Unsteady Hydro-magnetic Stagnation Flow and Heat and Mass Transfer Past A Stretching Surface in the Presence Chemical Reaction Embedded in a Porous Medium

Deva Kanta Phukan

doi:doi:10.11648/j.ajam.20251306.16

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Unsteady Hydro-magnetic Stagnation Flow and Heat and Mass Transfer Past A Stretching Surface in the Presence Chemical Reaction Embedded in a Porous Medium

Deva Kanta Phukan^*

Published in American Journal of Applied Mathematics (Volume 13, Issue 6)

Received: 9 September 2025 Accepted: 4 October 2025 Published: 19 December 2025

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Abstract

A theoretical analysis is made on the unsteady stagnation point flow of a conducting fluid over a flat stretching surface in the presence of magnetic field with chemically reactive species concentration and mass diffusion under Soret and Dufour effects. The governing partial differential equations of continuity, momentum, energy and concentration have been converted to self-similar unsteady equations by using similarity transformations and solved numerically by the Runge-Kutta algorithm with Newton iteration in double precisions along with the shooting method across the boundary layer for the whole transient domain from the initial state to the final steady state flow. The effects of existing flow parameters viz Soret number, Dufour number, chemical reaction parameter, Darcy number and magnetic parameter are shown graphically for the dimensionless velocity, temperature and concentration of the conducting fluid.The velocity of the conducting fluid is seen to decrease across the boundary layer with increasing the magnetic parameter, Prandtl number, Schmidt number and chemical reaction parameter; and the velocity profiles are seen to increase with increasing the thermal Grashof number, mass Grashof number, Soret number, stretching parameter and Dufour number. The temperature is seen to decrease with increasing the Prandtl number, Soret number, stretching parameter, and the same temperature are found to increase with increasing Dufor number and Chemical reaction parameter across the boundary layer.In the same way, the concentration is seen to reduce with increasing Schmidt number, Dufour number, stretching parameter,chemical reaction parameter and but concentration increases with increasing Soret number. Further more, numerical results for the skin friction, Nusselt number and Sherwood number are tabulated for various flow parameters.It is clearly observed from the result that a smooth transition of flow of conducting fluid is seen from unsteady stage to the final steady stage. Skin friction decreases with the increasing magnetic parameter, Schmidt number, Prandtl number and chemical reaction parameter and same skin friction increases with the increasing Soret numbe, Dufour number, thermal and concentration buoyancy parameters, Darcy number, stretching parameter and dimensionless time. Nusselt number is seen to increase with increasing the value of Soret number, Prandtl number, stretching parameter, dimensionless time and the same Nusselt number decreases with increasing the value of Dufour number, chemical reaction parameter and Schmidt number. Sherwood number is seen to decrease with increasing the value of Soret number, Dufour number, Prandtl number and dimensionless time and is seen to increase with increasing Chemical reaction parameter, stretching parameter and Schmidt number. The results obtained in this investigation are seen good agreement with earlier published results in some particular cases.

Published in	American Journal of Applied Mathematics (Volume 13, Issue 6)
DOI	10.11648/j.ajam.20251306.16
Page(s)	438-451
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

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

References

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[2]	Sakiadis, B. C. (1961). Boundary layer behaviour on continuous solid flat surfaces, Journal of AICHE, 7: 26-28.
[3]	Crane, L. (1970). Flow past a stretching sheet. ZAMP, 21: 645-647.
[4]	Chiam, T. C. (1994). Stagnation point flow towards a stretching plate. Journal of physical society of Japan, 63: 2443-2444.
[5]	Andersson, K. I. Hansen, O. R. and Holmedal, B. (1994). Diffusion of a chemically reactive species from a stretching sheet. Int. Jr. Heat and Mass Transfer, 37: 659-664.
[6]	Anjalidevi, S. P. and Kandasamy, R. (1999). Effect of chemical reaction, heat and mass transfer on laminar flow along a semi infinite horizontal plate convection in a porous medium. Heat Mass Transfer, Vol.28: 909-918.
[7]	Muthucumaraswamy, R. (2002). Effects of chemical reaction on a moving isothermal vertical surface with suction. Acta Mech., 155: 65-70.
[8]	Chamkha, A. J. Al-Mudhaf, A. and Al-Yatam, J. (2004). Double diffusive convective flow of a micro-polar fluid over a vertical plate embedded in a porous medium with a chemical reaction. Int. Jr. Fluid Mech. Res., 6: 529-551.
[9]	Aboeldahab, E. M. and Azzam, G. E. A. (2006). Unsteady three dimensional combined heat and mass free convective flow over a stretching surface with timedependent chemical reaction. Acta Mech., 184: 121-136.
[10]	Tsai, R. and Huang, J. S. (2009). Heat and mass transfer for Soret and Dufour effects on Hiemenz flow through porous medium onto a stretching surface. Int. J. Heat Mass Transfer, 52 : 2399-2406.
[11]	Rashad, A. M. and El-Kabeir, S. M. (2010). Heat and mass transfer in transient flow by mixed convection boundary layer over a stretching sheet embedded in a porous medium with chemically reactive species. Journal of Porous Media, 13(1): 75-85.
[12]	Nayak, A., Panda, S. and Phukan, D. K. (2014). Soret and Dufour effect in a on mixed convection unsteady MHD boundary layer flow over stretching sheet in porous medium with chemically reactive species. Appl. Math. Mech.-Engl. Ed., 35(7): 849-862.
[13]	Abbas, Z., Sheikh, M. and Pop, I. (2015). Stagnation point flow of a hydro-magnetic viscous fluid over a stretching/shrinking with generalized slip condition in the presence of homogeneous-heterogeneous reaction. Journal of the Taiwan Institute of chemical Engineers, 55: 69-75.
[14]	Dash, G. C., Tripathy, R. S., Rashid, M. M. and Mishra, S. R. (2016). A numerical approach to boundary layer stagnation point flow past a stretching/ shrinking sheet. Journal of Molecular liquid, 221: 860-886.
[15]	Seth, G. S., Singha, A. K., Mandal, M. ., Benerjee, A. and Bhattacharyya, K. (2017). MHD stagnation point flow and heat transfer past a non-isothermal shrinking/stretching sheet in porous medium with heat sink or source effect. International Journal of Mechanical Science, 134: 98-111.
[16]	Veerkrishna, M., Gangadhara Reddy, M., and Chamkha, A. J. (2018). 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.
[17]	ShankarGoud, B. and Ganji, N. (2019). Stagnation point flow through a porous medium towards a stretching surface in the presence oh heat generation. International Journal of engineering and Advance Technology, 9(1): 2646-2650. https://doi.org/10.35940/ijeat.A.9880.109119
[18]	Feleke, B. T., Oluwole, D. M. and Lemiguta, E. (2021). Stagnation flow of a magnetite ferro fluid past a convectively heated permeable stretching /shrinking sheet in a Darcy-Forchheimer porous medium. Sadhana (Indian Academy of Science), 46: 115. https://doi.org/10.1007/s12046-021-01643-46789
[19]	Makinde, O. D., Borah, R. and Dey, D. (2022). Analysis of Dual Solutions in MHD Fluid Flow with Heat and Mass Transfer Past an Exponentially Shrinking/Stretching Surface in a Porous Medium. International Journal of Applied and Computational Mathematics, 8(article no.66).
[20]	Vishalakshi, A. B., Mahabaleshwar, U. S., Parez, L. M. and Manca, O. (June 2023). Hiemenz stagnation point flow with computational modelling of variety of boundary conditions. Journal of Magnetism and Magnetic Materials, 575(1): 170747. https://doi.org/10.1016/j.jmmm.2023.170747
[21]	Reddy, K. V. and Reddy, G. V. R. (2023). Outlining the impact modeling on MHD cassion fluid flow past a stretching sheet in a ,porous medium with radiation. Bioinferface Research in Apllied Chemistry, 13(1): 42. https://doi.org/10.33263/BRIAC131.042
[22]	Kandagal, M. and Kampepatti, R. (2024). An investigation of the heat and mass transfer effects in vertical channels with immiscible fluid flow through a porous matrix, J. Appl. Math. Mech. (ZAMM), 104(10). https://doi.org/10.1002/zamm.202300998
[23]	Sunitha, R. Y., Kalyan, K. P., Raghunath, K. and Farwa, A. (2024). Unsteady MHD rotating mixed convective flow through an infinite vertical plate subject to Joule heating, thermal radiation, Hall current, radiation absorption. Journal of Thermal Analysis and Calorimetry, 149: 8813-8826.
[24]	Choudhary, S. and Choudhary, M. K. (2025). Heat and mass transfer by MHD flow near the stagnation point over a stretching or shrinking sheet in a porous medium. Indian Journal of Pure and Applied Physics, 54(3): 10681. https://doi.org/10.56042/ijpap.v54i3.10681

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APA Style

Phukan, D. K. (2025). Unsteady Hydro-magnetic Stagnation Flow and Heat and Mass Transfer Past A Stretching Surface in the Presence Chemical Reaction Embedded in a Porous Medium. American Journal of Applied Mathematics, 13(6), 438-451. https://doi.org/10.11648/j.ajam.20251306.16

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ACS Style

Phukan, D. K. Unsteady Hydro-magnetic Stagnation Flow and Heat and Mass Transfer Past A Stretching Surface in the Presence Chemical Reaction Embedded in a Porous Medium. Am. J. Appl. Math. 2025, 13(6), 438-451. doi: 10.11648/j.ajam.20251306.16

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AMA Style

Phukan DK. Unsteady Hydro-magnetic Stagnation Flow and Heat and Mass Transfer Past A Stretching Surface in the Presence Chemical Reaction Embedded in a Porous Medium. Am J Appl Math. 2025;13(6):438-451. doi: 10.11648/j.ajam.20251306.16

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@article{10.11648/j.ajam.20251306.16,
  author = {Deva Kanta Phukan},
  title = {Unsteady Hydro-magnetic Stagnation Flow and Heat and Mass Transfer Past A Stretching Surface in the Presence Chemical Reaction Embedded in a Porous Medium
},
  journal = {American Journal of Applied Mathematics},
  volume = {13},
  number = {6},
  pages = {438-451},
  doi = {10.11648/j.ajam.20251306.16},
  url = {https://doi.org/10.11648/j.ajam.20251306.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20251306.16},
  abstract = {A theoretical analysis is made on the unsteady stagnation point flow of a conducting fluid over a flat stretching surface in the presence of magnetic field with chemically reactive species concentration and mass diffusion under Soret and Dufour effects. The governing partial differential equations of continuity, momentum, energy and concentration have been converted to self-similar unsteady equations by using similarity transformations and solved numerically by the Runge-Kutta algorithm with Newton iteration in double precisions along with the shooting method across the boundary layer for the whole transient domain from the initial state to the final steady state flow. The effects of existing flow parameters viz Soret number, Dufour number, chemical reaction parameter, Darcy number and magnetic parameter are shown graphically for the dimensionless velocity, temperature and concentration of the conducting fluid.The velocity of the conducting fluid is seen to decrease across the boundary layer with increasing the magnetic parameter, Prandtl number, Schmidt number and chemical reaction parameter; and the velocity profiles are seen to increase with increasing the thermal Grashof number, mass Grashof number, Soret number, stretching parameter and Dufour number. The temperature is seen to decrease with increasing the Prandtl number, Soret number, stretching parameter, and the same temperature are found to increase with increasing Dufor number and Chemical reaction parameter across the boundary layer.In the same way, the concentration is seen to reduce with increasing Schmidt number, Dufour number, stretching parameter,chemical reaction parameter and but concentration increases with increasing Soret number. Further more, numerical results for the skin friction, Nusselt number and Sherwood number are tabulated for various flow parameters.It is clearly observed from the result that a smooth transition of flow of conducting fluid is seen from unsteady stage to the final steady stage. Skin friction decreases with the increasing magnetic parameter, Schmidt number, Prandtl number and chemical reaction parameter and same skin friction increases with the increasing Soret numbe, Dufour number, thermal and concentration buoyancy parameters, Darcy number, stretching parameter and dimensionless time. Nusselt number is seen to increase with increasing the value of Soret number, Prandtl number, stretching parameter, dimensionless time and the same Nusselt number decreases with increasing the value of Dufour number, chemical reaction parameter and Schmidt number. Sherwood number is seen to decrease with increasing the value of Soret number, Dufour number, Prandtl number and dimensionless time and is seen to increase with increasing Chemical reaction parameter, stretching parameter and Schmidt number. The results obtained in this investigation are seen good agreement with earlier published results in some particular cases.
},
 year = {2025}
}

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TY  - JOUR
T1  - Unsteady Hydro-magnetic Stagnation Flow and Heat and Mass Transfer Past A Stretching Surface in the Presence Chemical Reaction Embedded in a Porous Medium

AU  - Deva Kanta Phukan
Y1  - 2025/12/19
PY  - 2025
N1  - https://doi.org/10.11648/j.ajam.20251306.16
DO  - 10.11648/j.ajam.20251306.16
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 438
EP  - 451
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20251306.16
AB  - A theoretical analysis is made on the unsteady stagnation point flow of a conducting fluid over a flat stretching surface in the presence of magnetic field with chemically reactive species concentration and mass diffusion under Soret and Dufour effects. The governing partial differential equations of continuity, momentum, energy and concentration have been converted to self-similar unsteady equations by using similarity transformations and solved numerically by the Runge-Kutta algorithm with Newton iteration in double precisions along with the shooting method across the boundary layer for the whole transient domain from the initial state to the final steady state flow. The effects of existing flow parameters viz Soret number, Dufour number, chemical reaction parameter, Darcy number and magnetic parameter are shown graphically for the dimensionless velocity, temperature and concentration of the conducting fluid.The velocity of the conducting fluid is seen to decrease across the boundary layer with increasing the magnetic parameter, Prandtl number, Schmidt number and chemical reaction parameter; and the velocity profiles are seen to increase with increasing the thermal Grashof number, mass Grashof number, Soret number, stretching parameter and Dufour number. The temperature is seen to decrease with increasing the Prandtl number, Soret number, stretching parameter, and the same temperature are found to increase with increasing Dufor number and Chemical reaction parameter across the boundary layer.In the same way, the concentration is seen to reduce with increasing Schmidt number, Dufour number, stretching parameter,chemical reaction parameter and but concentration increases with increasing Soret number. Further more, numerical results for the skin friction, Nusselt number and Sherwood number are tabulated for various flow parameters.It is clearly observed from the result that a smooth transition of flow of conducting fluid is seen from unsteady stage to the final steady stage. Skin friction decreases with the increasing magnetic parameter, Schmidt number, Prandtl number and chemical reaction parameter and same skin friction increases with the increasing Soret numbe, Dufour number, thermal and concentration buoyancy parameters, Darcy number, stretching parameter and dimensionless time. Nusselt number is seen to increase with increasing the value of Soret number, Prandtl number, stretching parameter, dimensionless time and the same Nusselt number decreases with increasing the value of Dufour number, chemical reaction parameter and Schmidt number. Sherwood number is seen to decrease with increasing the value of Soret number, Dufour number, Prandtl number and dimensionless time and is seen to increase with increasing Chemical reaction parameter, stretching parameter and Schmidt number. The results obtained in this investigation are seen good agreement with earlier published results in some particular cases.

VL  - 13
IS  - 6
ER  -

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Deva Kanta Phukan

Demow College (Sivasagar), Dibrugarh, India

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Phukan, D. K. (2025). Unsteady Hydro-magnetic Stagnation Flow and Heat and Mass Transfer Past A Stretching Surface in the Presence Chemical Reaction Embedded in a Porous Medium. American Journal of Applied Mathematics, 13(6), 438-451. https://doi.org/10.11648/j.ajam.20251306.16

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ACS Style

Phukan, D. K. Unsteady Hydro-magnetic Stagnation Flow and Heat and Mass Transfer Past A Stretching Surface in the Presence Chemical Reaction Embedded in a Porous Medium. Am. J. Appl. Math. 2025, 13(6), 438-451. doi: 10.11648/j.ajam.20251306.16

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AMA Style

Phukan DK. Unsteady Hydro-magnetic Stagnation Flow and Heat and Mass Transfer Past A Stretching Surface in the Presence Chemical Reaction Embedded in a Porous Medium. Am J Appl Math. 2025;13(6):438-451. doi: 10.11648/j.ajam.20251306.16

Copy | Download

@article{10.11648/j.ajam.20251306.16,
  author = {Deva Kanta Phukan},
  title = {Unsteady Hydro-magnetic Stagnation Flow and Heat and Mass Transfer Past A Stretching Surface in the Presence Chemical Reaction Embedded in a Porous Medium
},
  journal = {American Journal of Applied Mathematics},
  volume = {13},
  number = {6},
  pages = {438-451},
  doi = {10.11648/j.ajam.20251306.16},
  url = {https://doi.org/10.11648/j.ajam.20251306.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20251306.16},
  abstract = {A theoretical analysis is made on the unsteady stagnation point flow of a conducting fluid over a flat stretching surface in the presence of magnetic field with chemically reactive species concentration and mass diffusion under Soret and Dufour effects. The governing partial differential equations of continuity, momentum, energy and concentration have been converted to self-similar unsteady equations by using similarity transformations and solved numerically by the Runge-Kutta algorithm with Newton iteration in double precisions along with the shooting method across the boundary layer for the whole transient domain from the initial state to the final steady state flow. The effects of existing flow parameters viz Soret number, Dufour number, chemical reaction parameter, Darcy number and magnetic parameter are shown graphically for the dimensionless velocity, temperature and concentration of the conducting fluid.The velocity of the conducting fluid is seen to decrease across the boundary layer with increasing the magnetic parameter, Prandtl number, Schmidt number and chemical reaction parameter; and the velocity profiles are seen to increase with increasing the thermal Grashof number, mass Grashof number, Soret number, stretching parameter and Dufour number. The temperature is seen to decrease with increasing the Prandtl number, Soret number, stretching parameter, and the same temperature are found to increase with increasing Dufor number and Chemical reaction parameter across the boundary layer.In the same way, the concentration is seen to reduce with increasing Schmidt number, Dufour number, stretching parameter,chemical reaction parameter and but concentration increases with increasing Soret number. Further more, numerical results for the skin friction, Nusselt number and Sherwood number are tabulated for various flow parameters.It is clearly observed from the result that a smooth transition of flow of conducting fluid is seen from unsteady stage to the final steady stage. Skin friction decreases with the increasing magnetic parameter, Schmidt number, Prandtl number and chemical reaction parameter and same skin friction increases with the increasing Soret numbe, Dufour number, thermal and concentration buoyancy parameters, Darcy number, stretching parameter and dimensionless time. Nusselt number is seen to increase with increasing the value of Soret number, Prandtl number, stretching parameter, dimensionless time and the same Nusselt number decreases with increasing the value of Dufour number, chemical reaction parameter and Schmidt number. Sherwood number is seen to decrease with increasing the value of Soret number, Dufour number, Prandtl number and dimensionless time and is seen to increase with increasing Chemical reaction parameter, stretching parameter and Schmidt number. The results obtained in this investigation are seen good agreement with earlier published results in some particular cases.
},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Unsteady Hydro-magnetic Stagnation Flow and Heat and Mass Transfer Past A Stretching Surface in the Presence Chemical Reaction Embedded in a Porous Medium

AU  - Deva Kanta Phukan
Y1  - 2025/12/19
PY  - 2025
N1  - https://doi.org/10.11648/j.ajam.20251306.16
DO  - 10.11648/j.ajam.20251306.16
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 438
EP  - 451
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20251306.16
AB  - A theoretical analysis is made on the unsteady stagnation point flow of a conducting fluid over a flat stretching surface in the presence of magnetic field with chemically reactive species concentration and mass diffusion under Soret and Dufour effects. The governing partial differential equations of continuity, momentum, energy and concentration have been converted to self-similar unsteady equations by using similarity transformations and solved numerically by the Runge-Kutta algorithm with Newton iteration in double precisions along with the shooting method across the boundary layer for the whole transient domain from the initial state to the final steady state flow. The effects of existing flow parameters viz Soret number, Dufour number, chemical reaction parameter, Darcy number and magnetic parameter are shown graphically for the dimensionless velocity, temperature and concentration of the conducting fluid.The velocity of the conducting fluid is seen to decrease across the boundary layer with increasing the magnetic parameter, Prandtl number, Schmidt number and chemical reaction parameter; and the velocity profiles are seen to increase with increasing the thermal Grashof number, mass Grashof number, Soret number, stretching parameter and Dufour number. The temperature is seen to decrease with increasing the Prandtl number, Soret number, stretching parameter, and the same temperature are found to increase with increasing Dufor number and Chemical reaction parameter across the boundary layer.In the same way, the concentration is seen to reduce with increasing Schmidt number, Dufour number, stretching parameter,chemical reaction parameter and but concentration increases with increasing Soret number. Further more, numerical results for the skin friction, Nusselt number and Sherwood number are tabulated for various flow parameters.It is clearly observed from the result that a smooth transition of flow of conducting fluid is seen from unsteady stage to the final steady stage. Skin friction decreases with the increasing magnetic parameter, Schmidt number, Prandtl number and chemical reaction parameter and same skin friction increases with the increasing Soret numbe, Dufour number, thermal and concentration buoyancy parameters, Darcy number, stretching parameter and dimensionless time. Nusselt number is seen to increase with increasing the value of Soret number, Prandtl number, stretching parameter, dimensionless time and the same Nusselt number decreases with increasing the value of Dufour number, chemical reaction parameter and Schmidt number. Sherwood number is seen to decrease with increasing the value of Soret number, Dufour number, Prandtl number and dimensionless time and is seen to increase with increasing Chemical reaction parameter, stretching parameter and Schmidt number. The results obtained in this investigation are seen good agreement with earlier published results in some particular cases.

VL  - 13
IS  - 6
ER  -

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