Heat Source and Chemical Reaction Effects on the Unsteady Radiative Free Convection Flow of Conducting Fluid from an Impulsively Started Infinite Vertical Plate in the Presence of Magnetic Field

Deva Kanta Phukan

doi:doi:10.11648/j.ajam.20251305.15

Research Article |

| Peer-Reviewed

Heat Source and Chemical Reaction Effects on the Unsteady Radiative Free Convection Flow of Conducting Fluid from an Impulsively Started Infinite Vertical Plate in the Presence of Magnetic Field

Deva Kanta Phukan^*

Published in American Journal of Applied Mathematics (Volume 13, Issue 5)

Received: 11 August 2025 Accepted: 8 September 2025 Published: 22 October 2025

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

An investigation is made on the unsteady electrically conducting Newtonian fluid flow past a suddenly started vertical infinite flat plate under the influence of heat and mass transfer in the presence of magnetic field. The radiation and heat absorption effects are studied in this investigation. Mass diffusion are taken in to account the homogeneous chemical reaction of first order. By systematically transforming the governing set of partial differential equations into non dimensional form using selected similarity variables. An exact analytical solution is obtained from the dimensionless governing equations by using Laplace transform technique and inverse Laplace transform technique. The velocity, temperature and concentration profiles are presented for different existing flow parameters with the help of graphical representation. The velocity of the conducting fluid decreases with increasing magnetic parameter, heat absorption parameter, chemical reaction parameter and the velocity increases with increasing buoyancy parameter and time. The temperature of the fluid decreases with increasing the Prandtl number, heat absorption parameter and increases with increasing time. Similarly, the concentration of the fluid decreases with increasing the Schmidt number, chemical reaction parameter and increases with increasing time. The velocity, temperature and concentration profiles are studied for different existing parameters have been compared with earlier published works and the present results are found good agreement with the published results. The skin friction co-efficient, Nussult number and Sherwood number have also been calculated for all the existing parameters in this paper. Skin-friction decreases with increasing the magnetic parameter but skin friction increases with the increasing chemical reaction parameter, Prandtl number, Schmidt number, heat absorption parameter and time. No magnetic effect is observed on Nusselt and Sherwood number but with the increase of Prandtl number and Schmidt number, Nusselt number and Sherwood number are seen to increase respectively but both decrease with increasing time.

Published in	American Journal of Applied Mathematics (Volume 13, Issue 5)
DOI	10.11648/j.ajam.20251305.15
Page(s)	348-359
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

Unsteady Flow, Vertical Late, Conducting Fluid, Magnetic Field, Heat Transfer, Mass Transfer

References

[1]	Ahmed, N. (2012). Soret and radiation effects on transient MHD free convection from an impulsively started infinite vertical plate, J. Heat transfer, 134: 1-9.
[2]	Viskanta, R. and Grosh, R. J. (1962). Boundary layer in thermal radiation absorbing and emitting media. Int. J. H eat Mass Transfer, 5: 795-806.
[3]	Cess, R. D. (1964). The interaction of thermal radiation with conduction and convection heat transfer. Adv. Heat transfer, 1, Academic press, New York, 1-50.
[4]	Sparrow, E. M. and Cess, R. D. (1978). The radiation Heat transfer, Hemisphere publishing Coporation, Washington.
[5]	Chen, H. T., and Chen, C. K. (1988). Free convection flow of non-Newtonian fluids along a vertical plate embedded in a porous medium. J. Heat Transfer, 110: 257260.
[6]	Hossain, M. A. (1992). Unsteady MHD convective transfer past a semi-infinite vertical porous moving plate with variable plate temperature. Int. J. Heat Mass Transfer, 35: 3485.
[7]	H. S Takhar, H. S., Goria, S. R. and Soundalgekar, V. M. (1996). Radiation effects on MHD free convection flow of a radiating gas past a semi-infinite vertical plate. Int. J. Numer. Methods Heat fluid flow, 6: 7783.
[8]	Hossain, M. A., Alin, M. A. and Rees, D. A. S. (1999). Effects of radiation on free convection from a porous vertical plate. Int. J. Heat Mass Transfer, 42: 181191.
[9]	Hossain, M. A., Khanaier, K. and Vafai, K. (2001). The effect of radiation on free convection flow of fluid with variable viscosity from a porous vertical plate. Int. J. Therm. Sci, 40: 115-124.
[10]	Kumar, B. V. R., Singh, V. and Bansud, V. J. (2002). Effects of thermal stratification on double diffusive natural convection in a vertical porous enclosure. Numer. Heat Transfer, Part A Appl. 41(4): 421447.
[11]	Muthucumaraswamy, R. and Kumar, G. S. (2004). Heat and Mass transfer effect on moving vertical plate in the presence of thermal radiation. Theor. Appl. Mech., 31: 3546.
[12]	Muthucumaraswamy, R. and Janakriraman, B. (2008). Mass transfer effects on isothermal vertical oscillating plate in the presence of chemical reaction. Int. J. Appl. Math. Mech., 4(1): 66-74.
[13]	Ahmed, N. and Sharma, H. K. (2009). The radiation effect on a transient MHD flow with mass transfer past an impulsively fixed infinite vertical plate. Int. J. Appl. Math. Mech., 5: 8798.
[14]	Ishak, A., (2009). Mixed convection boundary layer flow over a horizontal plate with thermal radiation. Heat mass transfer, 46: 147-151.
[15]	D. Paul, D. and Talukdar, B. (2010). Perturbation analysis of unsteady magneto-hydrodynamic convective heat and mass transfer in a boundary layer slip flow past a vertical permeable plate with thermal radiation and chemical reaction, Commun nonlinear Sci. Numer Simulation: 15: 1813-1830.
[16]	Turkyilmazoglu, M. and Pop, I. (2012). Soret and heat source effects on the unsteady radiative MHD free convective flow from an impulsively started infinite vertical plate. Int. J. Heat Mass Transfer: 55, 7635-7644.
[17]	Muthucumaraswamy, M. and Radhakrishnan, M. (2012). Chemical reaction effects on flow past an accelerated vertical plate with variable temperature and mass diffusion in the presence of magnetic field. Journal of Mechanical Engineering and science. 32: 51-260. http://dx.doi.org/10.15282/jmes.3.2012.1.0023
[18]	Sarki, M. N. and Ahmed, A. (2012). Heat and Mass transfer with chemical reaction and exponential mass diffusion. International journal of Engineering Research and technology, 1(8).
[19]	Rajput, U. S. and Kumar, S. (2012). Radiation effects on MHD flow past an impulsively started vertical plate with variable heat and mass transfer. Int. J. Appl. Math. Mech., 8(1): 66-85.
[20]	Nayak, A., Panda, S. and Phukan, D. K. (2014). Soret and Dufour effect 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. https://doi.org/10.1007/s10483-014-1830-9
[21]	Meyer, T. (2015). Analytical solution for combined heat and mass transfer in laminar falling film absorption with uniform film velocity-adiabatic wall boundary. Int. J. Heat Mass Transfer, 80: 802-811.
[22]	Seth, G., Sharma, R., Kumbhakar, B. (2016). Heat and mass transfer effects on unsteady MHD natural convection flow of a chemically reactive and radiating fluid through a porous medium past a moving vertical plate with arbitrary ramped temperature. J Appl Fluid Mech., 9(1): 103-117.
[23]	Dharmaiah, G., Kumar, U. Y. and Vedavathi, N. (2017). Magneto-hydrodynamic convective flow past a vertical porous surface in slip flow regime. Int. J. Theor. Appl. Mech., 12(1): 71-81. http://www.ripublication.com
[24]	Ahmed, S. and Zueco, J. (2017). Effects of chemical reaction, heat and mass transfer and viscous dissipation over a MHD flow in a vertical porous wall using perturbation method. Int. J. Heat Mass Transfer, 104: 409-418.
[25]	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): 1-5.
[26]	Krishna, MV., Anand, PVS., Chamkha, AJ. (2019). Heat and mass transfer on free convective flow of a micropolar fluid through a porous surface with inclined magnetic field and hall effects. Spec Top Rev Porous Media: Int J., 10(3), 203-223.
[27]	Veerkrishna, M., Jyothi, K., and Chamkha, A. J. (2020)., Heat and mass transfer of second grade fluid through porous medium over a semi-infinite vertical stretching sheet. J. Porous Media, 23(8): 751-765. https://doi.org/10.1615/JPorMedia.2020023817
[28]	Appidi L, Malga BS, Kumar PP., Effect of thermal radiation on an unsteady MHD flow over an impulse vertical infinite plate with variant temperature in existence of Hall current, Heat Transfer. 51 2367-2382 (2021). https://doi.org/10.1002/htj.22402
[29]	Asjad, M. N., Faridi, W. A., Abubakar, M. and Aleem, M. (2021). Enhancement of heat and mass transfer of a physical model using caputo fractional derivative of variable order and modified Laplace transform method. Journal of Math Anal and Model, 2(3): 41-61. https://doi.org/10.48185/jmam.v2i3.380
[30]	Choudhury, K., Ahmed, N. and Chamuah, K. (2022). Radiation effect on MHD flow past a porous vertical plate in the presence of heat sink. Heat Transfer, 51: 5302-5319. https://doi.org/10.1002/htj.22548
[31]	Choudhury, K. and Agarwalla, S. (2023)., Hydromagnetic convective flow past a porous vertical plate with constant heat flux and heat sink. Math Eng Sci Aerosp., 14(2): 579-595.
[32]	Phukan, D. K. (2025). Study of thermal buoyancy and concentration buoyancy effects on the electrically conducting fluid flow past an impulsively started vertical plate with temperature and mass diffusion in the presence of inclined magnetic field. International J. of Math. Sci. Engg. Appls. (IJMSEA), 19(I): 15-31.
[33]	Shah, N. A., Ali, F., Yook, S. J. and Zafar, S. S. (2025). Dynamic of chemical reactive on magneto Hybrid Nano meterial with heat radiation due to porous exponential plate: Laplace tranfom technique for heat and mass. Journal of radiation research and applied sciences,18(1): 101295.
[34]	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. Int. J. Theo. Appl. Math., 11(2): 34-44.
[35]	Cogley, A. C. L., Vinvent, W. G. and Giles, E. S. (1968). Differential approximation for radiative heat transfer in non-linear equations-grey gas near equilibrium. American Institute of Aeronautics and Astronautics, 6: 551-553.
[36]	Hetnarski, R. B. (1975). An algorithm for generating some inverse Laplace transforms of exponential form. ZAMP, 26: 249-253.
[37]	Spiegel M. R. (1986). Theory and problems of Laplace transforms, McGraw-HillBookCompany, NewYork, 97.
[38]	Campbell, G. A. and Foster, R. M. (1948). Fourier integrals for practical applications, D. Van Nostrand Company, Inc. New York.

Cite This Article

Plain Text BibTeX RIS

APA Style

Phukan, D. K. (2025). Heat Source and Chemical Reaction Effects on the Unsteady Radiative Free Convection Flow of Conducting Fluid from an Impulsively Started Infinite Vertical Plate in the Presence of Magnetic Field. American Journal of Applied Mathematics, 13(5), 348-359. https://doi.org/10.11648/j.ajam.20251305.15

Copy | Download

ACS Style

Phukan, D. K. Heat Source and Chemical Reaction Effects on the Unsteady Radiative Free Convection Flow of Conducting Fluid from an Impulsively Started Infinite Vertical Plate in the Presence of Magnetic Field. Am. J. Appl. Math. 2025, 13(5), 348-359. doi: 10.11648/j.ajam.20251305.15

Copy | Download

AMA Style

Phukan DK. Heat Source and Chemical Reaction Effects on the Unsteady Radiative Free Convection Flow of Conducting Fluid from an Impulsively Started Infinite Vertical Plate in the Presence of Magnetic Field. Am J Appl Math. 2025;13(5):348-359. doi: 10.11648/j.ajam.20251305.15

Copy | Download

@article{10.11648/j.ajam.20251305.15,
  author = {Deva Kanta Phukan},
  title = {Heat Source and Chemical Reaction Effects on the Unsteady Radiative Free Convection Flow of Conducting Fluid from an Impulsively Started Infinite Vertical Plate in the Presence of Magnetic Field
},
  journal = {American Journal of Applied Mathematics},
  volume = {13},
  number = {5},
  pages = {348-359},
  doi = {10.11648/j.ajam.20251305.15},
  url = {https://doi.org/10.11648/j.ajam.20251305.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20251305.15},
  abstract = {An investigation is made on the unsteady electrically conducting Newtonian fluid flow past a suddenly started vertical infinite flat plate under the influence of heat and mass transfer in the presence of magnetic field. The radiation and heat absorption effects are studied in this investigation. Mass diffusion are taken in to account the homogeneous chemical reaction of first order. By systematically transforming the governing set of partial differential equations into non dimensional form using selected similarity variables. An exact analytical solution is obtained from the dimensionless governing equations by using Laplace transform technique and inverse Laplace transform technique. The velocity, temperature and concentration profiles are presented for different existing flow parameters with the help of graphical representation. The velocity of the conducting fluid decreases with increasing magnetic parameter, heat absorption parameter, chemical reaction parameter and the velocity increases with increasing buoyancy parameter and time. The temperature of the fluid decreases with increasing the Prandtl number, heat absorption parameter and increases with increasing time. Similarly, the concentration of the fluid decreases with increasing the Schmidt number, chemical reaction parameter and increases with increasing time. The velocity, temperature and concentration profiles are studied for different existing parameters have been compared with earlier published works and the present results are found good agreement with the published results. The skin friction co-efficient, Nussult number and Sherwood number have also been calculated for all the existing parameters in this paper. Skin-friction decreases with increasing the magnetic parameter but skin friction increases with the increasing chemical reaction parameter, Prandtl number, Schmidt number, heat absorption parameter and time. No magnetic effect is observed on Nusselt and Sherwood number but with the increase of Prandtl number and Schmidt number, Nusselt number and Sherwood number are seen to increase respectively but both decrease with increasing time.
},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Heat Source and Chemical Reaction Effects on the Unsteady Radiative Free Convection Flow of Conducting Fluid from an Impulsively Started Infinite Vertical Plate in the Presence of Magnetic Field

AU  - Deva Kanta Phukan
Y1  - 2025/10/22
PY  - 2025
N1  - https://doi.org/10.11648/j.ajam.20251305.15
DO  - 10.11648/j.ajam.20251305.15
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 348
EP  - 359
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20251305.15
AB  - An investigation is made on the unsteady electrically conducting Newtonian fluid flow past a suddenly started vertical infinite flat plate under the influence of heat and mass transfer in the presence of magnetic field. The radiation and heat absorption effects are studied in this investigation. Mass diffusion are taken in to account the homogeneous chemical reaction of first order. By systematically transforming the governing set of partial differential equations into non dimensional form using selected similarity variables. An exact analytical solution is obtained from the dimensionless governing equations by using Laplace transform technique and inverse Laplace transform technique. The velocity, temperature and concentration profiles are presented for different existing flow parameters with the help of graphical representation. The velocity of the conducting fluid decreases with increasing magnetic parameter, heat absorption parameter, chemical reaction parameter and the velocity increases with increasing buoyancy parameter and time. The temperature of the fluid decreases with increasing the Prandtl number, heat absorption parameter and increases with increasing time. Similarly, the concentration of the fluid decreases with increasing the Schmidt number, chemical reaction parameter and increases with increasing time. The velocity, temperature and concentration profiles are studied for different existing parameters have been compared with earlier published works and the present results are found good agreement with the published results. The skin friction co-efficient, Nussult number and Sherwood number have also been calculated for all the existing parameters in this paper. Skin-friction decreases with increasing the magnetic parameter but skin friction increases with the increasing chemical reaction parameter, Prandtl number, Schmidt number, heat absorption parameter and time. No magnetic effect is observed on Nusselt and Sherwood number but with the increase of Prandtl number and Schmidt number, Nusselt number and Sherwood number are seen to increase respectively but both decrease with increasing time.

VL  - 13
IS  - 5
ER  -

Copy | Download

Author Information

Deva Kanta Phukan

Demow College (Sivasagar), Dibrugarh, India

Contact Email

Download PDF

Submit an Article

Sections

Plain Text BibTeX RIS

APA Style

Phukan, D. K. (2025). Heat Source and Chemical Reaction Effects on the Unsteady Radiative Free Convection Flow of Conducting Fluid from an Impulsively Started Infinite Vertical Plate in the Presence of Magnetic Field. American Journal of Applied Mathematics, 13(5), 348-359. https://doi.org/10.11648/j.ajam.20251305.15

Copy | Download

ACS Style

Phukan, D. K. Heat Source and Chemical Reaction Effects on the Unsteady Radiative Free Convection Flow of Conducting Fluid from an Impulsively Started Infinite Vertical Plate in the Presence of Magnetic Field. Am. J. Appl. Math. 2025, 13(5), 348-359. doi: 10.11648/j.ajam.20251305.15

Copy | Download

AMA Style

Phukan DK. Heat Source and Chemical Reaction Effects on the Unsteady Radiative Free Convection Flow of Conducting Fluid from an Impulsively Started Infinite Vertical Plate in the Presence of Magnetic Field. Am J Appl Math. 2025;13(5):348-359. doi: 10.11648/j.ajam.20251305.15

Copy | Download

@article{10.11648/j.ajam.20251305.15,
  author = {Deva Kanta Phukan},
  title = {Heat Source and Chemical Reaction Effects on the Unsteady Radiative Free Convection Flow of Conducting Fluid from an Impulsively Started Infinite Vertical Plate in the Presence of Magnetic Field
},
  journal = {American Journal of Applied Mathematics},
  volume = {13},
  number = {5},
  pages = {348-359},
  doi = {10.11648/j.ajam.20251305.15},
  url = {https://doi.org/10.11648/j.ajam.20251305.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20251305.15},
  abstract = {An investigation is made on the unsteady electrically conducting Newtonian fluid flow past a suddenly started vertical infinite flat plate under the influence of heat and mass transfer in the presence of magnetic field. The radiation and heat absorption effects are studied in this investigation. Mass diffusion are taken in to account the homogeneous chemical reaction of first order. By systematically transforming the governing set of partial differential equations into non dimensional form using selected similarity variables. An exact analytical solution is obtained from the dimensionless governing equations by using Laplace transform technique and inverse Laplace transform technique. The velocity, temperature and concentration profiles are presented for different existing flow parameters with the help of graphical representation. The velocity of the conducting fluid decreases with increasing magnetic parameter, heat absorption parameter, chemical reaction parameter and the velocity increases with increasing buoyancy parameter and time. The temperature of the fluid decreases with increasing the Prandtl number, heat absorption parameter and increases with increasing time. Similarly, the concentration of the fluid decreases with increasing the Schmidt number, chemical reaction parameter and increases with increasing time. The velocity, temperature and concentration profiles are studied for different existing parameters have been compared with earlier published works and the present results are found good agreement with the published results. The skin friction co-efficient, Nussult number and Sherwood number have also been calculated for all the existing parameters in this paper. Skin-friction decreases with increasing the magnetic parameter but skin friction increases with the increasing chemical reaction parameter, Prandtl number, Schmidt number, heat absorption parameter and time. No magnetic effect is observed on Nusselt and Sherwood number but with the increase of Prandtl number and Schmidt number, Nusselt number and Sherwood number are seen to increase respectively but both decrease with increasing time.
},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Heat Source and Chemical Reaction Effects on the Unsteady Radiative Free Convection Flow of Conducting Fluid from an Impulsively Started Infinite Vertical Plate in the Presence of Magnetic Field

AU  - Deva Kanta Phukan
Y1  - 2025/10/22
PY  - 2025
N1  - https://doi.org/10.11648/j.ajam.20251305.15
DO  - 10.11648/j.ajam.20251305.15
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 348
EP  - 359
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20251305.15
AB  - An investigation is made on the unsteady electrically conducting Newtonian fluid flow past a suddenly started vertical infinite flat plate under the influence of heat and mass transfer in the presence of magnetic field. The radiation and heat absorption effects are studied in this investigation. Mass diffusion are taken in to account the homogeneous chemical reaction of first order. By systematically transforming the governing set of partial differential equations into non dimensional form using selected similarity variables. An exact analytical solution is obtained from the dimensionless governing equations by using Laplace transform technique and inverse Laplace transform technique. The velocity, temperature and concentration profiles are presented for different existing flow parameters with the help of graphical representation. The velocity of the conducting fluid decreases with increasing magnetic parameter, heat absorption parameter, chemical reaction parameter and the velocity increases with increasing buoyancy parameter and time. The temperature of the fluid decreases with increasing the Prandtl number, heat absorption parameter and increases with increasing time. Similarly, the concentration of the fluid decreases with increasing the Schmidt number, chemical reaction parameter and increases with increasing time. The velocity, temperature and concentration profiles are studied for different existing parameters have been compared with earlier published works and the present results are found good agreement with the published results. The skin friction co-efficient, Nussult number and Sherwood number have also been calculated for all the existing parameters in this paper. Skin-friction decreases with increasing the magnetic parameter but skin friction increases with the increasing chemical reaction parameter, Prandtl number, Schmidt number, heat absorption parameter and time. No magnetic effect is observed on Nusselt and Sherwood number but with the increase of Prandtl number and Schmidt number, Nusselt number and Sherwood number are seen to increase respectively but both decrease with increasing time.

VL  - 13
IS  - 5
ER  -

Copy | Download