Mathematical Modelling of Multiphase Hybrid Gyro-tactic Nanofluid Flow Through Porous Convergent Pipe with Injection and Suction Using BVP4c

Chepkonga David; Mathew Kinyanjui; Roy Kiogora; Kang’ethe Giterere

doi:doi:10.11648/j.acm.20241306.11

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Mathematical Modelling of Multiphase Hybrid Gyro-tactic Nanofluid Flow Through Porous Convergent Pipe with Injection and Suction Using BVP4c

Chepkonga David, Mathew Kinyanjui, Roy Kiogora, Kang’ethe Giterere

Published in Applied and Computational Mathematics (Volume 13, Issue 6)

Received: 23 July 2024 Accepted: 2 September 2024 Published: 18 December 2024

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Abstract

This research focuses on enhancing fluid mobility by optimizing heat transfer, a crucial aspect in various industrial applications, including oil recovery. The study introduces an innovative framework that integrates microorganisms, hybrid nanoparticles, non-Newtonian fluid properties, a power law model, and inclined magnetic fields. The underlying dynamics are described by nonlinear partial differential equations, which are converted to ordinary differential equations using similarity transformation and subsequently solved through the BVP4c method. Key results demonstrate that fluid velocity increases with higher Reynolds, Hartman, Thermal Grashof, and Mass Grashof numbers due to factors such as reduced viscous drag, the Lorentz force’s acceleration effect, and enhanced buoyancy. On the other hand, a higher Prandtl number slightly reduces velocity, while an increased Schmidt number raises it by steepening the velocity gradient. Regarding temperature, higher Reynolds and Prandtl numbers, along with increased Eckert and Radiation parameters, result in elevated fluid temperatures due to enhanced convective heat transfer, decreased thermal diffusivity, viscous dissipation, and radiative heat effects. The insights gained from this study are valuable for improving oil extraction efficiency by identifying and manipulating key parameters that affect fluid behavior.

Published in	Applied and Computational Mathematics (Volume 13, Issue 6)
DOI	10.11648/j.acm.20241306.11
Page(s)	211-223
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

Multiphase, Hybrid, Gyro-tactic, Numerical Solution, Nanofluid, BVP4c

References

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[2]	A. Alsaedi, M. I. Khan, M. Farooq, N. Gull, and T. Hayat, “Magnetohydrodynamic (MHD) stratified bioconvective flow of nanofluid due to gyrotactic microorganisms,” Advanced Powder Technology, vol. 28, no. 1, pp. 288- 298, 2017.
[3]	M. Jawad, K. Shehzad, and R. Safdar, “Novel computational study on MHD flow of nanofluid flow with gyrotactic microorganism due to porous stretching sheet,” Punjab University Journal of Mathematics, vol. 52, no. 12, 2021.
[4]	S. U. Khan, S. A. Shehzad, and N. Ali, “Darcy- Forchheimer MHD couple stress liquid flow by oscillatory stretched sheet with thermophoresis and heat generation/absorption,” Journal of Porous Media, vol. 21, no. 12, 2018.
[5]	M. Sheikholeslami, S. Shehzad, Z. Li, and A. Shafee, “Numerical modeling for alumina nanofluid magnetohydrodynamic convective heat transfer in a permeable medium using Darcy law,” International Journal of Heat and Mass Transfer, vol. 127, pp. 614- 622, 2018.
[6]	N. S. Khan, “Bioconvection in second grade nanofluid flow containing nanoparticles and gyrotactic microorganisms,” Brazilian Journal of Physics, vol. 48, no. 3, pp. 227-241, 2018.
[7]	S. Ahmad, M. Ashraf, and K. Ali, “Nanofluid flow comprising gyrotactic microorganisms through a porous medium,” Journal of Applied Fluid Mechanics, vol. 13, no. 5, pp. 1539-1549, 2020.
[8]	A. K. Pandey and M. Kumar, “Natural convection and thermal radiation influence on nanofluid flow over a stretching cylinder in a porous medium with viscous dissipation,” Alexandria Engineering Journal, vol. 56, no. 1, pp. 55-62, 2017.
[9]	M. Yaseen, S. K. Rawat, N. A. Shah, M. Kumar, and S. M. Eldin, “Ternary hybrid nanofluid flow containing gyrotactic microorganisms over three different geometries with Cattaneo-Christov model,” Mathematics, vol. 11, no. 5, p. 1237, 2023.
[10]	N. Lisha and A. Vijaya Kumar, “Mixed bio-convection analysis on MHD Casson hybrid nanofluid flow over a spinning cone/plate embedded in a variable porosity medium: A comparative study,” The European Physical Journal Plus, vol. 138, no. 11, p. 1042, 2022.
[11]	D. Chepkonga, R. Kiogora, and K. Giterere, “Fluid flow and heat transfer through a vertical cylindrical collapsible tube in the presence of magnetic field and an obstacle,” International Journal of Advances in Applied Mathematics and Mechanics, vol. 71, pp. 62-71, 2019.
[12]	M. N. Othman, A. Jedi, and N. A. A. Bakar, “MHD flow and heat transfer of hybrid nanofluid over an exponentially shrinking surface with heat source/sink,” Applied Sciences, vol. 11, no. 17, p. 8199, 2021.
[13]	A. Mavi and T. Chinyoka, “Finite volume computational analysis of the heat transfer characteristic in a double- cylinder counter-flow heat exchanger with viscoelastic fluids,” in Defect and Diffusion Forum, vol. 424, pp. 19- 43, Trans Tech Publ, 2023.

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APA Style

David, C., Kinyanjui, M., Kiogora, R., Giterere, K. (2024). Mathematical Modelling of Multiphase Hybrid Gyro-tactic Nanofluid Flow Through Porous Convergent Pipe with Injection and Suction Using BVP4c. Applied and Computational Mathematics, 13(6), 211-223. https://doi.org/10.11648/j.acm.20241306.11

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ACS Style

David, C.; Kinyanjui, M.; Kiogora, R.; Giterere, K. Mathematical Modelling of Multiphase Hybrid Gyro-tactic Nanofluid Flow Through Porous Convergent Pipe with Injection and Suction Using BVP4c. Appl. Comput. Math. 2024, 13(6), 211-223. doi: 10.11648/j.acm.20241306.11

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AMA Style

David C, Kinyanjui M, Kiogora R, Giterere K. Mathematical Modelling of Multiphase Hybrid Gyro-tactic Nanofluid Flow Through Porous Convergent Pipe with Injection and Suction Using BVP4c. Appl Comput Math. 2024;13(6):211-223. doi: 10.11648/j.acm.20241306.11

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@article{10.11648/j.acm.20241306.11,
  author = {Chepkonga David and Mathew Kinyanjui and Roy Kiogora and Kang’ethe Giterere},
  title = {Mathematical Modelling of Multiphase Hybrid Gyro-tactic Nanofluid Flow Through Porous Convergent Pipe with Injection and Suction Using BVP4c},
  journal = {Applied and Computational Mathematics},
  volume = {13},
  number = {6},
  pages = {211-223},
  doi = {10.11648/j.acm.20241306.11},
  url = {https://doi.org/10.11648/j.acm.20241306.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20241306.11},
  abstract = {This research focuses on enhancing fluid mobility by optimizing heat transfer, a crucial aspect in various industrial applications, including oil recovery. The study introduces an innovative framework that integrates microorganisms, hybrid nanoparticles, non-Newtonian fluid properties, a power law model, and inclined magnetic fields. The underlying dynamics are described by nonlinear partial differential equations, which are converted to ordinary differential equations using similarity transformation and subsequently solved through the BVP4c method. Key results demonstrate that fluid velocity increases with higher Reynolds, Hartman, Thermal Grashof, and Mass Grashof numbers due to factors such as reduced viscous drag, the Lorentz force’s acceleration effect, and enhanced buoyancy. On the other hand, a higher Prandtl number slightly reduces velocity, while an increased Schmidt number raises it by steepening the velocity gradient. Regarding temperature, higher Reynolds and Prandtl numbers, along with increased Eckert and Radiation parameters, result in elevated fluid temperatures due to enhanced convective heat transfer, decreased thermal diffusivity, viscous dissipation, and radiative heat effects. The insights gained from this study are valuable for improving oil extraction efficiency by identifying and manipulating key parameters that affect fluid behavior.},
 year = {2024}
}

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TY  - JOUR
T1  - Mathematical Modelling of Multiphase Hybrid Gyro-tactic Nanofluid Flow Through Porous Convergent Pipe with Injection and Suction Using BVP4c
AU  - Chepkonga David
AU  - Mathew Kinyanjui
AU  - Roy Kiogora
AU  - Kang’ethe Giterere
Y1  - 2024/12/18
PY  - 2024
N1  - https://doi.org/10.11648/j.acm.20241306.11
DO  - 10.11648/j.acm.20241306.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 211
EP  - 223
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20241306.11
AB  - This research focuses on enhancing fluid mobility by optimizing heat transfer, a crucial aspect in various industrial applications, including oil recovery. The study introduces an innovative framework that integrates microorganisms, hybrid nanoparticles, non-Newtonian fluid properties, a power law model, and inclined magnetic fields. The underlying dynamics are described by nonlinear partial differential equations, which are converted to ordinary differential equations using similarity transformation and subsequently solved through the BVP4c method. Key results demonstrate that fluid velocity increases with higher Reynolds, Hartman, Thermal Grashof, and Mass Grashof numbers due to factors such as reduced viscous drag, the Lorentz force’s acceleration effect, and enhanced buoyancy. On the other hand, a higher Prandtl number slightly reduces velocity, while an increased Schmidt number raises it by steepening the velocity gradient. Regarding temperature, higher Reynolds and Prandtl numbers, along with increased Eckert and Radiation parameters, result in elevated fluid temperatures due to enhanced convective heat transfer, decreased thermal diffusivity, viscous dissipation, and radiative heat effects. The insights gained from this study are valuable for improving oil extraction efficiency by identifying and manipulating key parameters that affect fluid behavior.
VL  - 13
IS  - 6
ER  -

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Author Information

Chepkonga David

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

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Mathew Kinyanjui

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

Department Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Kang’ethe Giterere

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

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Plain Text BibTeX RIS

APA Style

David, C., Kinyanjui, M., Kiogora, R., Giterere, K. (2024). Mathematical Modelling of Multiphase Hybrid Gyro-tactic Nanofluid Flow Through Porous Convergent Pipe with Injection and Suction Using BVP4c. Applied and Computational Mathematics, 13(6), 211-223. https://doi.org/10.11648/j.acm.20241306.11

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ACS Style

David, C.; Kinyanjui, M.; Kiogora, R.; Giterere, K. Mathematical Modelling of Multiphase Hybrid Gyro-tactic Nanofluid Flow Through Porous Convergent Pipe with Injection and Suction Using BVP4c. Appl. Comput. Math. 2024, 13(6), 211-223. doi: 10.11648/j.acm.20241306.11

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AMA Style

David C, Kinyanjui M, Kiogora R, Giterere K. Mathematical Modelling of Multiphase Hybrid Gyro-tactic Nanofluid Flow Through Porous Convergent Pipe with Injection and Suction Using BVP4c. Appl Comput Math. 2024;13(6):211-223. doi: 10.11648/j.acm.20241306.11

Copy | Download

@article{10.11648/j.acm.20241306.11,
  author = {Chepkonga David and Mathew Kinyanjui and Roy Kiogora and Kang’ethe Giterere},
  title = {Mathematical Modelling of Multiphase Hybrid Gyro-tactic Nanofluid Flow Through Porous Convergent Pipe with Injection and Suction Using BVP4c},
  journal = {Applied and Computational Mathematics},
  volume = {13},
  number = {6},
  pages = {211-223},
  doi = {10.11648/j.acm.20241306.11},
  url = {https://doi.org/10.11648/j.acm.20241306.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20241306.11},
  abstract = {This research focuses on enhancing fluid mobility by optimizing heat transfer, a crucial aspect in various industrial applications, including oil recovery. The study introduces an innovative framework that integrates microorganisms, hybrid nanoparticles, non-Newtonian fluid properties, a power law model, and inclined magnetic fields. The underlying dynamics are described by nonlinear partial differential equations, which are converted to ordinary differential equations using similarity transformation and subsequently solved through the BVP4c method. Key results demonstrate that fluid velocity increases with higher Reynolds, Hartman, Thermal Grashof, and Mass Grashof numbers due to factors such as reduced viscous drag, the Lorentz force’s acceleration effect, and enhanced buoyancy. On the other hand, a higher Prandtl number slightly reduces velocity, while an increased Schmidt number raises it by steepening the velocity gradient. Regarding temperature, higher Reynolds and Prandtl numbers, along with increased Eckert and Radiation parameters, result in elevated fluid temperatures due to enhanced convective heat transfer, decreased thermal diffusivity, viscous dissipation, and radiative heat effects. The insights gained from this study are valuable for improving oil extraction efficiency by identifying and manipulating key parameters that affect fluid behavior.},
 year = {2024}
}

Copy | Download

TY  - JOUR
T1  - Mathematical Modelling of Multiphase Hybrid Gyro-tactic Nanofluid Flow Through Porous Convergent Pipe with Injection and Suction Using BVP4c
AU  - Chepkonga David
AU  - Mathew Kinyanjui
AU  - Roy Kiogora
AU  - Kang’ethe Giterere
Y1  - 2024/12/18
PY  - 2024
N1  - https://doi.org/10.11648/j.acm.20241306.11
DO  - 10.11648/j.acm.20241306.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 211
EP  - 223
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20241306.11
AB  - This research focuses on enhancing fluid mobility by optimizing heat transfer, a crucial aspect in various industrial applications, including oil recovery. The study introduces an innovative framework that integrates microorganisms, hybrid nanoparticles, non-Newtonian fluid properties, a power law model, and inclined magnetic fields. The underlying dynamics are described by nonlinear partial differential equations, which are converted to ordinary differential equations using similarity transformation and subsequently solved through the BVP4c method. Key results demonstrate that fluid velocity increases with higher Reynolds, Hartman, Thermal Grashof, and Mass Grashof numbers due to factors such as reduced viscous drag, the Lorentz force’s acceleration effect, and enhanced buoyancy. On the other hand, a higher Prandtl number slightly reduces velocity, while an increased Schmidt number raises it by steepening the velocity gradient. Regarding temperature, higher Reynolds and Prandtl numbers, along with increased Eckert and Radiation parameters, result in elevated fluid temperatures due to enhanced convective heat transfer, decreased thermal diffusivity, viscous dissipation, and radiative heat effects. The insights gained from this study are valuable for improving oil extraction efficiency by identifying and manipulating key parameters that affect fluid behavior.
VL  - 13
IS  - 6
ER  -

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