Homotopy Perturbation Solution Research Articles

Entropy generation on EMHD Darcy-Forchheimer flow of Carreau hybrid nanofluid over a permeable rotating disk with radiation and heat generation: Homotopy perturbation solution

The intention of this article is to explore the entropy generation of the Carreau hybrid nanofluid in a permeable rotating disk in the presence of thermal radiation, heat generation, and viscous dissipation. By applying the self-similarity variables, the partial differential equations are converted into ordinary differential equations and then the homotopy perturbation method is performed. Graphene oxide (Go) and Silver (Ag) are nanoparticles and kerosene oil as a base fluid is considered. Compared to the numerical technique (Runge-Kutta method), the homotopy perturbation method generates more precise and dependable results. The influence of sundry parameters is exhibited graphically for velocity, temperature, entropy generation, Bejan number, skin friction coefficient, and Nusselt number. The higher values of the Weissenberg number enhance the velocity profile and the opposite nature is observed in the porosity parameter. The entropy generation increases for larger values of the thermal radiation and electric field parameters. Carreau nanofluid expands under higher stress on the surface of the wall than Newtonian fluid. This type of problem would be used for electric devices and solar thermal systems. Moreover, the selected nanoparticles Graphene oxide and Silver play an important role in the biofunctionalization of protein, antibacterial, and anticancer therapy.

Improved Homotopy Perturbation Solution for Nonlinear Transverse Vibration of Orthotropic Membrane

Improved Homotopy Perturbation Solution for Nonlinear Transverse Vibration of Orthotropic Membrane

New approximate analytical solution of the large deflection problem of an uniformly loaded thin circular plate with edge simply hinged

In this paper, the large deflection problem of an uniformly loaded circular plate with edge simply hinged is considered. First, a new algorithm for the deflection problem is proposed based on Adomian decomposition method. Then, a new approximate analytic solution of the large deflection problem is obtained by the algorithm. Final, its bending moments are analyzed corresponding to different center deflections. And the relationship between the center deflection and the external load is discussed. Through comparing the errors of the obtained approximate solution with the previous perturbation solution and homotopy perturbation solution, one can see that the obtained solution in this paper is a better one and the result in this paper has a certain practical value.

Entropy generation on EMHD stagnation point flow of hybrid nanofluid over a stretching sheet: Homotopy perturbation solution

The intention of this article is to explore the entropy generation in EMHD hybrid nanofluid on a stagnation point in the presence of slips, heat generation and viscous dissipation. The fluid in the enclosure is water containing hybrid nanoparticles Ag-Cu. Suitable self-similarity variables are employed to transform the nonlinear differential systems into an ordinary differential system, which computed via homotopy perturbation method (HPM). The comparison with the homotopy perturbation method (HPM) gives an accurate and reliable result than the numerical method (Runge-Kutta method). The graphical results are expressed for velocity, temperature, entropy generation, Bejan number, skin friction and Nusselt number with an impact of active parameters. The higher values of electric field enhancing the velocity whereas the opposite nature for a magnetic field parameter. The entropy generation rises for higher values of a magnetic parameter, Eckert number and temperature difference parameter. In the magnetic field and electromagnetic field plays an important role in biomedical applications especially radiofRequency ablation (RFA), magnetic resonance imaging (MRI), cancer therapy, tumor therapy, malaria infection. This theoretical investigation may be profitable in biomedical engineering, especially cardiology, cure of skin disorders and treat tumors in Uterus.

Generalized least square homotopy perturbation solution of fractional telegraph equations

In this paper, we present generalized aspect of least square homotopy perturbation method (generalized LSHPM) using fractional calculus. We consider the linear/nonlinear telegraph equations in which second-order time/space derivatives are replaced by fractional derivative of order $$ \alpha $$ $$ (1 < \alpha \le 2) $$ in Caputo sense. The approximate solutions are achieved by taking the coupling of homotopy perturbation method and least square method. The multiple solution approach is also discussed. The scheme is accurate and easy to apply.

Analytical solution of groundwater waves in unconfined aquifers with sloping boundary

A new analytical solution is derived for tide-driven groundwater waves in coastal aquifers using higher-order Boussinesq equation. The homotopy perturbation solution is derived using a virtual perturbation approach without any pre-defined physical parameters. The secular term removal is performed using a combination of parameter expansion and auxiliary term. This approach is unique compared with existing perturbation solutions. The present first-order solution compares well with the previous analytical solutions and a 2D FEFLOW solution for a steep beach slope. This is due to the fact that the higher-order Boussinesq equation captures the streamlines better than ordinary Boussinesq equation based on Dupuit’s assumption. The slope of the beach emerges as an implicit physical parameter from the solution process.

Homotopy perturbation method to MHD non-Newtonian nanofluid flow through a porous medium in eccentric annuli with peristalsis

In this contribution, the magnetohydrodynamic non-Newtonian nanofluid flow through a porous medium in eccentric annuli with peristalsis is investigated. This has been done under the combined effect of viscous dissipation and radiation. The inner annulus is rigid and at rest, while the outer annulus has a sinusoidal wave traveling down its wall. The fundamental equations are modulated under the long wave length assumptions, and a closed form of solution is obtained for the axial velocity. While, homotopy perturbation solution is obtained, which satisfies the energy and nanoparticles equations. Numerical results for the axial velocity, temperature, and nanoparticles phenomena distributions as well as the reduced Nusselt and Sherwood numbers are obtained and tabulated for various parametric conditions.

Comparative Solution of Nonlinear Quintic Cubic Oscillator Using Modified Homotopy Perturbation Method

We use modified homotopy perturbation method to find out the solution of nonlinear cubic quintic equation. Besides this method solution of the problem with the following methods is discussed, Energy Balance Method and He’s Frequency Formulation method and then compare the results with each other and Global Error Method. The results show that these three methods are effective as global error method for nonlinear cubic quintic oscillator equation with multiple nonlinear terms and have different effects on the solution. In particular, the homotopy perturbation solution is quite surprising. A cubic quintic nonlinear oscillator is used as an example to compare the results.

Homotopy perturbation solution and periodicity analysis of nonlinear vibration of thin rectangular functionally graded plates

In this paper nonlinear analysis of a thin rectangular functionally graded plate is formulated in terms of von-Karman's dynamic equations. Functionally Graded Material (FGM) properties vary through the constant thickness of the plate at ambient temperature. By expansion of the solution as a series of mode functions, we reduce the governing equations of motion to a Duffing's equation. The homotopy perturbation solution of generated Duffing's equation is also obtained and compared with numerical solutions. The sufficient conditions for the existence of periodic oscillatory behavior of the plate are established by using Green's function and Schauder's fixed point theorem.

MHD Squeezing Flow of a Micropolar Fluid Between Parallel Disks

The squeezing flow of an incompressible micropolar fluid between two parallel infinite disks is investigated in the presence of a magnetic flied. An analysis of strong and weak interactions has been carried out. Similarity solutions are derived by homotopy analysis method. The variation of dimensionless velocities are sketched in order to see the influence of pertinent parameters. Skin friction coefficient and wall couple stress coefficient have been tabulated. In addition, the derived results are compared with the homotopy perturbation solution in a viscous fluid.

MHD squeezing flow of second‐grade fluid between two parallel disks

SUMMARYThis paper examines the unsteady two‐dimensional flow of a second‐grade fluid between parallel disks in the presence of an applied magnetic field. The continuity and momentum equations governing the unsteady two‐dimensional flow of a second‐grade fluid are reduced to a single differential equation through similarity transformations. The resulting differential system is computed by a homotopy analysis method. Graphical results are discussed for both suction and blowing cases. In addition, the derived results are compared with the homotopy perturbation solution in a viscous fluid (Math. Probl. Eng., DOI: 10.1155/2009/603916). Copyright © 2011 John Wiley &amp; Sons, Ltd.

Homotopy perturbation solution for peristaltic flow of a third order fluid

The peristaltic transport of a third order fluid in a planar channel as well as in an axisymmetric tube having walls that are transversely displaced by an infinite, harmonic travelling wave of large wavelength and negligibly small Reynolds number, has been analyzed using homotopy perturbation technique. Unlike perturbation method, this method does not restrict the Deborah number $\Gamma $ to be very large or small and works fairly well for any choice of $\Gamma $. The expressions for stream function and pressure rise per wavelength have been obtained up to second order of approximation.