Hydromagnetic Nanofluid Flow Through Stretching Convergent-divergent Conduit with Heat and Mass Transfer

Paul Wachira Githaiga; Mathew Ngugi Kinyanjui; Roy Phineas Kiogora

doi:doi:10.11648/j.ijfmts.20241002.12

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Hydromagnetic Nanofluid Flow Through Stretching Convergent-divergent Conduit with Heat and Mass Transfer

Paul Wachira Githaiga, Mathew Ngugi Kinyanjui, Roy Phineas Kiogora

Published in International Journal of Fluid Mechanics & Thermal Sciences (Volume 10, Issue 2)

Received: 29 September 2024 Accepted: 22 October 2024 Published: 18 November 2024

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Abstract

This present study investigates hydromagnetic non-Newtonian nanofluid flow past linearly stretching convergent-divergent conduit with variable magnetic field and variable thermal conductivity with skin friction, heat and mass transfer using spectral relaxation numerical technique. The nanofluid considered in this current study is electrically conducting which is subjected to constant pressure gradient and magnetic field considered to be variable applied at an angle. The two walls which are non-parallel are not intersecting so as to allow nanofluid to flow, the angle in between the non-parallel walls is θ. The equations governing the nanofluid flow are continuity, energy, magnetic induction and conservation of momentum equations. After modelling, the specific equations governing the nano-fluid flow are partial differential equations which are highly nonlinear, the specific equations are first transformed through similarity transformation into a systems of ordinary differential equations. The boundary value problem formed is solved numerically using spectral relaxation numerical technique. The results of effects of varying various dimensionless parameters of the model are represented graphically and results discussed at each stage. The knowledge of nanofluids can be used in nuclear power production where it acts as a coolant. In Africa, South Africa is the only country producing nuclear power for commercial use, different governments on the continent are exploring nuclear energy as a climate-friendly for power production to enhance industrialization even in rural areas. In nuclear power production, water is used as a coolant. Using nanofluid instead of water it could increase the thermophyical properties which increases the rate of cooling. The usage of nanofluids as a coolant could also be used in emergency cooling systems, where they could cool down overheat machines quickly leading to an efficient and improved power plant safety.

Published in	International Journal of Fluid Mechanics & Thermal Sciences (Volume 10, Issue 2)
DOI	10.11648/j.ijfmts.20241002.12
Page(s)	31-44
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, Skin Friction, Heat and Mass Transfer

References

[1]	Makinde O, D, Investigatation of non-linear 2D Navier-Stokes equations modeling the flow field using a perturbation technique, International Journal of Engineering Sciences, 2008, 181(2), 966-972.
[2]	Moffat, W, Effect of MHD on convergent divergent flow, Applied Mathematics and Computations, 2007, 225(2), 347-353.
[3]	Voropayev, S I, Two−dimensional steady state incompressible viscous flow, Applied Mathematics and Computations, 2015, 20.
[4]	Ojiambo, V and Kimathi, M and Kinyanjui, M, Int. J. of Adv. in Applied Math. and Mech, 5(4), 21–32, 2018.
[5]	Githaiga, Paul Wachira and Kinyanjui, Mathew Ngugi and Giterere, Kangethe and Kogora, Phineous Roy, “Magneto Hydrodynamics Fluid Flow in Convergent- Divergent Conduit,” International Journal of Engineering Science and Innovative Technology(IJESIT), 7(6), 1–10, 2018.
[6]	Sheikholeslami, Mohsen and Rokni, Houman B, “Simulation of nanofluid heat transfer in presence of magnetic field: a review,” International Journal of Heat and Mass Transfer, 115, 1203–1233, 2017, Elsevier.
[7]	Kaigalula, Victor and Mutua, Samuel, Soret and Dufour Effects on MHD Fluid Flow Through a Collapssible Tube Using Spectral Based Collocation Method, Applied and Computational Mathematics, 13(1), 8–28, 2024.
[8]	Githaiga, P. W., Kinyanjui, M. N., Kiogora, R. P, Hydromagnetic Non-Newtonian Nanofluid Flow Past Linealy Stretching Convergent-Divergent Conduit with Chemical Reaction, pplied and Computational Mathematics, 13(5), 130-139. https://doi.org/10.11648/j.acm.20241305.12 .
[9]	Mutuku-Njane, WN and Makinde, OD, MHD nanofluid flow over a permeable vertical plate with convective heating, Journal of Computational and Theoretical Nanoscience, 11(3), 667–675, 2014.
[10]	Nagler, J, Jeffery-Hamel flow of non-Newtonian fluid with nonlinear viscosity and wall friction, Applied Mathematics and Mechanics, 38(6), 815–830, 2017.
[11]	Boyd, John P, Chebyshev and Fourier spectral methods, Courier Corporation, 2001.

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APA Style

Githaiga, P. W., Kinyanjui, M. N., Kiogora, R. P. (2024). Hydromagnetic Nanofluid Flow Through Stretching Convergent-divergent Conduit with Heat and Mass Transfer. International Journal of Fluid Mechanics & Thermal Sciences, 10(2), 31-44. https://doi.org/10.11648/j.ijfmts.20241002.12

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ACS Style

Githaiga, P. W.; Kinyanjui, M. N.; Kiogora, R. P. Hydromagnetic Nanofluid Flow Through Stretching Convergent-divergent Conduit with Heat and Mass Transfer. Int. J. Fluid Mech. Therm. Sci. 2024, 10(2), 31-44. doi: 10.11648/j.ijfmts.20241002.12

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AMA Style

Githaiga PW, Kinyanjui MN, Kiogora RP. Hydromagnetic Nanofluid Flow Through Stretching Convergent-divergent Conduit with Heat and Mass Transfer. Int J Fluid Mech Therm Sci. 2024;10(2):31-44. doi: 10.11648/j.ijfmts.20241002.12

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@article{10.11648/j.ijfmts.20241002.12,
  author = {Paul Wachira Githaiga and Mathew Ngugi Kinyanjui and Roy Phineas Kiogora},
  title = {Hydromagnetic Nanofluid Flow Through Stretching Convergent-divergent Conduit with Heat and Mass Transfer},
  journal = {International Journal of Fluid Mechanics & Thermal Sciences},
  volume = {10},
  number = {2},
  pages = {31-44},
  doi = {10.11648/j.ijfmts.20241002.12},
  url = {https://doi.org/10.11648/j.ijfmts.20241002.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijfmts.20241002.12},
  abstract = {This present study investigates hydromagnetic non-Newtonian nanofluid flow past linearly stretching convergent-divergent conduit with variable magnetic field and variable thermal conductivity with skin friction, heat and mass transfer using spectral relaxation numerical technique. The nanofluid considered in this current study is electrically conducting which is subjected to constant pressure gradient and magnetic field considered to be variable  applied at an angle. The two walls which are non-parallel are not intersecting so as to allow nanofluid to flow, the angle in between the non-parallel walls is θ. The equations governing the nanofluid flow are continuity, energy, magnetic induction and conservation of momentum equations. After modelling, the specific equations governing the nano-fluid flow are partial differential equations which are highly nonlinear, the specific equations are first transformed through similarity transformation into a systems of ordinary differential equations. The boundary value problem formed is solved numerically using spectral relaxation numerical technique. The results of effects of varying various dimensionless parameters  of the model are represented graphically and results discussed at each stage. The knowledge of nanofluids can be used in nuclear power production where it acts as a coolant. In Africa, South Africa is the only country producing nuclear power for commercial use, different governments on the continent are exploring nuclear energy as a climate-friendly for power production to enhance industrialization even in rural areas. In nuclear power production, water is used as a coolant. Using nanofluid instead of water it could increase the thermophyical properties which increases the rate of cooling. The usage of nanofluids as a coolant could also be used in emergency cooling systems, where they could cool down overheat  machines quickly leading to an efficient and improved power plant safety.},
 year = {2024}
}

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TY  - JOUR
T1  - Hydromagnetic Nanofluid Flow Through Stretching Convergent-divergent Conduit with Heat and Mass Transfer
AU  - Paul Wachira Githaiga
AU  - Mathew Ngugi Kinyanjui
AU  - Roy Phineas Kiogora
Y1  - 2024/11/18
PY  - 2024
N1  - https://doi.org/10.11648/j.ijfmts.20241002.12
DO  - 10.11648/j.ijfmts.20241002.12
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  - 31
EP  - 44
PB  - Science Publishing Group
SN  - 2469-8113
UR  - https://doi.org/10.11648/j.ijfmts.20241002.12
AB  - This present study investigates hydromagnetic non-Newtonian nanofluid flow past linearly stretching convergent-divergent conduit with variable magnetic field and variable thermal conductivity with skin friction, heat and mass transfer using spectral relaxation numerical technique. The nanofluid considered in this current study is electrically conducting which is subjected to constant pressure gradient and magnetic field considered to be variable  applied at an angle. The two walls which are non-parallel are not intersecting so as to allow nanofluid to flow, the angle in between the non-parallel walls is θ. The equations governing the nanofluid flow are continuity, energy, magnetic induction and conservation of momentum equations. After modelling, the specific equations governing the nano-fluid flow are partial differential equations which are highly nonlinear, the specific equations are first transformed through similarity transformation into a systems of ordinary differential equations. The boundary value problem formed is solved numerically using spectral relaxation numerical technique. The results of effects of varying various dimensionless parameters  of the model are represented graphically and results discussed at each stage. The knowledge of nanofluids can be used in nuclear power production where it acts as a coolant. In Africa, South Africa is the only country producing nuclear power for commercial use, different governments on the continent are exploring nuclear energy as a climate-friendly for power production to enhance industrialization even in rural areas. In nuclear power production, water is used as a coolant. Using nanofluid instead of water it could increase the thermophyical properties which increases the rate of cooling. The usage of nanofluids as a coolant could also be used in emergency cooling systems, where they could cool down overheat  machines quickly leading to an efficient and improved power plant safety.
VL  - 10
IS  - 2
ER  -

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Author Information

Paul Wachira Githaiga

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

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Mathew Ngugi Kinyanjui

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

Contact Email
Roy Phineas Kiogora

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

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Plain Text BibTeX RIS

APA Style

Githaiga, P. W., Kinyanjui, M. N., Kiogora, R. P. (2024). Hydromagnetic Nanofluid Flow Through Stretching Convergent-divergent Conduit with Heat and Mass Transfer. International Journal of Fluid Mechanics & Thermal Sciences, 10(2), 31-44. https://doi.org/10.11648/j.ijfmts.20241002.12

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ACS Style

Githaiga, P. W.; Kinyanjui, M. N.; Kiogora, R. P. Hydromagnetic Nanofluid Flow Through Stretching Convergent-divergent Conduit with Heat and Mass Transfer. Int. J. Fluid Mech. Therm. Sci. 2024, 10(2), 31-44. doi: 10.11648/j.ijfmts.20241002.12

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AMA Style

Githaiga PW, Kinyanjui MN, Kiogora RP. Hydromagnetic Nanofluid Flow Through Stretching Convergent-divergent Conduit with Heat and Mass Transfer. Int J Fluid Mech Therm Sci. 2024;10(2):31-44. doi: 10.11648/j.ijfmts.20241002.12

Copy | Download

@article{10.11648/j.ijfmts.20241002.12,
  author = {Paul Wachira Githaiga and Mathew Ngugi Kinyanjui and Roy Phineas Kiogora},
  title = {Hydromagnetic Nanofluid Flow Through Stretching Convergent-divergent Conduit with Heat and Mass Transfer},
  journal = {International Journal of Fluid Mechanics & Thermal Sciences},
  volume = {10},
  number = {2},
  pages = {31-44},
  doi = {10.11648/j.ijfmts.20241002.12},
  url = {https://doi.org/10.11648/j.ijfmts.20241002.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijfmts.20241002.12},
  abstract = {This present study investigates hydromagnetic non-Newtonian nanofluid flow past linearly stretching convergent-divergent conduit with variable magnetic field and variable thermal conductivity with skin friction, heat and mass transfer using spectral relaxation numerical technique. The nanofluid considered in this current study is electrically conducting which is subjected to constant pressure gradient and magnetic field considered to be variable  applied at an angle. The two walls which are non-parallel are not intersecting so as to allow nanofluid to flow, the angle in between the non-parallel walls is θ. The equations governing the nanofluid flow are continuity, energy, magnetic induction and conservation of momentum equations. After modelling, the specific equations governing the nano-fluid flow are partial differential equations which are highly nonlinear, the specific equations are first transformed through similarity transformation into a systems of ordinary differential equations. The boundary value problem formed is solved numerically using spectral relaxation numerical technique. The results of effects of varying various dimensionless parameters  of the model are represented graphically and results discussed at each stage. The knowledge of nanofluids can be used in nuclear power production where it acts as a coolant. In Africa, South Africa is the only country producing nuclear power for commercial use, different governments on the continent are exploring nuclear energy as a climate-friendly for power production to enhance industrialization even in rural areas. In nuclear power production, water is used as a coolant. Using nanofluid instead of water it could increase the thermophyical properties which increases the rate of cooling. The usage of nanofluids as a coolant could also be used in emergency cooling systems, where they could cool down overheat  machines quickly leading to an efficient and improved power plant safety.},
 year = {2024}
}

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TY  - JOUR
T1  - Hydromagnetic Nanofluid Flow Through Stretching Convergent-divergent Conduit with Heat and Mass Transfer
AU  - Paul Wachira Githaiga
AU  - Mathew Ngugi Kinyanjui
AU  - Roy Phineas Kiogora
Y1  - 2024/11/18
PY  - 2024
N1  - https://doi.org/10.11648/j.ijfmts.20241002.12
DO  - 10.11648/j.ijfmts.20241002.12
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  - 31
EP  - 44
PB  - Science Publishing Group
SN  - 2469-8113
UR  - https://doi.org/10.11648/j.ijfmts.20241002.12
AB  - This present study investigates hydromagnetic non-Newtonian nanofluid flow past linearly stretching convergent-divergent conduit with variable magnetic field and variable thermal conductivity with skin friction, heat and mass transfer using spectral relaxation numerical technique. The nanofluid considered in this current study is electrically conducting which is subjected to constant pressure gradient and magnetic field considered to be variable  applied at an angle. The two walls which are non-parallel are not intersecting so as to allow nanofluid to flow, the angle in between the non-parallel walls is θ. The equations governing the nanofluid flow are continuity, energy, magnetic induction and conservation of momentum equations. After modelling, the specific equations governing the nano-fluid flow are partial differential equations which are highly nonlinear, the specific equations are first transformed through similarity transformation into a systems of ordinary differential equations. The boundary value problem formed is solved numerically using spectral relaxation numerical technique. The results of effects of varying various dimensionless parameters  of the model are represented graphically and results discussed at each stage. The knowledge of nanofluids can be used in nuclear power production where it acts as a coolant. In Africa, South Africa is the only country producing nuclear power for commercial use, different governments on the continent are exploring nuclear energy as a climate-friendly for power production to enhance industrialization even in rural areas. In nuclear power production, water is used as a coolant. Using nanofluid instead of water it could increase the thermophyical properties which increases the rate of cooling. The usage of nanofluids as a coolant could also be used in emergency cooling systems, where they could cool down overheat  machines quickly leading to an efficient and improved power plant safety.
VL  - 10
IS  - 2
ER  -

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