Heat and Mass Transfer Effects on Unsteady Magnetohydrodynamics Stokes Free-Convective Flow Past an Infinite Vertical Porous Plate in a Rotating System

Mayaka Augustine Ayanga; Mathew Ngugi Kinyanjui; Jeconia Okelo Abonyo; Johana Kibet Sigey

doi:doi:10.11648/j.ajam.20221005.13

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Heat and Mass Transfer Effects on Unsteady Magnetohydrodynamics Stokes Free-Convective Flow Past an Infinite Vertical Porous Plate in a Rotating System

Mayaka Augustine Ayanga, Mathew Ngugi Kinyanjui, Jeconia Okelo Abonyo, Johana Kibet Sigey

Published in American Journal of Applied Mathematics (Volume 10, Issue 5)

Received: 30 August 2022 Accepted: 12 October 2022 Published: 24 October 2022

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Abstract

In this paper, Stokes first problem for an unsteady MHD free convective flow of a viscous incompressible fluid past an infinite vertical porous plate in the presence of a transverse variable magnetic field in a rotating system has been studied. The dimensionless governing partial differential equations are solved numerically by the finite difference method based on the forward-time central-space scheme. The resulting difference equations are simulated in MATLAB software to obtain the profiles of the flow variables. The skin-friction coefficient and the rates of heat and mass transfer are also computed. The simulation results are presented graphically and in tabular forms, and also discussed. The main findings are that an increase in the joule heating parameter results in a uniform increase in the velocity and temperature profiles near the plate but remain constantly distributed away from the plate. This observation implies that the flow is influenced substantially by the strength of joule heating near the plate and in the bulk of the fluid. The results obtained in this study regarding thermal and mass diffusion effects can be applied in the industry, for instance, in the separation of isotopes contained in a mixture of very light molecular-weight gases (for instance, hydrogen and helium) and medium molecular-weight gases (for instance, nitrogen and air).

Published in	American Journal of Applied Mathematics (Volume 10, Issue 5)
DOI	10.11648/j.ajam.20221005.13
Page(s)	212-222
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), 2022. Published by Science Publishing Group

Keywords

MHD-Flow, Rotating-System, Stokes-Problem, Vertical-Porous-Plate, Variable-Magnetic-Field, Skin-Friction, Heat-Transfer, Mass-Transfer

References

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[2]	J. Prakash, D. Bhanumathi, A. V. Kumar, and S. Varma, “Diffusionthermo and radiation effects on unsteady mhd flow through porous medium past an impulsively started infinite vertical plate with variable temperature and mass diffusion,” Transport in porous media, vol. 96, no. 1, pp. 135–151, 2013.
[3]	M. Narahari, S. Tippa, and R. Pendyala, “Unsteady magnetohydrodynamic free convection flow of a radiative fluid past an infinite vertical plate with constant heat and mass flux,” in Applied Mechanics and Materials, vol. 465. Trans Tech Publ, 2014, pp. 149–154.
[4]	M. R. Murthy, R. S. Raju, and J. A. Rao, “Heat and mass transfer effects on mhd natural convective flow past an infinite vertical porous plate with thermal radiation and hall current,” Procedia Engineering, vol. 127, pp. 1330–1337, 2015.
[5]	R. S. Raju, “Combined influence of thermal diffusion and diffusion thermo on unsteady mhd free convective fluid flow past an infinite vertical porous plate in presence of chemical reaction,” Journal of The Institution of Engineers (India): Series C, vol. 97, no. 4, pp. 505–515, 2016.
[6]	J. Pattnaik, G. Dash, and S. Singh, “Diffusion-thermo effect with hall current on unsteady hydromagnetic flow past an infinite vertical porous plate,” Alexandria Engineering Journal, vol. 56, no. 1, pp. 13–25, 2017.
[7]	M. V. Krishna, M. G. Reddy, and A. Chamkha, “Heat and mass transfer on mhd rotating flow of second grade fluid past an infinite vertical plate embedded in uniform porous medium with hall effects,” in Applied Mathematics and Scientific Computing. Springer, 2019, pp. 417–427.
[8]	F. O. Ochieng, “Hydromagnetic jeffery-hamel unsteady flow of a dissipative non-newtonian fluid with nonlinear viscosity,” Ph.D. dissertation, JKUAT-PAUSTI, 2018.
[9]	B. Parent, M. N. Shneider, and S. O. Macheret, “Generalized ohms law and potential equation in computational weakly-ionized plasmadynamics,” Journal of Computational Physics, vol. 230, no. 4, pp. 1439–1453, 2011.
[10]	M. Kinyanjui, M. Emmah, J. Marigi, and K. Kwanza, “Hydromagnetic turbulent flow of a rotating system past a semiinfinite vertical plate with hall current.,” International Journal of Heat and Mass transfer, vol. 79, pp. 97–119, 2012.
[11]	M. Moorthy and K. Senthilvadivu, “Soret and dufour effects on natural convection flow past a vertical surface in a porous medium with variable viscosity,” Journal of Applied Mathematics, vol. 2012, 2012.
[12]	K. Giterere, “Magnetohydrodynamic flow in porous media over a stretching surface in a rotating system with heat and mass transfer,” Ph.D. dissertation, 2013.
[13]	A. Maguna and N. Mutua, “Hall current effects on free convection flow and mass transfer past semi-infinite vertical flat plate,” Int. Jnl. of Mathematics and Statistics Studies, vol. 1, no. 4, pp. 1–22, 2013.
[14]	H. Zaman, A. Sohail et al., “Stokes first problem for an unsteady mhd third-grade fluid in a non-porous half space with hall currents,” Open Journal of Applied Sciences, vol. 2014, 2014.
[15]	N. Marneni, S. Tippa, and R. Pendyala, “Ramp temperature and dufour effects on transient mhd natural convection flow past an infinite vertical plate in a porous medium,” The European Physical Journal Plus, vol. 130, no. 12, p. 251, 2015.
[16]	K. Subbanna, S. G. Mohiddin, and R. B. Vijaya, “Combined effects on mhd flow of newtonian fluid past infinite vertical porous plate,” in AIP Conference Proceedings, vol. 1953, no. 1. AIP Publishing LLC, 2018, p. 140099.

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APA Style

Mayaka Augustine Ayanga, Mathew Ngugi Kinyanjui, Jeconia Okelo Abonyo, Johana Kibet Sigey. (2022). Heat and Mass Transfer Effects on Unsteady Magnetohydrodynamics Stokes Free-Convective Flow Past an Infinite Vertical Porous Plate in a Rotating System. American Journal of Applied Mathematics, 10(5), 212-222. https://doi.org/10.11648/j.ajam.20221005.13

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ACS Style

Mayaka Augustine Ayanga; Mathew Ngugi Kinyanjui; Jeconia Okelo Abonyo; Johana Kibet Sigey. Heat and Mass Transfer Effects on Unsteady Magnetohydrodynamics Stokes Free-Convective Flow Past an Infinite Vertical Porous Plate in a Rotating System. Am. J. Appl. Math. 2022, 10(5), 212-222. doi: 10.11648/j.ajam.20221005.13

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AMA Style

Mayaka Augustine Ayanga, Mathew Ngugi Kinyanjui, Jeconia Okelo Abonyo, Johana Kibet Sigey. Heat and Mass Transfer Effects on Unsteady Magnetohydrodynamics Stokes Free-Convective Flow Past an Infinite Vertical Porous Plate in a Rotating System. Am J Appl Math. 2022;10(5):212-222. doi: 10.11648/j.ajam.20221005.13

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@article{10.11648/j.ajam.20221005.13,
  author = {Mayaka Augustine Ayanga and Mathew Ngugi Kinyanjui and Jeconia Okelo Abonyo and Johana Kibet Sigey},
  title = {Heat and Mass Transfer Effects on Unsteady Magnetohydrodynamics Stokes Free-Convective Flow Past an Infinite Vertical Porous Plate in a Rotating System},
  journal = {American Journal of Applied Mathematics},
  volume = {10},
  number = {5},
  pages = {212-222},
  doi = {10.11648/j.ajam.20221005.13},
  url = {https://doi.org/10.11648/j.ajam.20221005.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20221005.13},
  abstract = {In this paper, Stokes first problem for an unsteady MHD free convective flow of a viscous incompressible fluid past an infinite vertical porous plate in the presence of a transverse variable magnetic field in a rotating system has been studied. The dimensionless governing partial differential equations are solved numerically by the finite difference method based on the forward-time central-space scheme. The resulting difference equations are simulated in MATLAB software to obtain the profiles of the flow variables. The skin-friction coefficient and the rates of heat and mass transfer are also computed. The simulation results are presented graphically and in tabular forms, and also discussed. The main findings are that an increase in the joule heating parameter results in a uniform increase in the velocity and temperature profiles near the plate but remain constantly distributed away from the plate. This observation implies that the flow is influenced substantially by the strength of joule heating near the plate and in the bulk of the fluid. The results obtained in this study regarding thermal and mass diffusion effects can be applied in the industry, for instance, in the separation of isotopes contained in a mixture of very light molecular-weight gases (for instance, hydrogen and helium) and medium molecular-weight gases (for instance, nitrogen and air).},
 year = {2022}
}

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TY  - JOUR
T1  - Heat and Mass Transfer Effects on Unsteady Magnetohydrodynamics Stokes Free-Convective Flow Past an Infinite Vertical Porous Plate in a Rotating System
AU  - Mayaka Augustine Ayanga
AU  - Mathew Ngugi Kinyanjui
AU  - Jeconia Okelo Abonyo
AU  - Johana Kibet Sigey
Y1  - 2022/10/24
PY  - 2022
N1  - https://doi.org/10.11648/j.ajam.20221005.13
DO  - 10.11648/j.ajam.20221005.13
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 212
EP  - 222
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20221005.13
AB  - In this paper, Stokes first problem for an unsteady MHD free convective flow of a viscous incompressible fluid past an infinite vertical porous plate in the presence of a transverse variable magnetic field in a rotating system has been studied. The dimensionless governing partial differential equations are solved numerically by the finite difference method based on the forward-time central-space scheme. The resulting difference equations are simulated in MATLAB software to obtain the profiles of the flow variables. The skin-friction coefficient and the rates of heat and mass transfer are also computed. The simulation results are presented graphically and in tabular forms, and also discussed. The main findings are that an increase in the joule heating parameter results in a uniform increase in the velocity and temperature profiles near the plate but remain constantly distributed away from the plate. This observation implies that the flow is influenced substantially by the strength of joule heating near the plate and in the bulk of the fluid. The results obtained in this study regarding thermal and mass diffusion effects can be applied in the industry, for instance, in the separation of isotopes contained in a mixture of very light molecular-weight gases (for instance, hydrogen and helium) and medium molecular-weight gases (for instance, nitrogen and air).
VL  - 10
IS  - 5
ER  -

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Author Information

Mayaka Augustine Ayanga

Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Mathew Ngugi Kinyanjui

Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Jeconia Okelo Abonyo

Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Johana Kibet Sigey

Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

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APA Style

Mayaka Augustine Ayanga, Mathew Ngugi Kinyanjui, Jeconia Okelo Abonyo, Johana Kibet Sigey. (2022). Heat and Mass Transfer Effects on Unsteady Magnetohydrodynamics Stokes Free-Convective Flow Past an Infinite Vertical Porous Plate in a Rotating System. American Journal of Applied Mathematics, 10(5), 212-222. https://doi.org/10.11648/j.ajam.20221005.13

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ACS Style

Mayaka Augustine Ayanga; Mathew Ngugi Kinyanjui; Jeconia Okelo Abonyo; Johana Kibet Sigey. Heat and Mass Transfer Effects on Unsteady Magnetohydrodynamics Stokes Free-Convective Flow Past an Infinite Vertical Porous Plate in a Rotating System. Am. J. Appl. Math. 2022, 10(5), 212-222. doi: 10.11648/j.ajam.20221005.13

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AMA Style

Mayaka Augustine Ayanga, Mathew Ngugi Kinyanjui, Jeconia Okelo Abonyo, Johana Kibet Sigey. Heat and Mass Transfer Effects on Unsteady Magnetohydrodynamics Stokes Free-Convective Flow Past an Infinite Vertical Porous Plate in a Rotating System. Am J Appl Math. 2022;10(5):212-222. doi: 10.11648/j.ajam.20221005.13

Copy | Download

@article{10.11648/j.ajam.20221005.13,
  author = {Mayaka Augustine Ayanga and Mathew Ngugi Kinyanjui and Jeconia Okelo Abonyo and Johana Kibet Sigey},
  title = {Heat and Mass Transfer Effects on Unsteady Magnetohydrodynamics Stokes Free-Convective Flow Past an Infinite Vertical Porous Plate in a Rotating System},
  journal = {American Journal of Applied Mathematics},
  volume = {10},
  number = {5},
  pages = {212-222},
  doi = {10.11648/j.ajam.20221005.13},
  url = {https://doi.org/10.11648/j.ajam.20221005.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20221005.13},
  abstract = {In this paper, Stokes first problem for an unsteady MHD free convective flow of a viscous incompressible fluid past an infinite vertical porous plate in the presence of a transverse variable magnetic field in a rotating system has been studied. The dimensionless governing partial differential equations are solved numerically by the finite difference method based on the forward-time central-space scheme. The resulting difference equations are simulated in MATLAB software to obtain the profiles of the flow variables. The skin-friction coefficient and the rates of heat and mass transfer are also computed. The simulation results are presented graphically and in tabular forms, and also discussed. The main findings are that an increase in the joule heating parameter results in a uniform increase in the velocity and temperature profiles near the plate but remain constantly distributed away from the plate. This observation implies that the flow is influenced substantially by the strength of joule heating near the plate and in the bulk of the fluid. The results obtained in this study regarding thermal and mass diffusion effects can be applied in the industry, for instance, in the separation of isotopes contained in a mixture of very light molecular-weight gases (for instance, hydrogen and helium) and medium molecular-weight gases (for instance, nitrogen and air).},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - Heat and Mass Transfer Effects on Unsteady Magnetohydrodynamics Stokes Free-Convective Flow Past an Infinite Vertical Porous Plate in a Rotating System
AU  - Mayaka Augustine Ayanga
AU  - Mathew Ngugi Kinyanjui
AU  - Jeconia Okelo Abonyo
AU  - Johana Kibet Sigey
Y1  - 2022/10/24
PY  - 2022
N1  - https://doi.org/10.11648/j.ajam.20221005.13
DO  - 10.11648/j.ajam.20221005.13
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 212
EP  - 222
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20221005.13
AB  - In this paper, Stokes first problem for an unsteady MHD free convective flow of a viscous incompressible fluid past an infinite vertical porous plate in the presence of a transverse variable magnetic field in a rotating system has been studied. The dimensionless governing partial differential equations are solved numerically by the finite difference method based on the forward-time central-space scheme. The resulting difference equations are simulated in MATLAB software to obtain the profiles of the flow variables. The skin-friction coefficient and the rates of heat and mass transfer are also computed. The simulation results are presented graphically and in tabular forms, and also discussed. The main findings are that an increase in the joule heating parameter results in a uniform increase in the velocity and temperature profiles near the plate but remain constantly distributed away from the plate. This observation implies that the flow is influenced substantially by the strength of joule heating near the plate and in the bulk of the fluid. The results obtained in this study regarding thermal and mass diffusion effects can be applied in the industry, for instance, in the separation of isotopes contained in a mixture of very light molecular-weight gases (for instance, hydrogen and helium) and medium molecular-weight gases (for instance, nitrogen and air).
VL  - 10
IS  - 5
ER  -

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