Hydromagnetic Non-Newtonian Nanofluid Flow Past Linealy Stretching Convergent-Divergent Conduit with Chemical Reaction

Paul Wachira; Mathew Ngugi; Roy Phineas

doi:doi:10.11648/j.acm.20241305.12

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Hydromagnetic Non-Newtonian Nanofluid Flow Past Linealy Stretching Convergent-Divergent Conduit with Chemical Reaction

Paul Wachira, Mathew Ngugi, Roy Phineas^*

Published in Applied and Computational Mathematics (Volume 13, Issue 5)

Received: 17 July 2024 Accepted: 24 August 2024 Published: 5 September 2024

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Abstract

This paper investigates hydromagnetic non-Newtonian nanofluid flow past linearly stretching convergent-divergent conduit with chemical reaction using spectral ralaxation method. The fluid considered here is electrically conducting and is subjected to a constant pressure gradient and variable magnetic field. The two non-parallel walls are assumed not to intersect and the angle between the inclined walls is θ. The governing equations are continuity equation, momentum equation, species concentration, induction equation and energy equation. On modelling, the resulting partial differential equations are non-linear and are first transformed into system of ordinary differential equations through similarity transformation. The resulting boundary value problem is solved numerically using Spectral Relaxation Method. The results obtained after varying Hartman number, Unsteadiness parameter, Reynolds number, Solutal and Thermal Grashof number on velocity, concentration, temperature and induction profiles are represented in form of graphs. Some of the application of this study are, when extracting the energy from earth crust that varies in length between five to ten kilometres and temperature in between 500° and 1000°, nano-fluids are employed to cool the machinery and equipment working under high friction and high temperature. This present study considers nanofluid acting as a coolant of such equipment as well as acting as a lubricant thus reducing the rate of wear and tear of the equipment. The copper-water increases the thermophysical properties thus increasing heat transfer coefficient and hence increasing cooling rate.

Published in	Applied and Computational Mathematics (Volume 13, Issue 5)
DOI	10.11648/j.acm.20241305.12
Page(s)	130-139
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

Hydromagnetic, Spectral Relaxation Method, Collocation, Chemical Reaction, Non-Newtonian, Nanofluid, Thermophysical Properties

References

[1]	Md S Alam. (2013) “Critical analysis of the influence of magnetic reynolds number on mhd jeffery-hamel flows”, Journal of Naval Architecture and Marine Engineering, Academic publisher, China. vol. 9(5), 31-46.
[2]	Sheikholeslami, M and Mollabasi, H and Ganji, DD. (2015) “Analytical investigation of MHD Jeffery--Hamel nanofluid flow in non-parallel walls”, International Journal of Nanoscience and Nanotechnology, Iranian Nanotechnology Society, Iran. vol. 11(4), 241-248.
[3]	Githaiga, Paul Wachira and Kinyanjui, Mathew Ngugi and Giterere, Kangethe and Kogora, Phineous Roy. (2018) “Magneto Hydrodynamics Fluid Flow in Convergent-Divergent Conduit”, International Journal of Engineering Science and Innovative Technology(IJESIT), vol. 7, 1-10.
[4]	Nagler, J. (2017) “Jeffery-Hamel flow of non-Newtonian fluid with nonlinear viscosity and wall friction”, Applied Mathematics and Mechanics, Springer, Germany. vol. 38, 815-830.
[5]	Onyango, Edward Richard and Kinyanjui, Mathew Ngugi and Kimathi, Mark and Uppal, Surindar M. (2020) “Unsteady Jeffrey-Hamel Flow in the Presence of Oblique Magnetic Field with Suction and Injection”, Applied and Computational Mathematics, Science Publishing Group. vol. 9(1), 1-13.
[6]	Khan, Ilyas and Alqahtani, Aisha M. (2019) “MHD Nanofluids in a Permeable Channel with Porosity”, Symmetry, Multidisciplinary Digital Publishing Institute. vol. 11(3), 378.
[7]	Moghimi, Seyed Morteza and others. (2023) “Heat Transfer of MHD Flow over a Wedge with Surface of Mutable Temperature”, Authorea Preprints, Authorea. vol. 11(3), 4.
[8]	Soumahoro, Moussa and Kinkoh, Hubert and Aikins, Enoch Randy and Louw-Vaudran, Liesl. (2023) “Tracking Africa's implementation of Agenda 2063 milestones”, ISS Peace and Security Council Report, Institute for Security Studies (ISS). vol. 155(3), 11-14.
[9]	Arthur, Kingsley K and Asongu, Simplice A and Darko, Peter and Ansah, Marvin O and Adom, Sampson and Hlortu, Omega. (2023) “Financial crimes in Africa and economic growth: Implications for achieving sustainable development goals (SDGs)”, Journal of Economic Surveys, Wiley Online Library.
[10]	Boyd, John P. (2001) “Chebyshev and Fourier spectral methods”, Courier Corporation.
[11]	Kaigalula, Victor and Mutua, Samuel. (2024) “Soret and Dufour Effects on MHD Fluid Flow Through a Collapssible Tube Using Spectral Based Collocation Method”, Applied and Computational Mathematics.
[12]	Trefethen, Lloyd N Spectral methods in MATLAB, SIAM. (2000).

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APA Style

Wachira, P., Ngugi, M., Phineas, R. (2024). Hydromagnetic Non-Newtonian Nanofluid Flow Past Linealy Stretching Convergent-Divergent Conduit with Chemical Reaction. Applied and Computational Mathematics, 13(5), 130-139. https://doi.org/10.11648/j.acm.20241305.12

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ACS Style

Wachira, P.; Ngugi, M.; Phineas, R. Hydromagnetic Non-Newtonian Nanofluid Flow Past Linealy Stretching Convergent-Divergent Conduit with Chemical Reaction. Appl. Comput. Math. 2024, 13(5), 130-139. doi: 10.11648/j.acm.20241305.12

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AMA Style

Wachira P, Ngugi M, Phineas R. Hydromagnetic Non-Newtonian Nanofluid Flow Past Linealy Stretching Convergent-Divergent Conduit with Chemical Reaction. Appl Comput Math. 2024;13(5):130-139. doi: 10.11648/j.acm.20241305.12

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@article{10.11648/j.acm.20241305.12,
  author = {Paul Wachira and Mathew Ngugi and Roy Phineas},
  title = {Hydromagnetic Non-Newtonian Nanofluid Flow Past Linealy Stretching Convergent-Divergent Conduit with Chemical Reaction},
  journal = {Applied and Computational Mathematics},
  volume = {13},
  number = {5},
  pages = {130-139},
  doi = {10.11648/j.acm.20241305.12},
  url = {https://doi.org/10.11648/j.acm.20241305.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20241305.12},
  abstract = {This paper investigates hydromagnetic non-Newtonian nanofluid flow past linearly stretching convergent-divergent conduit with chemical reaction using spectral ralaxation method. The fluid considered here is electrically conducting and is subjected to a constant pressure gradient and variable magnetic field. The two non-parallel walls are assumed not to intersect and the angle between the inclined walls is θ. The governing equations are continuity equation, momentum equation, species concentration, induction equation and energy equation. On modelling, the resulting partial differential equations are non-linear and are first transformed into system of ordinary differential equations through similarity transformation. The resulting boundary value problem is solved numerically using Spectral Relaxation Method. The results obtained after varying Hartman number, Unsteadiness parameter, Reynolds number, Solutal and Thermal Grashof number on velocity, concentration, temperature and induction profiles are represented in form of graphs. Some of the application of this study are, when extracting the energy from earth crust that varies in length between five to ten kilometres and temperature in between 500° and 1000°, nano-fluids are employed to cool the machinery and equipment working under high friction and high temperature. This present study considers nanofluid acting as a coolant of such equipment as well as acting as a lubricant thus reducing the rate of wear and tear of the equipment. The copper-water increases the thermophysical properties thus increasing heat transfer coefficient and hence increasing cooling rate.},
 year = {2024}
}

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TY  - JOUR
T1  - Hydromagnetic Non-Newtonian Nanofluid Flow Past Linealy Stretching Convergent-Divergent Conduit with Chemical Reaction
AU  - Paul Wachira
AU  - Mathew Ngugi
AU  - Roy Phineas
Y1  - 2024/09/05
PY  - 2024
N1  - https://doi.org/10.11648/j.acm.20241305.12
DO  - 10.11648/j.acm.20241305.12
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 130
EP  - 139
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20241305.12
AB  - This paper investigates hydromagnetic non-Newtonian nanofluid flow past linearly stretching convergent-divergent conduit with chemical reaction using spectral ralaxation method. The fluid considered here is electrically conducting and is subjected to a constant pressure gradient and variable magnetic field. The two non-parallel walls are assumed not to intersect and the angle between the inclined walls is θ. The governing equations are continuity equation, momentum equation, species concentration, induction equation and energy equation. On modelling, the resulting partial differential equations are non-linear and are first transformed into system of ordinary differential equations through similarity transformation. The resulting boundary value problem is solved numerically using Spectral Relaxation Method. The results obtained after varying Hartman number, Unsteadiness parameter, Reynolds number, Solutal and Thermal Grashof number on velocity, concentration, temperature and induction profiles are represented in form of graphs. Some of the application of this study are, when extracting the energy from earth crust that varies in length between five to ten kilometres and temperature in between 500° and 1000°, nano-fluids are employed to cool the machinery and equipment working under high friction and high temperature. This present study considers nanofluid acting as a coolant of such equipment as well as acting as a lubricant thus reducing the rate of wear and tear of the equipment. The copper-water increases the thermophysical properties thus increasing heat transfer coefficient and hence increasing cooling rate.
VL  - 13
IS  - 5
ER  -

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Author Information

Paul Wachira

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

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Mathew Ngugi

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

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Roy Phineas

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

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APA Style

Wachira, P., Ngugi, M., Phineas, R. (2024). Hydromagnetic Non-Newtonian Nanofluid Flow Past Linealy Stretching Convergent-Divergent Conduit with Chemical Reaction. Applied and Computational Mathematics, 13(5), 130-139. https://doi.org/10.11648/j.acm.20241305.12

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ACS Style

Wachira, P.; Ngugi, M.; Phineas, R. Hydromagnetic Non-Newtonian Nanofluid Flow Past Linealy Stretching Convergent-Divergent Conduit with Chemical Reaction. Appl. Comput. Math. 2024, 13(5), 130-139. doi: 10.11648/j.acm.20241305.12

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AMA Style

Wachira P, Ngugi M, Phineas R. Hydromagnetic Non-Newtonian Nanofluid Flow Past Linealy Stretching Convergent-Divergent Conduit with Chemical Reaction. Appl Comput Math. 2024;13(5):130-139. doi: 10.11648/j.acm.20241305.12

Copy | Download

@article{10.11648/j.acm.20241305.12,
  author = {Paul Wachira and Mathew Ngugi and Roy Phineas},
  title = {Hydromagnetic Non-Newtonian Nanofluid Flow Past Linealy Stretching Convergent-Divergent Conduit with Chemical Reaction},
  journal = {Applied and Computational Mathematics},
  volume = {13},
  number = {5},
  pages = {130-139},
  doi = {10.11648/j.acm.20241305.12},
  url = {https://doi.org/10.11648/j.acm.20241305.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20241305.12},
  abstract = {This paper investigates hydromagnetic non-Newtonian nanofluid flow past linearly stretching convergent-divergent conduit with chemical reaction using spectral ralaxation method. The fluid considered here is electrically conducting and is subjected to a constant pressure gradient and variable magnetic field. The two non-parallel walls are assumed not to intersect and the angle between the inclined walls is θ. The governing equations are continuity equation, momentum equation, species concentration, induction equation and energy equation. On modelling, the resulting partial differential equations are non-linear and are first transformed into system of ordinary differential equations through similarity transformation. The resulting boundary value problem is solved numerically using Spectral Relaxation Method. The results obtained after varying Hartman number, Unsteadiness parameter, Reynolds number, Solutal and Thermal Grashof number on velocity, concentration, temperature and induction profiles are represented in form of graphs. Some of the application of this study are, when extracting the energy from earth crust that varies in length between five to ten kilometres and temperature in between 500° and 1000°, nano-fluids are employed to cool the machinery and equipment working under high friction and high temperature. This present study considers nanofluid acting as a coolant of such equipment as well as acting as a lubricant thus reducing the rate of wear and tear of the equipment. The copper-water increases the thermophysical properties thus increasing heat transfer coefficient and hence increasing cooling rate.},
 year = {2024}
}

Copy | Download

TY  - JOUR
T1  - Hydromagnetic Non-Newtonian Nanofluid Flow Past Linealy Stretching Convergent-Divergent Conduit with Chemical Reaction
AU  - Paul Wachira
AU  - Mathew Ngugi
AU  - Roy Phineas
Y1  - 2024/09/05
PY  - 2024
N1  - https://doi.org/10.11648/j.acm.20241305.12
DO  - 10.11648/j.acm.20241305.12
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 130
EP  - 139
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20241305.12
AB  - This paper investigates hydromagnetic non-Newtonian nanofluid flow past linearly stretching convergent-divergent conduit with chemical reaction using spectral ralaxation method. The fluid considered here is electrically conducting and is subjected to a constant pressure gradient and variable magnetic field. The two non-parallel walls are assumed not to intersect and the angle between the inclined walls is θ. The governing equations are continuity equation, momentum equation, species concentration, induction equation and energy equation. On modelling, the resulting partial differential equations are non-linear and are first transformed into system of ordinary differential equations through similarity transformation. The resulting boundary value problem is solved numerically using Spectral Relaxation Method. The results obtained after varying Hartman number, Unsteadiness parameter, Reynolds number, Solutal and Thermal Grashof number on velocity, concentration, temperature and induction profiles are represented in form of graphs. Some of the application of this study are, when extracting the energy from earth crust that varies in length between five to ten kilometres and temperature in between 500° and 1000°, nano-fluids are employed to cool the machinery and equipment working under high friction and high temperature. This present study considers nanofluid acting as a coolant of such equipment as well as acting as a lubricant thus reducing the rate of wear and tear of the equipment. The copper-water increases the thermophysical properties thus increasing heat transfer coefficient and hence increasing cooling rate.
VL  - 13
IS  - 5
ER  -

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