The Application of Homotopy Perturbation Method in Newtonian Fluids

Adetoye Solomon Ojo; Peter Onyelukachukwu Nwabuzor; Chijioke Aloysius Egbo; Edikan Sunday Umoh

doi:doi:10.11648/j.fm.20261101.11

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The Application of Homotopy Perturbation Method in Newtonian Fluids

Adetoye Solomon Ojo^*

, Peter Onyelukachukwu Nwabuzor

, Chijioke Aloysius Egbo

, Edikan Sunday Umoh

Published in Fluid Mechanics (Volume 11, Issue 1)

Received: 17 January 2026 Accepted: 27 January 2026 Published: 9 February 2026

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Abstract

The Homotopy Perturbation Method (HPM) has advanced as an efficient semi-analytical technique for solving nonlinear differential equation arising in fluid mechanics. In this study, the application of HPM to Newtonian fluid flow problems is investigated in order to obtain accurate approximate solutions with reduced computational effort. The governing momentum equations of a Newtonian fluid flow, with a focus on deriving and analyzing engineering parameters like skin friction, Nusselt number, and Sherwood number was formulated under appropriate boundary conditions. The nonlinear partial differential equations describing the momentum, Navier-stokes equation and concentration equation were transformed into a homotopy framework by embedding an auxiliary a parameter. The solution is constructed in form of a rapidly convergent series without the need for small perturbation parameters or linearization. The analytical results obtaining using (HPM) are discussed and, where possible, compared with exact or numerical solutions to validate the accuracy and convergence of the method. The impact of the material parameters from the basic hydrodynamic equations were noticed and the findings demonstrate that the Homotopy Perturbation Method provides a reliable, Straightforward, and computationally efficient approach for analyzing Newtonian fluid flow phenomena and can be readily extended to more complex transport and heat transfer problems in engineering and applied sciences, making it a valuable tool for solving a wide range of nonlinear fluid mechanics models.

Published in	Fluid Mechanics (Volume 11, Issue 1)
DOI	10.11648/j.fm.20261101.11
Page(s)	1-11
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), 2026. Published by Science Publishing Group

Keywords

Homotopy Perturbation Method, Newtonian Fluids, Application Performance, Ordinary Differential Equations, Dimensionless Parameter

References

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[7]	A. S. Ojo, C. A. Egbo, “Effect of radiation and chemical reaction on ozone layer healing” Open Journal of Physical Science. 6(2), pp 1-13, 2025.
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APA Style

Ojo, A. S., Nwabuzor, P. O., Egbo, C. A., Umoh, E. S. (2026). The Application of Homotopy Perturbation Method in Newtonian Fluids. Fluid Mechanics, 11(1), 1-11. https://doi.org/10.11648/j.fm.20261101.11

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ACS Style

Ojo, A. S.; Nwabuzor, P. O.; Egbo, C. A.; Umoh, E. S. The Application of Homotopy Perturbation Method in Newtonian Fluids. Fluid Mech. 2026, 11(1), 1-11. doi: 10.11648/j.fm.20261101.11

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AMA Style

Ojo AS, Nwabuzor PO, Egbo CA, Umoh ES. The Application of Homotopy Perturbation Method in Newtonian Fluids. Fluid Mech. 2026;11(1):1-11. doi: 10.11648/j.fm.20261101.11

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@article{10.11648/j.fm.20261101.11,
  author = {Adetoye Solomon Ojo and Peter Onyelukachukwu Nwabuzor and Chijioke Aloysius Egbo and Edikan Sunday Umoh},
  title = {The Application of Homotopy Perturbation Method in Newtonian Fluids},
  journal = {Fluid Mechanics},
  volume = {11},
  number = {1},
  pages = {1-11},
  doi = {10.11648/j.fm.20261101.11},
  url = {https://doi.org/10.11648/j.fm.20261101.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.fm.20261101.11},
  abstract = {The Homotopy Perturbation Method (HPM) has advanced as an efficient semi-analytical technique for solving nonlinear differential equation arising in fluid mechanics. In this study, the application of HPM to Newtonian fluid flow problems is investigated in order to obtain accurate approximate solutions with reduced computational effort. The governing momentum equations of a Newtonian fluid flow, with a focus on deriving and analyzing engineering parameters like skin friction, Nusselt number, and Sherwood number was formulated under appropriate boundary conditions. The nonlinear partial differential equations describing the momentum, Navier-stokes equation and concentration equation were transformed into a homotopy framework by embedding an auxiliary a parameter. The solution is constructed in form of a rapidly convergent series without the need for small perturbation parameters or linearization. The analytical results obtaining using (HPM) are discussed and, where possible, compared with exact or numerical solutions to validate the accuracy and convergence of the method. The impact of the material parameters from the basic hydrodynamic equations were noticed and the findings demonstrate that the Homotopy Perturbation Method provides a reliable, Straightforward, and computationally efficient approach for analyzing Newtonian fluid flow phenomena and can be readily extended to more complex transport and heat transfer problems in engineering and applied sciences, making it a valuable tool for solving a wide range of nonlinear fluid mechanics models.},
 year = {2026}
}

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TY  - JOUR
T1  - The Application of Homotopy Perturbation Method in Newtonian Fluids
AU  - Adetoye Solomon Ojo
AU  - Peter Onyelukachukwu Nwabuzor
AU  - Chijioke Aloysius Egbo
AU  - Edikan Sunday Umoh
Y1  - 2026/02/09
PY  - 2026
N1  - https://doi.org/10.11648/j.fm.20261101.11
DO  - 10.11648/j.fm.20261101.11
T2  - Fluid Mechanics
JF  - Fluid Mechanics
JO  - Fluid Mechanics
SP  - 1
EP  - 11
PB  - Science Publishing Group
SN  - 2575-1816
UR  - https://doi.org/10.11648/j.fm.20261101.11
AB  - The Homotopy Perturbation Method (HPM) has advanced as an efficient semi-analytical technique for solving nonlinear differential equation arising in fluid mechanics. In this study, the application of HPM to Newtonian fluid flow problems is investigated in order to obtain accurate approximate solutions with reduced computational effort. The governing momentum equations of a Newtonian fluid flow, with a focus on deriving and analyzing engineering parameters like skin friction, Nusselt number, and Sherwood number was formulated under appropriate boundary conditions. The nonlinear partial differential equations describing the momentum, Navier-stokes equation and concentration equation were transformed into a homotopy framework by embedding an auxiliary a parameter. The solution is constructed in form of a rapidly convergent series without the need for small perturbation parameters or linearization. The analytical results obtaining using (HPM) are discussed and, where possible, compared with exact or numerical solutions to validate the accuracy and convergence of the method. The impact of the material parameters from the basic hydrodynamic equations were noticed and the findings demonstrate that the Homotopy Perturbation Method provides a reliable, Straightforward, and computationally efficient approach for analyzing Newtonian fluid flow phenomena and can be readily extended to more complex transport and heat transfer problems in engineering and applied sciences, making it a valuable tool for solving a wide range of nonlinear fluid mechanics models.
VL  - 11
IS  - 1
ER  -

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Author Information

Adetoye Solomon Ojo

Department of Physics, University of Port Harcourt, Port Harcourt, Nigeria

Contact Email

http://orcid.org/0009-0005-3139-0704
Peter Onyelukachukwu Nwabuzor

Department of Physics with Electronics, University of Port Harcourt, Port Harcourt, Nigeria

Contact Email

http://orcid.org/0009-0001-2144-7245
Chijioke Aloysius Egbo

Department of Science Laboratory Technology, Federal Polytechnic of Oil and Gas, Bonny, Nigeria

Contact Email

http://orcid.org/0000-0003-3598-9982
Edikan Sunday Umoh

Department of Physics, University of Port Harcourt, Port Harcourt, Nigeria

Contact Email

http://orcid.org/0009-0005-2140-9838

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APA Style

Ojo, A. S., Nwabuzor, P. O., Egbo, C. A., Umoh, E. S. (2026). The Application of Homotopy Perturbation Method in Newtonian Fluids. Fluid Mechanics, 11(1), 1-11. https://doi.org/10.11648/j.fm.20261101.11

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ACS Style

Ojo, A. S.; Nwabuzor, P. O.; Egbo, C. A.; Umoh, E. S. The Application of Homotopy Perturbation Method in Newtonian Fluids. Fluid Mech. 2026, 11(1), 1-11. doi: 10.11648/j.fm.20261101.11

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AMA Style

Ojo AS, Nwabuzor PO, Egbo CA, Umoh ES. The Application of Homotopy Perturbation Method in Newtonian Fluids. Fluid Mech. 2026;11(1):1-11. doi: 10.11648/j.fm.20261101.11

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@article{10.11648/j.fm.20261101.11,
  author = {Adetoye Solomon Ojo and Peter Onyelukachukwu Nwabuzor and Chijioke Aloysius Egbo and Edikan Sunday Umoh},
  title = {The Application of Homotopy Perturbation Method in Newtonian Fluids},
  journal = {Fluid Mechanics},
  volume = {11},
  number = {1},
  pages = {1-11},
  doi = {10.11648/j.fm.20261101.11},
  url = {https://doi.org/10.11648/j.fm.20261101.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.fm.20261101.11},
  abstract = {The Homotopy Perturbation Method (HPM) has advanced as an efficient semi-analytical technique for solving nonlinear differential equation arising in fluid mechanics. In this study, the application of HPM to Newtonian fluid flow problems is investigated in order to obtain accurate approximate solutions with reduced computational effort. The governing momentum equations of a Newtonian fluid flow, with a focus on deriving and analyzing engineering parameters like skin friction, Nusselt number, and Sherwood number was formulated under appropriate boundary conditions. The nonlinear partial differential equations describing the momentum, Navier-stokes equation and concentration equation were transformed into a homotopy framework by embedding an auxiliary a parameter. The solution is constructed in form of a rapidly convergent series without the need for small perturbation parameters or linearization. The analytical results obtaining using (HPM) are discussed and, where possible, compared with exact or numerical solutions to validate the accuracy and convergence of the method. The impact of the material parameters from the basic hydrodynamic equations were noticed and the findings demonstrate that the Homotopy Perturbation Method provides a reliable, Straightforward, and computationally efficient approach for analyzing Newtonian fluid flow phenomena and can be readily extended to more complex transport and heat transfer problems in engineering and applied sciences, making it a valuable tool for solving a wide range of nonlinear fluid mechanics models.},
 year = {2026}
}

Copy | Download

TY  - JOUR
T1  - The Application of Homotopy Perturbation Method in Newtonian Fluids
AU  - Adetoye Solomon Ojo
AU  - Peter Onyelukachukwu Nwabuzor
AU  - Chijioke Aloysius Egbo
AU  - Edikan Sunday Umoh
Y1  - 2026/02/09
PY  - 2026
N1  - https://doi.org/10.11648/j.fm.20261101.11
DO  - 10.11648/j.fm.20261101.11
T2  - Fluid Mechanics
JF  - Fluid Mechanics
JO  - Fluid Mechanics
SP  - 1
EP  - 11
PB  - Science Publishing Group
SN  - 2575-1816
UR  - https://doi.org/10.11648/j.fm.20261101.11
AB  - The Homotopy Perturbation Method (HPM) has advanced as an efficient semi-analytical technique for solving nonlinear differential equation arising in fluid mechanics. In this study, the application of HPM to Newtonian fluid flow problems is investigated in order to obtain accurate approximate solutions with reduced computational effort. The governing momentum equations of a Newtonian fluid flow, with a focus on deriving and analyzing engineering parameters like skin friction, Nusselt number, and Sherwood number was formulated under appropriate boundary conditions. The nonlinear partial differential equations describing the momentum, Navier-stokes equation and concentration equation were transformed into a homotopy framework by embedding an auxiliary a parameter. The solution is constructed in form of a rapidly convergent series without the need for small perturbation parameters or linearization. The analytical results obtaining using (HPM) are discussed and, where possible, compared with exact or numerical solutions to validate the accuracy and convergence of the method. The impact of the material parameters from the basic hydrodynamic equations were noticed and the findings demonstrate that the Homotopy Perturbation Method provides a reliable, Straightforward, and computationally efficient approach for analyzing Newtonian fluid flow phenomena and can be readily extended to more complex transport and heat transfer problems in engineering and applied sciences, making it a valuable tool for solving a wide range of nonlinear fluid mechanics models.
VL  - 11
IS  - 1
ER  -

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