Homotopy perturbation method for peristaltic motion of gold-blood nanofluid with heat source

2019 ◽  
Vol 30 (6) ◽  
pp. 3121-3138 ◽  
Author(s):  
Abdelhalim Ebaid ◽  
Abdulrahman F. Aljohani ◽  
Emad H. Aly
Keyword(s):  
Gold Nanoparticles ◽  
Heat Source ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Human Cancer ◽  
Content Type ◽  
Homotopy Perturbation ◽  
Blood Temperature ◽  
Flow And Heat Transfer ◽  
Diagnosis Therapy

PurposeThis paper aims to investigate the impacts of the gold nanoparticles on the peristaltic flow and heat transfer of blood in the presence of heat source. This element has been chosen because on comparing with the other common nanoparticles, gold nanoparticles are preferred due to their unique properties in absorbing the temperature when a heat source exists.Design/methodology/approachOn simplifying the governing equations under the assumption of long-wavelength and low-Reynolds number approximations, the resulted system has been solved by applying the homotopy perturbation method. Then, detailed physical discussion has been introduced through several plots while focusing on the consequences of the current results on the treatment of cancer.FindingsThe present results revealed that the heat source has a great effect on the blood velocity, blood temperature and concentration of the gold nanoparticles within the artery/vein cavity when represented as asymmetric channel. Moreover, the accuracy of the current solutions was validated through several plots of the remainder error for each studied phenomenon.Originality/valueThe current idea gives some light on the attempts of using the gold nanoparticles in the treatment of cancer and therefore may lead to possible applications for diagnosis/therapy of the human cancer. To the best of authors’ knowledge, this is novel, very efficient and applicable.

Application of the homotopy perturbation method to an inverse heat problem

2014 ◽  
Vol 24 (6) ◽  
pp. 1331-1337 ◽  
Author(s):  
Guanglu Zhou ◽  
Boying Wu
Keyword(s):  
Inverse Problems ◽  
Heat Source ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Numerical Technique ◽  
Convergent Sequence ◽  
Approximate Solutions ◽  
Content Type ◽  
Homotopy Perturbation ◽  
Inverse Heat Source

Purpose – The purpose of this paper is to present a general framework of Homotopy perturbation method (HPM) for analytic inverse heat source problems. Design/methodology/approach – The proposed numerical technique is based on HPM to determine a heat source in the parabolic heat equation using the usual conditions. Then this shows the pertinent features of the technique in inverse problems. Findings – Using this HPM, a rapid convergent sequence which tends to the exact solution of the problem can be obtained. And the HPM does not require the discretization of the inverse problems. So HPM is a powerful and efficient technique in finding exact and approximate solutions without dispersing the inverse problems. Originality/value – The essential idea of this method is to introduce a homotopy parameter p which takes values from 0 to 1. When p=0, the system of equations usually reduces to a sufficiently simplified form, which normally admits a rather simple solution. As p is gradually increased to 1, the system goes through a sequence of deformations, the solution for each of which is close to that at the previous stage of deformation.

scholarly journals Homotopy Perturbation Method for Thin Film Flow and Heat Transfer over an Unsteady Stretching Sheet with Internal Heating and Variable Heat Flux

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
I-Chung Liu ◽  
Ahmed M. Megahed
Keyword(s):  
Thin Film ◽  
Heat Transfer ◽  
Heat Flux ◽  
Differential Equations ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Homotopy Perturbation ◽  
Flow And Heat Transfer ◽  
Variable Heat ◽  
Variable Heat Flux

We have analyzed the effects of variable heat flux and internal heat generation on the flow and heat transfer in a thin film on a horizontal sheet in the presence of thermal radiation. Similarity transformations are used to transform the governing equations to a set of coupled nonlinear ordinary differential equations. The obtained differential equations are solved approximately by the homotopy perturbation method (HPM). The effects of various parameters governing the flow and heat transfer in this study are discussed and presented graphically. Comparison of numerical results is made with the earlier published results under limiting cases.

The homotopy perturbation method for fractional differential equations: part 1 Mohand transform

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Muhammad Nadeem ◽  
Ji-Huan He ◽  
Asad Islam
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Content Type ◽  
Homotopy Perturbation ◽  
Fractional Pdes ◽  
Specific Objective ◽  
Multiple Behaviors ◽  
Fractional Differential ◽  
Positive Integers

Purpose This study aims that very lately, Mohand transform is introduced to solve the ordinary and partial differential equations (PDEs). In this paper, the authors modify this transformation and associate it with a further analytical method called homotopy perturbation method (HPM) for the fractional view of Newell–Whitehead–Segel equation (NWSE). As Mohand transform is restricted to linear obstacles only, as a consequence, HPM is used to crack the nonlinear terms arising in the illustrated problems. The fractional derivatives are taken into the Caputo sense. Design/methodology/approach The specific objective of this study is to examine the problem which performs an efficient role in the form of stripe orders of two dimensional systems. The authors achieve the multiple behaviors and properties of fractional NWSE with different positive integers. Findings The main finding of this paper is to analyze the fractional view of NWSE. The obtain results perform very good in agreement with exact solution. The authors show that this strategy is absolutely very easy and smooth and have no assumption for the constriction of this approach. Research limitations/implications This paper invokes these two main inspirations: first, Mohand transform is associated with HPM, secondly, fractional view of NWSE with different positive integers. Practical implications In this paper, the graph of approximate solution has the excellent promise with the graphs of exact solutions. Social implications This paper presents valuable technique for handling the fractional PDEs without involving any restrictions or hypothesis. Originality/value The authors discuss the fractional view of NWSE by a Mohand transform. The work of the present paper is original and advanced. Significantly, to the best of the authors’ knowledge, no such work has yet been published in the literature.

The homotopy perturbation method for fractional differential equations: part 2, two-scale transform

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Muhammad Nadeem ◽  
Ji-Huan He
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Perturbation Method ◽  
Fractional Differential Equations ◽  
Homotopy Perturbation Method ◽  
Solution Process ◽  
Solid State Physics ◽  
Content Type ◽  
Homotopy Perturbation ◽  
Fractional Differential

Purpose The purpose of this paper is to find an approximate solution of a fractional differential equation. The fractional Newell–Whitehead–Segel equation (FNWSE) is used to elucidate the solution process, which is one of the nonlinear amplitude equation, and it enhances a significant role in the modeling of various physical phenomena arising in fluid mechanics, solid-state physics, optics, plasma physics, dispersion and convection systems. Design/methodology/approach In Part 1, the authors adopted Mohand transform to find the analytical solution of FNWSE. In this part, the authors apply the fractional complex transform (the two-scale transform) to convert the problem into its differential partner, and then they introduce the homotopy perturbation method (HPM) to bring down the nonlinear terms for the approximate solution. Findings The HPM makes numerical simulation for the fractional differential equations easy, and the two-scale transform is a strong tool for fractal models. Originality/value The HPM with the two-scale transform sheds a bright light on numerical approach to fractional calculus.

Homotopy perturbation method for predicting tsunami wave propagation with crisp and uncertain parameters

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Perumandla Karunakar ◽  
Snehashish Chakraverty
Keyword(s):  
Wave Propagation ◽  
Perturbation Method ◽  
Water Wave ◽  
Design Methodology ◽  
Homotopy Perturbation Method ◽  
Tsunami Wave ◽  
Uncertain Parameters ◽  
Content Type ◽  
Homotopy Perturbation ◽  
Good Agreement

Purpose The purpose of this paper is to find the solution of classical nonlinear shallow-water wave (SWW) equations in particular to the tsunami wave propagation in crisp and interval environment. Design/methodology/approach Homotopy perturbation method (HPM) has been used for handling crisp and uncertain differential equations governing SWW equations. Findings The wave height and depth-averaged velocity of a tsunami wave in crisp and interval cases have been obtained. Originality/value Present results by HPM are compared with the existing solution (in crisp case), and they are found to be in good agreement. Also, the residual error of the solutions is found for the convergence conformation and reliability of the present results.

Homotopy perturbation method for the nonlinear dispersive K(m, n, 1) equations with fractional time derivatives

2010 ◽  
Vol 20 (2) ◽  
pp. 174-185 ◽  
Author(s):  
Hüseyin Koçak ◽  
Turgut Öziş ◽  
Ahmet Yıldırım
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Time Derivative ◽  
Approximate Solutions ◽  
Dispersive Equations ◽  
Content Type ◽  
Nonlinear Dispersive Equations ◽  
Homotopy Perturbation ◽  
Solitary Solutions ◽  
Fractional Time Derivative

PurposeThis paper aims to apply He's homotopy perturbation method (HPM) to obtain solitary solutions for the nonlinear dispersive equations with fractional time derivatives.Design/methodology/approachThe authors choose as an example the nonlinear dispersive and equations with fractional time derivatives to illustrate the validity and the advantages of the proposed method.FindingsThe paper extends the application of the HPM to obtain analytic and approximate solutions to the nonlinear dispersive equations with fractional time derivatives.Originality/valueThis paper extends the HPM to the equation with fractional time derivative.

On Spectral-Homotopy Perturbation Method Solution of Nonlinear Differential Equations in Bounded Domains

2013 ◽  
Vol 1 (1) ◽  
pp. 25-37
Author(s):  
Ahmed A. Khidir
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Boundary ◽  
Nonlinear Differential Equations ◽  
Iteration Algorithm ◽  
Test Problems ◽  
Nonlinear Boundary Value Problems ◽  
Homotopy Perturbation ◽  
Spectral Technique ◽  
Homotopy Analysis

In this study, a combination of the hybrid Chebyshev spectral technique and the homotopy perturbation method is used to construct an iteration algorithm for solving nonlinear boundary value problems. Test problems are solved in order to demonstrate the efficiency, accuracy and reliability of the new technique and comparisons are made between the obtained results and exact solutions. The results demonstrate that the new spectral homotopy perturbation method is more efficient and converges faster than the standard homotopy analysis method. The methodology presented in the work is useful for solving the BVPs consisting of more than one differential equation in bounded domains. 

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