The Effect of Strong Magnetic Field on Unsteady MHD Nanofluid Flow Through Convergent-Divergent Channel with Heat and Mass Transfer

Felicien Habiyaremye; Mary Wainaina; Mark Kimathi

doi:doi:10.11648/j.ijfmts.20220803.11

| Peer-Reviewed

The Effect of Strong Magnetic Field on Unsteady MHD Nanofluid Flow Through Convergent-Divergent Channel with Heat and Mass Transfer

Felicien Habiyaremye, Mary Wainaina, Mark Kimathi

Published in International Journal of Fluid Mechanics & Thermal Sciences (Volume 8, Issue 3)

Received: 20 June 2022 Accepted: 6 July 2022 Published: 13 July 2022

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

Magnetohydrodynamic Nanofluid flow (Silver-water) through a converging-diverging channel under a strong magnetic field has been investigated. The induction equation is derived from electromagnetism. The non-linear partial differential equations are reduced to first-order non-linear ordinary differential equations using the similarity transformation and dimensionless numbers. The implicit Runge - Kutta fourth-order method via the bvp4c function in MATLAB has been used to generate the graphs of the fluid flow. It was observed that the high value of the Schmidt number leads to an increase in the velocity of the Nanofluid flow. The variation of the Schmidt number leads to a decrease in the temperature profile of the Nanofluid flow in the stretching channel and leads to an increase in the shrinking channel. The higher value of the Schmidt number leads to higher values in the concentration of the Nanofluid flow. Increasing the values of the Schmidt number leads to an augment in the magnetic induction of the Nanofluid flow for the divergent channel and a decrease is observed for a case of the convergent channel. Variation of the nanoparticle volume fraction increases the magnetic induction profiles of the Nanofluid flow for a stretching channel, and a decrease is observed for the case of the shrinking channel. The high value in Reynolds magnetic number leads to a high value in the velocity profile of Nanofluid flow. The change in Reynolds magnetic number leads to a high value in the temperature profiles of the Nanofluid flow for the case of a divergent channel and a decrease is observed for the case of a convergent channel. Varying the Reynolds magnetic number leads to a decrease in the magnetic induction profiles of the Nanofluid, this is due to the effectiveness of the relationship between the fluid flow and the magnetic field. Varying the Reynolds magnetic number leads to an augment in the induction profiles of the Nanofluid. This kind of study has a variety of applications such as geophysics, astrophysics, fire engineering, bio-medical, and blood flow through arteries and capillaries in the human body.

Published in	International Journal of Fluid Mechanics & Thermal Sciences (Volume 8, Issue 3)
DOI	10.11648/j.ijfmts.20220803.11
Page(s)	41-52
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), 2024. Published by Science Publishing Group

Keywords

Induction Equation, Electromagnetic Equations, Unsteadiness, MHD Nanofluid Flow, Divergent-Convergent Channel

References

[1]	Faraday. (1832). Experimental Research in Electricity, Phil. Trans, Vol. 15, p. 175.
[2]	Ritchie. (1932). Experimental Researches in Voltaic Electricity and Electromagnetism, Phil. Trans. Roy Soc. London Vol. 122. 279.
[3]	Smith. C. G. and Slepian. J. (1917). Electromagnetic Ships Lof, United States Patent 1, 249.
[4]	William. E. J (1930). The Induced of E. M. F's in a Moving Fluid by a Magnetic Field and its Application to an Investigation of the Flow of Liquids, Proc. Camb, Phil Soc (London), Vol 42, p. 466.
[5]	Young. F. B., Gerard. H. and Jevans. W. (1920). On Electrical Disturbances due to Tides and Waves, 6th Series, Phil. Vol. 40, p. 149.
[6]	Alfven. (1942). On the existence of Electromagnetic -Hydrodynamic Waves, -F. Mat. Astro. O. Fysic Bd, Vol. 298 (2).
[7]	Soundalgekar. V. M., Guta. S. K., and Aranake. R. N. (1979). Free Convection effects on MHD Stokes Problem for a Vertical Plate. Nuclear Engineering and Design 5 (3), 313-407.
[8]	Raptis. A. and Sing. A. K. (1983). MHD Free Convection Flow Past Accelerated Vertical Plate. International Communication in heat and Mass Transfer 10 (4), 313-321.
[9]	Helmy. K. A. (1998). MHD Unsteady Free Convection past a Vertical Porous Plate. ZAMM- Journal of Applied Mathematics and Mechanics 78 (4), 255-270.
[10]	Thiele. (1999). Stationary Transverse Diffusion in Horizontal Porous medium Boundary-Layer Flow with Concentration-Dependent Fluid Density and Viscosity. Transport in porous media, Vol. 36, pp. 341-355.
[11]	Ganesh. S. & Krishnambal. S. S. (2007). Unsteady MHD Stokes Flow of Viscous Fluid Between two Parallel Porous Plates, Journal of Applied Sciences 7, 374-379.
[12]	Sigh. B. and Okwoyo. M. J. M. J. (2008). Couette Flow Between two parallel Infinite Plates in the Presence of Transverse Magnetic Field. Kenya Meterol. Soc 2 (2). Pp. 90-94.
[13]	Mburu. N. A., Onyango. And Jackson. K. Kwanza. (2016). Investigation of MHD Flow Between two Parallel Infinite Plate Subjected to Inclined Magnetic Field under Applied Pressure Gradient. Journal of Multidisciplinary Science and Technology. ISSN 2455. 9403, Vol. 3.
[14]	Manyonge. W. A, Kiema D. W. and Iyaya. C. C. W. (2012). Steady MHD Poiseuille Flow Between two Infinite Parallel Porous Plates in an Inclined Magnetic Field, IJ- PAM, 76 (5), PP. 661-668.
[15]	Raiham. N. M. A. (2017). MHD Free Convective Fluid of Incompressible Viscous Fluid past a Vertical Plate in the Presence of Magnetic Field. Journal of Physics, Phys: Conf. Ser. 890 012009.
[16]	Lakshmi. (2014). The Numerical Solution of MHD Flow over a Moving Vertical Porous Plate with Heat and Mass Transfer. Int. J. Chem. Sci. 12 (4), 1487-1499.
[17]	Bhattachryya &Layek, G. (2014). Magneto hydrodynamic Boundary Layer Flow of Nanofluid over an exponentially stretching Permeable sheet. Hindawi Publishing Corporation Physics Research International. Volume 2014, Article ID 592536.
[18]	Makinde, O. D (2012). Analysis of Sakiadis Flow of Nanofluids with Viscous Dissipation and Newtonian Heating. Applied Mathematics and Mechanics. Engl. Ed. 33 (12), 1545-1554.
[19]	Virginia M. Kitetu, Thomas T. M. Onyango, Jackson Kwanza. (2019). Analysis of the Effect of Stretching Parameter and Time Parameter on MHD Nanofluid Flow in the Presence of Suction. Global Journal of Pure and Applied Mathematics. 4 (7): ISSN 0973-1768. Volume 15, Number 5, pp. 637-648.
[20]	Makinde, O. D. (2008). Effect of Arbitrary Magnetic Reynolds Number on MHD Flows in Convergent-Divergent Channels. International Journal of Numerical Methods for heat and Fluid Flow. Vol. 18 ISS: 6pp. 697-700.
[21]	Felicien Habiyaremye, Mary Wainaina, Mark Kimathi, the Effect of Heat and Mass Transfer on Unsteady MHD Nanofluid Flow Through Convergent-Divergent Channel, International Journal of Fluid Mechanics & Thermal Sciences. Volume 8, Issue 1, March 2022, pp. 10-22. doi: 10.11648/j.ijfmts.20220801.12.
[22]	Akbar, N. S.; Khan, Z. H. (2015). Influence of magnetic field for metachoronical beating of cilia for Nanofluid with Newtonian heating. J. Magn Magn Mater 381, 235-242.
[23]	Ghosh, S. K.; Beg, O. A.; Zueco, J, J, J, J, J. (2010). Hydro magnetic Free Convective Flow with Induced Magnetic field Effects. Meccanica, 14, 175-185.
[24]	Beg, O. A.; Bekier, A. Y.; Prasad, V. R; Zueco, J.; Ghosh, S. K. (2009). NonSimilar, Laminar, Steady, Electrically-Conducting Forced Convection Liquid Metal Boundary Layer Flow with Induced Magnetic Field effects. Int. J. Therm. Sci, 48, 1596-1606.
[25]	Misra JC, Sinha A, Shit GC. (2010). The flow of a Biomagnetic Viscoelastic Fluid. Application to Estimation of the Blood Flow in Arteries during Electromagnetic Hyperthermia, a Therapeutic Procedure for Cancer Treatment. Appl. Math Meth. Ed (31) pp 1401-1420.
[26]	Xuan. Roetzel. (2000). Conceptions for Heat Transfer Correlation of Nanofluid. International Journal of Heat and Mass Transfer, 43, 3701-3707.
[27]	Brinkman, H. C. (1952). The Viscosity of Concentration Suspensions and Solutions. The Journal of Chemical Physics, 20 (4) 571-581.
[28]	Batchelor, G. (1977). The Effect of Brownian motion on the Bulk Stress in a Suspension of Spherical Particle, Journal of Fluid Mechanics. Vol. 83, pp. 97-117.
[29]	Alam, M. S., & Huda, M. N. (2013). A New Approach for Local Similarity Solutions of an Unsteady Hydro magnetic Free Convective Heat Transfer Flow along a Permeable Flat surface. International Journal of Advances in Applied Mathematics and Mechanics, 1 (2), 39-52.
[30]	Nagler, J. (2017). Jeffery-Hamel Flow of Non-Newtonian Fluid with Nonlinear Viscosity and Wall Friction. Applied Mathematics and Mechanics, 38 (6), 815-830.
[31]	Sattar, M. A. (2013). Derivation of the Similarity Equation of the 2-D Unsteady Boundary Layer Equations and the Corresponding Similarity Conditions. American Journal of Fluid Dynamics. 3 (5), 135.
[32]	Th. Geis. (1958), “Bemerkungzuden Ahnlichen Instatinaren. Laminaren Grenzschiechstromungen”. ZAMM. Vol. 12, 1958, pp. 396-398. Vijayakumar.
[33]	Ascher, Uri M.; Petzold, Linda R. (2998). Computer Methods for Ordinary Differential Equations and Differential-Algebraic-Equations, Philadelphia Society for Industrial and Applied$ Mathematics. ISBN 978-0-8987-412-8.

Cite This Article

Plain Text BibTeX RIS

APA Style

Felicien Habiyaremye, Mary Wainaina, Mark Kimathi. (2022). The Effect of Strong Magnetic Field on Unsteady MHD Nanofluid Flow Through Convergent-Divergent Channel with Heat and Mass Transfer. International Journal of Fluid Mechanics & Thermal Sciences, 8(3), 41-52. https://doi.org/10.11648/j.ijfmts.20220803.11

Copy | Download

ACS Style

Felicien Habiyaremye; Mary Wainaina; Mark Kimathi. The Effect of Strong Magnetic Field on Unsteady MHD Nanofluid Flow Through Convergent-Divergent Channel with Heat and Mass Transfer. Int. J. Fluid Mech. Therm. Sci. 2022, 8(3), 41-52. doi: 10.11648/j.ijfmts.20220803.11

Copy | Download

AMA Style

Felicien Habiyaremye, Mary Wainaina, Mark Kimathi. The Effect of Strong Magnetic Field on Unsteady MHD Nanofluid Flow Through Convergent-Divergent Channel with Heat and Mass Transfer. Int J Fluid Mech Therm Sci. 2022;8(3):41-52. doi: 10.11648/j.ijfmts.20220803.11

Copy | Download

@article{10.11648/j.ijfmts.20220803.11,
  author = {Felicien Habiyaremye and Mary Wainaina and Mark Kimathi},
  title = {The Effect of Strong Magnetic Field on Unsteady MHD Nanofluid Flow Through Convergent-Divergent Channel with Heat and Mass Transfer},
  journal = {International Journal of Fluid Mechanics & Thermal Sciences},
  volume = {8},
  number = {3},
  pages = {41-52},
  doi = {10.11648/j.ijfmts.20220803.11},
  url = {https://doi.org/10.11648/j.ijfmts.20220803.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijfmts.20220803.11},
  abstract = {Magnetohydrodynamic Nanofluid flow (Silver-water) through a converging-diverging channel under a strong magnetic field has been investigated. The induction equation is derived from electromagnetism. The non-linear partial differential equations are reduced to first-order non-linear ordinary differential equations using the similarity transformation and dimensionless numbers. The implicit Runge - Kutta fourth-order method via the bvp4c function in MATLAB has been used to generate the graphs of the fluid flow. It was observed that the high value of the Schmidt number leads to an increase in the velocity of the Nanofluid flow. The variation of the Schmidt number leads to a decrease in the temperature profile of the Nanofluid flow in the stretching channel and leads to an increase in the shrinking channel. The higher value of the Schmidt number leads to higher values in the concentration of the Nanofluid flow. Increasing the values of the Schmidt number leads to an augment in the magnetic induction of the Nanofluid flow for the divergent channel and a decrease is observed for a case of the convergent channel. Variation of the nanoparticle volume fraction increases the magnetic induction profiles of the Nanofluid flow for a stretching channel, and a decrease is observed for the case of the shrinking channel. The high value in Reynolds magnetic number leads to a high value in the velocity profile of Nanofluid flow. The change in Reynolds magnetic number leads to a high value in the temperature profiles of the Nanofluid flow for the case of a divergent channel and a decrease is observed for the case of a convergent channel. Varying the Reynolds magnetic number leads to a decrease in the magnetic induction profiles of the Nanofluid, this is due to the effectiveness of the relationship between the fluid flow and the magnetic field. Varying the Reynolds magnetic number leads to an augment in the induction profiles of the Nanofluid. This kind of study has a variety of applications such as geophysics, astrophysics, fire engineering, bio-medical, and blood flow through arteries and capillaries in the human body.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - The Effect of Strong Magnetic Field on Unsteady MHD Nanofluid Flow Through Convergent-Divergent Channel with Heat and Mass Transfer
AU  - Felicien Habiyaremye
AU  - Mary Wainaina
AU  - Mark Kimathi
Y1  - 2022/07/13
PY  - 2022
N1  - https://doi.org/10.11648/j.ijfmts.20220803.11
DO  - 10.11648/j.ijfmts.20220803.11
T2  - International Journal of Fluid Mechanics & Thermal Sciences
JF  - International Journal of Fluid Mechanics & Thermal Sciences
JO  - International Journal of Fluid Mechanics & Thermal Sciences
SP  - 41
EP  - 52
PB  - Science Publishing Group
SN  - 2469-8113
UR  - https://doi.org/10.11648/j.ijfmts.20220803.11
AB  - Magnetohydrodynamic Nanofluid flow (Silver-water) through a converging-diverging channel under a strong magnetic field has been investigated. The induction equation is derived from electromagnetism. The non-linear partial differential equations are reduced to first-order non-linear ordinary differential equations using the similarity transformation and dimensionless numbers. The implicit Runge - Kutta fourth-order method via the bvp4c function in MATLAB has been used to generate the graphs of the fluid flow. It was observed that the high value of the Schmidt number leads to an increase in the velocity of the Nanofluid flow. The variation of the Schmidt number leads to a decrease in the temperature profile of the Nanofluid flow in the stretching channel and leads to an increase in the shrinking channel. The higher value of the Schmidt number leads to higher values in the concentration of the Nanofluid flow. Increasing the values of the Schmidt number leads to an augment in the magnetic induction of the Nanofluid flow for the divergent channel and a decrease is observed for a case of the convergent channel. Variation of the nanoparticle volume fraction increases the magnetic induction profiles of the Nanofluid flow for a stretching channel, and a decrease is observed for the case of the shrinking channel. The high value in Reynolds magnetic number leads to a high value in the velocity profile of Nanofluid flow. The change in Reynolds magnetic number leads to a high value in the temperature profiles of the Nanofluid flow for the case of a divergent channel and a decrease is observed for the case of a convergent channel. Varying the Reynolds magnetic number leads to a decrease in the magnetic induction profiles of the Nanofluid, this is due to the effectiveness of the relationship between the fluid flow and the magnetic field. Varying the Reynolds magnetic number leads to an augment in the induction profiles of the Nanofluid. This kind of study has a variety of applications such as geophysics, astrophysics, fire engineering, bio-medical, and blood flow through arteries and capillaries in the human body.
VL  - 8
IS  - 3
ER  -

Copy | Download

Author Information

Felicien Habiyaremye

Department of Mathematics and Actuarial Science, Catholic University of Eastern Africa, Nairobi, Kenya
Mary Wainaina

Department of Mathematics and Actuarial Science, Catholic University of Eastern Africa, Nairobi, Kenya
Mark Kimathi

Department of Mathematics, Statistics and Actuarial Science, Machakos University, Machakos, Kenya

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Felicien Habiyaremye, Mary Wainaina, Mark Kimathi. (2022). The Effect of Strong Magnetic Field on Unsteady MHD Nanofluid Flow Through Convergent-Divergent Channel with Heat and Mass Transfer. International Journal of Fluid Mechanics & Thermal Sciences, 8(3), 41-52. https://doi.org/10.11648/j.ijfmts.20220803.11

Copy | Download

ACS Style

Felicien Habiyaremye; Mary Wainaina; Mark Kimathi. The Effect of Strong Magnetic Field on Unsteady MHD Nanofluid Flow Through Convergent-Divergent Channel with Heat and Mass Transfer. Int. J. Fluid Mech. Therm. Sci. 2022, 8(3), 41-52. doi: 10.11648/j.ijfmts.20220803.11

Copy | Download

AMA Style

Felicien Habiyaremye, Mary Wainaina, Mark Kimathi. The Effect of Strong Magnetic Field on Unsteady MHD Nanofluid Flow Through Convergent-Divergent Channel with Heat and Mass Transfer. Int J Fluid Mech Therm Sci. 2022;8(3):41-52. doi: 10.11648/j.ijfmts.20220803.11

Copy | Download

@article{10.11648/j.ijfmts.20220803.11,
  author = {Felicien Habiyaremye and Mary Wainaina and Mark Kimathi},
  title = {The Effect of Strong Magnetic Field on Unsteady MHD Nanofluid Flow Through Convergent-Divergent Channel with Heat and Mass Transfer},
  journal = {International Journal of Fluid Mechanics & Thermal Sciences},
  volume = {8},
  number = {3},
  pages = {41-52},
  doi = {10.11648/j.ijfmts.20220803.11},
  url = {https://doi.org/10.11648/j.ijfmts.20220803.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijfmts.20220803.11},
  abstract = {Magnetohydrodynamic Nanofluid flow (Silver-water) through a converging-diverging channel under a strong magnetic field has been investigated. The induction equation is derived from electromagnetism. The non-linear partial differential equations are reduced to first-order non-linear ordinary differential equations using the similarity transformation and dimensionless numbers. The implicit Runge - Kutta fourth-order method via the bvp4c function in MATLAB has been used to generate the graphs of the fluid flow. It was observed that the high value of the Schmidt number leads to an increase in the velocity of the Nanofluid flow. The variation of the Schmidt number leads to a decrease in the temperature profile of the Nanofluid flow in the stretching channel and leads to an increase in the shrinking channel. The higher value of the Schmidt number leads to higher values in the concentration of the Nanofluid flow. Increasing the values of the Schmidt number leads to an augment in the magnetic induction of the Nanofluid flow for the divergent channel and a decrease is observed for a case of the convergent channel. Variation of the nanoparticle volume fraction increases the magnetic induction profiles of the Nanofluid flow for a stretching channel, and a decrease is observed for the case of the shrinking channel. The high value in Reynolds magnetic number leads to a high value in the velocity profile of Nanofluid flow. The change in Reynolds magnetic number leads to a high value in the temperature profiles of the Nanofluid flow for the case of a divergent channel and a decrease is observed for the case of a convergent channel. Varying the Reynolds magnetic number leads to a decrease in the magnetic induction profiles of the Nanofluid, this is due to the effectiveness of the relationship between the fluid flow and the magnetic field. Varying the Reynolds magnetic number leads to an augment in the induction profiles of the Nanofluid. This kind of study has a variety of applications such as geophysics, astrophysics, fire engineering, bio-medical, and blood flow through arteries and capillaries in the human body.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - The Effect of Strong Magnetic Field on Unsteady MHD Nanofluid Flow Through Convergent-Divergent Channel with Heat and Mass Transfer
AU  - Felicien Habiyaremye
AU  - Mary Wainaina
AU  - Mark Kimathi
Y1  - 2022/07/13
PY  - 2022
N1  - https://doi.org/10.11648/j.ijfmts.20220803.11
DO  - 10.11648/j.ijfmts.20220803.11
T2  - International Journal of Fluid Mechanics & Thermal Sciences
JF  - International Journal of Fluid Mechanics & Thermal Sciences
JO  - International Journal of Fluid Mechanics & Thermal Sciences
SP  - 41
EP  - 52
PB  - Science Publishing Group
SN  - 2469-8113
UR  - https://doi.org/10.11648/j.ijfmts.20220803.11
AB  - Magnetohydrodynamic Nanofluid flow (Silver-water) through a converging-diverging channel under a strong magnetic field has been investigated. The induction equation is derived from electromagnetism. The non-linear partial differential equations are reduced to first-order non-linear ordinary differential equations using the similarity transformation and dimensionless numbers. The implicit Runge - Kutta fourth-order method via the bvp4c function in MATLAB has been used to generate the graphs of the fluid flow. It was observed that the high value of the Schmidt number leads to an increase in the velocity of the Nanofluid flow. The variation of the Schmidt number leads to a decrease in the temperature profile of the Nanofluid flow in the stretching channel and leads to an increase in the shrinking channel. The higher value of the Schmidt number leads to higher values in the concentration of the Nanofluid flow. Increasing the values of the Schmidt number leads to an augment in the magnetic induction of the Nanofluid flow for the divergent channel and a decrease is observed for a case of the convergent channel. Variation of the nanoparticle volume fraction increases the magnetic induction profiles of the Nanofluid flow for a stretching channel, and a decrease is observed for the case of the shrinking channel. The high value in Reynolds magnetic number leads to a high value in the velocity profile of Nanofluid flow. The change in Reynolds magnetic number leads to a high value in the temperature profiles of the Nanofluid flow for the case of a divergent channel and a decrease is observed for the case of a convergent channel. Varying the Reynolds magnetic number leads to a decrease in the magnetic induction profiles of the Nanofluid, this is due to the effectiveness of the relationship between the fluid flow and the magnetic field. Varying the Reynolds magnetic number leads to an augment in the induction profiles of the Nanofluid. This kind of study has a variety of applications such as geophysics, astrophysics, fire engineering, bio-medical, and blood flow through arteries and capillaries in the human body.
VL  - 8
IS  - 3
ER  -

Copy | Download