Research Article
The Application of Homotopy Perturbation Method in Newtonian Fluids
Issue:
Volume 11, Issue 1, June 2026
Pages:
1-11
Received:
17 January 2026
Accepted:
27 January 2026
Published:
9 February 2026
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.
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 governin...
Show More
Research Article
Numerical Analysis of Magnetohydrodynamic (MHD) Glycerin Copper-Silver Hybrid Nano-Coolant Using Tiwari-Das Model
Issue:
Volume 11, Issue 1, June 2026
Pages:
12-21
Received:
15 August 2025
Accepted:
29 August 2025
Published:
21 October 2026
DOI:
10.11648/j.fm.20261101.12
Downloads:
Views:
Abstract: The existence of machines, electronic devices, environmental regulations and the blooming technology demands for endless efficient heat transfer fluid in automotive radiators, electronics heat sinks and dispersants in transformers coolers. The nanofluid flow is advanced with the aim of bridging the gap in fields such as engineering, industries and medical. The potential use of hydromagnetic (Cu/Ag-glycerine) hybrid nanofluid as a coolant is examined. The Tiwari-Das nanofluid model is applied in the formulation of the partial differential equations describing the flow. The introduction of similarity transformation variables converts the equations to nonlinear systems. The deployment of the state-space method linearizes the ordinary differential equations which numerically solves using the fourth-order Runge-Kutta method with a shooting technique in MATLAB. The ode45 function is invoked. The outputs of the simulation are displayed graphically and in tabular form. The results show the fluid velocity decays with the rise of magnetic strength and Prandtl number while it escalates with radiation parameter, Grashof and Darcy numbers correspondingly. Further, the temperature of the fluid increases with magnetic and radiation parameters and Eckert number. The opposite trend is observed with soaring Prandtl and Darcy numbers respectively. The local skin friction coefficient dwindles with the growth of porosity, magnetic field and radiation parameters. The rate of energy transfer is elevated with increase in magnetic field, radiation and porosity. The decrease in fluid velocity and the hike rate of heat transfer with magnetic field are utilized in thermal transfer, cooling and in heat flow management.
Abstract: The existence of machines, electronic devices, environmental regulations and the blooming technology demands for endless efficient heat transfer fluid in automotive radiators, electronics heat sinks and dispersants in transformers coolers. The nanofluid flow is advanced with the aim of bridging the gap in fields such as engineering, industries and ...
Show More
,
Peter Onyelukachukwu Nwabuzor
