(2), 34-44. https://doi.org/10.11648/j.ijtam.20251102.12

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ACS Style

Phukan, D. K. Heat and Mass Transfer Under the Effects of Soret and Dufour Parameters of Free Convective Flow Past a Vertical Porous Surface in the Presence of Magnetic Field. Int. J. Theor. Appl. Math. 2025, 11(2), 34-44. doi: 10.11648/j.ijtam.20251102.12

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AMA Style

Phukan DK. Heat and Mass Transfer Under the Effects of Soret and Dufour Parameters of Free Convective Flow Past a Vertical Porous Surface in the Presence of Magnetic Field. Int J Theor Appl Math. 2025;11(2):34-44. doi: 10.11648/j.ijtam.20251102.12

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@article{10.11648/j.ijtam.20251102.12,
  author = {Deva Kanta Phukan},
  title = {Heat and Mass Transfer Under the Effects of Soret and Dufour Parameters of Free Convective Flow Past a Vertical Porous Surface in the Presence of Magnetic Field
},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {11},
  number = {2},
  pages = {34-44},
  doi = {10.11648/j.ijtam.20251102.12},
  url = {https://doi.org/10.11648/j.ijtam.20251102.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20251102.12},
  abstract = {We have considered Soret and Dufour effects on two dimensional free convection flow of an electrically conducting, incompressible, viscous fluid along a semi-vertical permeable moving plate. A uniform transverse magnetic field is applied in the presence of thermal and concentration buoyancy forces. The thermal and concentration boundary layer effects have been considered. By systematically transforming the governing partial differential equations into non-dimensional forms using selected similarity variables and then the non dimensional governing equations converted to coupled non-linear ordinary differential equations by small perturbation technique. The confined similarity equations are solved using a shooting method together with a Runge-Kutta algorithm. A representative set of graphical results for the velocity, temperature and concentration have been plotted within the boundary layer region for various existing flow parameters. The skin friction coefficient is seen to increase with increasing Soret number, Dufour number, thermal Grasohf number, concentration Grashof number but decreases with increasing the magnetic parameter, Prandtl number and Schmidt number. Nussult number decreases with increasing Prandtl and Soret number but decreases with increasing Dufour number. Sherwood number increases with increasing Schmidt and Dufour number but decreases with increasing Soret number. The fluid velocity in the boundary layer become significantly higher with increasing Soret number, Dufour number, thermal Grasohf number, concentration Grashof number but decreases with increasing magnetic parameter, Prandtl number, Schmidt number, suction and permeability parameter. The fluid temperature is become higher in the boundary layer region with increasing Dufour number and become lower with increasing Soret and Prandtl number, but reverse effect is observed in case of concentration.
},
 year = {2025}
}

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TY  - JOUR
T1  - Heat and Mass Transfer Under the Effects of Soret and Dufour Parameters of Free Convective Flow Past a Vertical Porous Surface in the Presence of Magnetic Field

AU  - Deva Kanta Phukan
Y1  - 2025/08/05
PY  - 2025
N1  - https://doi.org/10.11648/j.ijtam.20251102.12
DO  - 10.11648/j.ijtam.20251102.12
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 34
EP  - 44
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20251102.12
AB  - We have considered Soret and Dufour effects on two dimensional free convection flow of an electrically conducting, incompressible, viscous fluid along a semi-vertical permeable moving plate. A uniform transverse magnetic field is applied in the presence of thermal and concentration buoyancy forces. The thermal and concentration boundary layer effects have been considered. By systematically transforming the governing partial differential equations into non-dimensional forms using selected similarity variables and then the non dimensional governing equations converted to coupled non-linear ordinary differential equations by small perturbation technique. The confined similarity equations are solved using a shooting method together with a Runge-Kutta algorithm. A representative set of graphical results for the velocity, temperature and concentration have been plotted within the boundary layer region for various existing flow parameters. The skin friction coefficient is seen to increase with increasing Soret number, Dufour number, thermal Grasohf number, concentration Grashof number but decreases with increasing the magnetic parameter, Prandtl number and Schmidt number. Nussult number decreases with increasing Prandtl and Soret number but decreases with increasing Dufour number. Sherwood number increases with increasing Schmidt and Dufour number but decreases with increasing Soret number. The fluid velocity in the boundary layer become significantly higher with increasing Soret number, Dufour number, thermal Grasohf number, concentration Grashof number but decreases with increasing magnetic parameter, Prandtl number, Schmidt number, suction and permeability parameter. The fluid temperature is become higher in the boundary layer region with increasing Dufour number and become lower with increasing Soret and Prandtl number, but reverse effect is observed in case of concentration.

VL  - 11
IS  - 2
ER  -

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Deva Kanta Phukan

Former Principal cum Professor, Dibrugarh, India

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APA Style

Phukan, D. K. (2025). Heat and Mass Transfer Under the Effects of Soret and Dufour Parameters of Free Convective Flow Past a Vertical Porous Surface in the Presence of Magnetic Field. International Journal of Theoretical and Applied Mathematics, 11(2), 34-44. https://doi.org/10.11648/j.ijtam.20251102.12

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ACS Style

Phukan, D. K. Heat and Mass Transfer Under the Effects of Soret and Dufour Parameters of Free Convective Flow Past a Vertical Porous Surface in the Presence of Magnetic Field. Int. J. Theor. Appl. Math. 2025, 11(2), 34-44. doi: 10.11648/j.ijtam.20251102.12

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AMA Style

Phukan DK. Heat and Mass Transfer Under the Effects of Soret and Dufour Parameters of Free Convective Flow Past a Vertical Porous Surface in the Presence of Magnetic Field. Int J Theor Appl Math. 2025;11(2):34-44. doi: 10.11648/j.ijtam.20251102.12

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@article{10.11648/j.ijtam.20251102.12,
  author = {Deva Kanta Phukan},
  title = {Heat and Mass Transfer Under the Effects of Soret and Dufour Parameters of Free Convective Flow Past a Vertical Porous Surface in the Presence of Magnetic Field
},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {11},
  number = {2},
  pages = {34-44},
  doi = {10.11648/j.ijtam.20251102.12},
  url = {https://doi.org/10.11648/j.ijtam.20251102.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20251102.12},
  abstract = {We have considered Soret and Dufour effects on two dimensional free convection flow of an electrically conducting, incompressible, viscous fluid along a semi-vertical permeable moving plate. A uniform transverse magnetic field is applied in the presence of thermal and concentration buoyancy forces. The thermal and concentration boundary layer effects have been considered. By systematically transforming the governing partial differential equations into non-dimensional forms using selected similarity variables and then the non dimensional governing equations converted to coupled non-linear ordinary differential equations by small perturbation technique. The confined similarity equations are solved using a shooting method together with a Runge-Kutta algorithm. A representative set of graphical results for the velocity, temperature and concentration have been plotted within the boundary layer region for various existing flow parameters. The skin friction coefficient is seen to increase with increasing Soret number, Dufour number, thermal Grasohf number, concentration Grashof number but decreases with increasing the magnetic parameter, Prandtl number and Schmidt number. Nussult number decreases with increasing Prandtl and Soret number but decreases with increasing Dufour number. Sherwood number increases with increasing Schmidt and Dufour number but decreases with increasing Soret number. The fluid velocity in the boundary layer become significantly higher with increasing Soret number, Dufour number, thermal Grasohf number, concentration Grashof number but decreases with increasing magnetic parameter, Prandtl number, Schmidt number, suction and permeability parameter. The fluid temperature is become higher in the boundary layer region with increasing Dufour number and become lower with increasing Soret and Prandtl number, but reverse effect is observed in case of concentration.
},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Heat and Mass Transfer Under the Effects of Soret and Dufour Parameters of Free Convective Flow Past a Vertical Porous Surface in the Presence of Magnetic Field

AU  - Deva Kanta Phukan
Y1  - 2025/08/05
PY  - 2025
N1  - https://doi.org/10.11648/j.ijtam.20251102.12
DO  - 10.11648/j.ijtam.20251102.12
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 34
EP  - 44
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20251102.12
AB  - We have considered Soret and Dufour effects on two dimensional free convection flow of an electrically conducting, incompressible, viscous fluid along a semi-vertical permeable moving plate. A uniform transverse magnetic field is applied in the presence of thermal and concentration buoyancy forces. The thermal and concentration boundary layer effects have been considered. By systematically transforming the governing partial differential equations into non-dimensional forms using selected similarity variables and then the non dimensional governing equations converted to coupled non-linear ordinary differential equations by small perturbation technique. The confined similarity equations are solved using a shooting method together with a Runge-Kutta algorithm. A representative set of graphical results for the velocity, temperature and concentration have been plotted within the boundary layer region for various existing flow parameters. The skin friction coefficient is seen to increase with increasing Soret number, Dufour number, thermal Grasohf number, concentration Grashof number but decreases with increasing the magnetic parameter, Prandtl number and Schmidt number. Nussult number decreases with increasing Prandtl and Soret number but decreases with increasing Dufour number. Sherwood number increases with increasing Schmidt and Dufour number but decreases with increasing Soret number. The fluid velocity in the boundary layer become significantly higher with increasing Soret number, Dufour number, thermal Grasohf number, concentration Grashof number but decreases with increasing magnetic parameter, Prandtl number, Schmidt number, suction and permeability parameter. The fluid temperature is become higher in the boundary layer region with increasing Dufour number and become lower with increasing Soret and Prandtl number, but reverse effect is observed in case of concentration.

VL  - 11
IS  - 2
ER  -

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