Hiemenz Steady Hydromagnetic Flow and Heat and Mass Transfer Through a Porous Medium onto a Stretching Surface

Deva Kanta Phukan

doi:doi:10.11648/j.ajmcm.20261101.12

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Hiemenz Steady Hydromagnetic Flow and Heat and Mass Transfer Through a Porous Medium onto a Stretching Surface

Deva Kanta Phukan^*

Published in American Journal of Mathematical and Computer Modelling (Volume 11, Issue 1)

Received: 20 October 2025 Accepted: 6 November 2025 Published: 20 January 2026

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Abstract

In the present paper, steady stagnation flow of conducting fluid through a porous medium over a flat stretching surface with heat absorption/generation and chemical reaction in the presence of magnetic field has been studied under Soret and Dufour effects. The governing partial differential equation involved in this analysis viz conservation of mass, momentum, energy and concentration are transformed into self similar steady equations using similarity transformations and are solved numerically by using the Runge-Kutta fourth order scheme along with shooting technique for the whole domain for different existing flow parameters in this investigation. A representative set of graphical results for the flow field, temperature and concentration are presented for the different existing non dimensional flow parameters. The dimensionless velocity profiles are seen to decrease with increasing the magnetic, Lewis, porosity, viscosity, radiation, chemical reaction parameters and increases with Soret, Dufour, Stretching, thermal and concentration buoyancy parameters. An enhancement of temperature and concentration profiles are observed with increasing magnetic, and porosity parameter and the both temperature and concentration fall down with increment of surface stretching parameter, Prandtl number, thermal and concentration buoyancy parameters. On the other hands, the concentration is seen to become more thicker with enhancement of Soret, radiation, viscosity parameters while the reversed effects is observed in the case of temperature distribution. The reduction in concentration is observed with the increasing Lewis, Dufour, heat absorption, chemical reaction parameter and enhancement in temperature is noted for these parameters. Furthermore, the shear stress parameters, the rate of heat transfer and mass transfer are derived for existing non-dimensional flow parameters. A special case of our results obtained during investigation is an excellent agreement with an earlier published work.

Published in	American Journal of Mathematical and Computer Modelling (Volume 11, Issue 1)
DOI	10.11648/j.ajmcm.20261101.12
Page(s)	13-29
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), 2026. Published by Science Publishing Group

Keywords

Stagnation Flow, Soret and Dufour Number, Conducting Fluid, Heat and Mass Transfer, Chemical Reaction, Heat Absorption, Magnetic Field

References

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[17]	Seddeek, M. A. (2001). Thermal radiation and buoyancy effects on MHD free convection heat generation flow over an accelerating permeable surface with temperature dependent viscosity. Can. J. Phys., 79: 725-732.
[18]	Seddeek, M. A. and Salem, A.M. (2007). The effect of an axial magnetic field on the flow and heat transfer about a fluid underlying the axi-symmetric spreading surface with temperature with temperature dependent viscosity and thermal diffusivity. Comput. Mech., 39: 401-408.
[19]	Liao, S. J. and Pop, I. (2004). Explicit analytic solution for similarity boundary layer equations. Int. J. Heat Mass Transfer, 47: 75-85.
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[21]	Chamkha, A. J. and Ben-Nakhi, A. (2008). MHD mixed convection âradiation interaction along a permeable surface immersed in a porous medium in the presence of Soret and Dufour effect. Heat Mass transfer, 4 : 845-856.
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APA Style

Phukan, D. K. (2026). Hiemenz Steady Hydromagnetic Flow and Heat and Mass Transfer Through a Porous Medium onto a Stretching Surface. American Journal of Mathematical and Computer Modelling, 11(1), 13-29. https://doi.org/10.11648/j.ajmcm.20261101.12

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ACS Style

Phukan, D. K. Hiemenz Steady Hydromagnetic Flow and Heat and Mass Transfer Through a Porous Medium onto a Stretching Surface. Am. J. Math. Comput. Model. 2026, 11(1), 13-29. doi: 10.11648/j.ajmcm.20261101.12

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AMA Style

Phukan DK. Hiemenz Steady Hydromagnetic Flow and Heat and Mass Transfer Through a Porous Medium onto a Stretching Surface. Am J Math Comput Model. 2026;11(1):13-29. doi: 10.11648/j.ajmcm.20261101.12

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@article{10.11648/j.ajmcm.20261101.12,
  author = {Deva Kanta Phukan},
  title = {Hiemenz Steady Hydromagnetic Flow and Heat and Mass Transfer Through a Porous Medium onto a Stretching Surface },
  journal = {American Journal of Mathematical and Computer Modelling},
  volume = {11},
  number = {1},
  pages = {13-29},
  doi = {10.11648/j.ajmcm.20261101.12},
  url = {https://doi.org/10.11648/j.ajmcm.20261101.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmcm.20261101.12},
  abstract = {In the present paper, steady stagnation flow of conducting fluid through a porous medium over a flat stretching surface with heat absorption/generation and chemical reaction in the presence of magnetic field has been studied under Soret and Dufour effects. The governing partial differential equation involved in this analysis viz conservation of mass, momentum, energy and concentration are transformed into self similar steady equations using similarity transformations and are solved numerically by using the Runge-Kutta fourth order scheme along with shooting technique for the whole domain for different existing flow parameters in this investigation. A representative set of graphical results for the flow field, temperature and concentration are presented for the different existing non dimensional flow parameters. The dimensionless velocity profiles are seen to decrease with increasing the magnetic, Lewis, porosity, viscosity, radiation, chemical reaction parameters and increases with Soret, Dufour, Stretching, thermal and concentration buoyancy parameters. An enhancement of temperature and concentration profiles are observed with increasing magnetic, and porosity parameter and the both temperature and concentration fall down with increment of surface stretching parameter, Prandtl number, thermal and concentration buoyancy parameters. On the other hands, the concentration is seen to become more thicker with enhancement of Soret, radiation, viscosity parameters while the reversed effects is observed in the case of temperature distribution. The reduction in concentration is observed with the increasing Lewis, Dufour, heat absorption, chemical reaction parameter and enhancement in temperature is noted for these parameters. Furthermore, the shear stress parameters, the rate of heat transfer and mass transfer are derived for existing non-dimensional flow parameters. A special case of our results obtained during investigation is an excellent agreement with an earlier published work.
},
 year = {2026}
}

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TY  - JOUR
T1  - Hiemenz Steady Hydromagnetic Flow and Heat and Mass Transfer Through a Porous Medium onto a Stretching Surface 
AU  - Deva Kanta Phukan
Y1  - 2026/01/20
PY  - 2026
N1  - https://doi.org/10.11648/j.ajmcm.20261101.12
DO  - 10.11648/j.ajmcm.20261101.12
T2  - American Journal of Mathematical and Computer Modelling
JF  - American Journal of Mathematical and Computer Modelling
JO  - American Journal of Mathematical and Computer Modelling
SP  - 13
EP  - 29
PB  - Science Publishing Group
SN  - 2578-8280
UR  - https://doi.org/10.11648/j.ajmcm.20261101.12
AB  - In the present paper, steady stagnation flow of conducting fluid through a porous medium over a flat stretching surface with heat absorption/generation and chemical reaction in the presence of magnetic field has been studied under Soret and Dufour effects. The governing partial differential equation involved in this analysis viz conservation of mass, momentum, energy and concentration are transformed into self similar steady equations using similarity transformations and are solved numerically by using the Runge-Kutta fourth order scheme along with shooting technique for the whole domain for different existing flow parameters in this investigation. A representative set of graphical results for the flow field, temperature and concentration are presented for the different existing non dimensional flow parameters. The dimensionless velocity profiles are seen to decrease with increasing the magnetic, Lewis, porosity, viscosity, radiation, chemical reaction parameters and increases with Soret, Dufour, Stretching, thermal and concentration buoyancy parameters. An enhancement of temperature and concentration profiles are observed with increasing magnetic, and porosity parameter and the both temperature and concentration fall down with increment of surface stretching parameter, Prandtl number, thermal and concentration buoyancy parameters. On the other hands, the concentration is seen to become more thicker with enhancement of Soret, radiation, viscosity parameters while the reversed effects is observed in the case of temperature distribution. The reduction in concentration is observed with the increasing Lewis, Dufour, heat absorption, chemical reaction parameter and enhancement in temperature is noted for these parameters. Furthermore, the shear stress parameters, the rate of heat transfer and mass transfer are derived for existing non-dimensional flow parameters. A special case of our results obtained during investigation is an excellent agreement with an earlier published work.

VL  - 11
IS  - 1
ER  -

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Deva Kanta Phukan

Demow College(Sivasagar), Dibrugarh, Assam, India

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Phukan, D. K. (2026). Hiemenz Steady Hydromagnetic Flow and Heat and Mass Transfer Through a Porous Medium onto a Stretching Surface. American Journal of Mathematical and Computer Modelling, 11(1), 13-29. https://doi.org/10.11648/j.ajmcm.20261101.12

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ACS Style

Phukan, D. K. Hiemenz Steady Hydromagnetic Flow and Heat and Mass Transfer Through a Porous Medium onto a Stretching Surface. Am. J. Math. Comput. Model. 2026, 11(1), 13-29. doi: 10.11648/j.ajmcm.20261101.12

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AMA Style

Phukan DK. Hiemenz Steady Hydromagnetic Flow and Heat and Mass Transfer Through a Porous Medium onto a Stretching Surface. Am J Math Comput Model. 2026;11(1):13-29. doi: 10.11648/j.ajmcm.20261101.12

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@article{10.11648/j.ajmcm.20261101.12,
  author = {Deva Kanta Phukan},
  title = {Hiemenz Steady Hydromagnetic Flow and Heat and Mass Transfer Through a Porous Medium onto a Stretching Surface },
  journal = {American Journal of Mathematical and Computer Modelling},
  volume = {11},
  number = {1},
  pages = {13-29},
  doi = {10.11648/j.ajmcm.20261101.12},
  url = {https://doi.org/10.11648/j.ajmcm.20261101.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmcm.20261101.12},
  abstract = {In the present paper, steady stagnation flow of conducting fluid through a porous medium over a flat stretching surface with heat absorption/generation and chemical reaction in the presence of magnetic field has been studied under Soret and Dufour effects. The governing partial differential equation involved in this analysis viz conservation of mass, momentum, energy and concentration are transformed into self similar steady equations using similarity transformations and are solved numerically by using the Runge-Kutta fourth order scheme along with shooting technique for the whole domain for different existing flow parameters in this investigation. A representative set of graphical results for the flow field, temperature and concentration are presented for the different existing non dimensional flow parameters. The dimensionless velocity profiles are seen to decrease with increasing the magnetic, Lewis, porosity, viscosity, radiation, chemical reaction parameters and increases with Soret, Dufour, Stretching, thermal and concentration buoyancy parameters. An enhancement of temperature and concentration profiles are observed with increasing magnetic, and porosity parameter and the both temperature and concentration fall down with increment of surface stretching parameter, Prandtl number, thermal and concentration buoyancy parameters. On the other hands, the concentration is seen to become more thicker with enhancement of Soret, radiation, viscosity parameters while the reversed effects is observed in the case of temperature distribution. The reduction in concentration is observed with the increasing Lewis, Dufour, heat absorption, chemical reaction parameter and enhancement in temperature is noted for these parameters. Furthermore, the shear stress parameters, the rate of heat transfer and mass transfer are derived for existing non-dimensional flow parameters. A special case of our results obtained during investigation is an excellent agreement with an earlier published work.
},
 year = {2026}
}

Copy | Download

TY  - JOUR
T1  - Hiemenz Steady Hydromagnetic Flow and Heat and Mass Transfer Through a Porous Medium onto a Stretching Surface 
AU  - Deva Kanta Phukan
Y1  - 2026/01/20
PY  - 2026
N1  - https://doi.org/10.11648/j.ajmcm.20261101.12
DO  - 10.11648/j.ajmcm.20261101.12
T2  - American Journal of Mathematical and Computer Modelling
JF  - American Journal of Mathematical and Computer Modelling
JO  - American Journal of Mathematical and Computer Modelling
SP  - 13
EP  - 29
PB  - Science Publishing Group
SN  - 2578-8280
UR  - https://doi.org/10.11648/j.ajmcm.20261101.12
AB  - In the present paper, steady stagnation flow of conducting fluid through a porous medium over a flat stretching surface with heat absorption/generation and chemical reaction in the presence of magnetic field has been studied under Soret and Dufour effects. The governing partial differential equation involved in this analysis viz conservation of mass, momentum, energy and concentration are transformed into self similar steady equations using similarity transformations and are solved numerically by using the Runge-Kutta fourth order scheme along with shooting technique for the whole domain for different existing flow parameters in this investigation. A representative set of graphical results for the flow field, temperature and concentration are presented for the different existing non dimensional flow parameters. The dimensionless velocity profiles are seen to decrease with increasing the magnetic, Lewis, porosity, viscosity, radiation, chemical reaction parameters and increases with Soret, Dufour, Stretching, thermal and concentration buoyancy parameters. An enhancement of temperature and concentration profiles are observed with increasing magnetic, and porosity parameter and the both temperature and concentration fall down with increment of surface stretching parameter, Prandtl number, thermal and concentration buoyancy parameters. On the other hands, the concentration is seen to become more thicker with enhancement of Soret, radiation, viscosity parameters while the reversed effects is observed in the case of temperature distribution. The reduction in concentration is observed with the increasing Lewis, Dufour, heat absorption, chemical reaction parameter and enhancement in temperature is noted for these parameters. Furthermore, the shear stress parameters, the rate of heat transfer and mass transfer are derived for existing non-dimensional flow parameters. A special case of our results obtained during investigation is an excellent agreement with an earlier published work.

VL  - 11
IS  - 1
ER  -

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