V. S. Sampath Kumar, N. P. Pai^†

Frontiers in Heat and Mass Transfer, Vol.12, pp. 1-9, 2019, DOI:10.5098/hmt.12.23

Abstract The present paper encorporates the effet of magnetic field on the incompressible Casson fluid flow between two parallel infinite rectangular plates approaching towards or away from each other with suction or injection at the porous plates. Using similarity transformations the governing Navier-Stokes equations are reduced to a nonlinear ordinary differential equation. Semi-analytical solution is obtained based on the Homotopy perturbation method. Further, the solution is compared with the classical finite difference method separately. The effect of magnetic field on velocity, skin friction and pressure is analysed on flow between two plates with suction or injection, where two plates moving towards… More >

V.S. Sampath Kumar, N.P. Pai^† , B. Devaki

Frontiers in Heat and Mass Transfer, Vol.20, pp. 1-13, 2023, DOI:10.5098/hmt.20.30

Abstract In the present study, we consider Casson fluid flow between two porous plates with permeability criteria in the presence of heat transfer and magnetic effect. A proper set of similarity transformations simplify the Navier-Stokes equations to non-linear ODEs with boundary conditions. The homotopy perturbation method is an efficient and stable method which is used to get solutions. Further, the results obtained are compared with the solution computed through an effective and efficient finite difference approach. The purpose of this analysis is to study the four different cases arise viz: suction, injection, mixed suction and mixed injection in this problem, along… More >

V. S. Sampath Kumar^a , N. P. Pai^a,† , B. Devaki^a

Frontiers in Heat and Mass Transfer, Vol.16, pp. 1-7, 2021, DOI:10.5098/hmt.16.3

Abstract A study is carried out for the two dimensional laminar flow of conducting fluid in presence of magnetic field. The governing non-linear equations of motion are transformed in to dimensionaless form. A solution is obtained by homotopy perturbation method and it is valid for moderately large Reynolds numbers for injection at the wall. Also an efficient algorithm based finite difference scheme is developed to solve the reduced coupled ordinary differential equations with necessary boundary conditions. The effects of Reynolds number, the magnetic parameter and the pradantle number on flow velocity and tempratare distribution is analysed by both the methods and… More >

Yusry O. El-Dib, Nasser S. Elgazery^*

Sound & Vibration, Vol.56, No.1, pp. 21-36, 2022, DOI:10.32604/sv.2022.014166

Abstract In this article, the main objective is to employ the homotopy perturbation method (HPM) as an alternative to classical perturbation methods for solving nonlinear equations having periodic coefficients. As a simple example, the nonlinear damping Mathieu equation has been investigated. In this investigation, two nonlinear solvability conditions are imposed. One of them was imposed in the first-order homotopy perturbation and used to study the stability behavior at resonance and non-resonance cases. The next level of the perturbation approaches another solvability condition and is applied to obtain the unknowns become clear in the solution for the first-order solvability condition. The approach… More >

Yanni Zhang^1,2, Jing Pang^1,2,*

Sound & Vibration, Vol.55, No.4, pp. 295-303, 2021, DOI:10.32604/sv.2021.014445

Abstract In this article, time fractional Fornberg-Whitham equation of He’s fractional derivative is studied. To transform the fractional model into its equivalent differential equation, the fractional complex transform is used and He’s homotopy perturbation method is implemented to get the approximate analytical solutions of the fractional-order problems. The graphs are plotted to analysis the fractional-order mathematical modeling. More >

Khaled A. Gepreel^1,2, Mohamed S. Mohamed^1,3, Hammad Alotaibi¹, Amr M. S. Mahdy^1,2,*

CMC-Computers, Materials & Continua, Vol.67, No.1, pp. 675-686, 2021, DOI:10.32604/cmc.2021.012200

Abstract The development of mathematical modeling of infectious diseases is a key research area in various fields including ecology and epidemiology. One aim of these models is to understand the dynamics of behavior in infectious diseases. For the new strain of coronavirus (COVID-19), there is no vaccine to protect people and to prevent its spread so far. Instead, control strategies associated with health care, such as social distancing, quarantine, travel restrictions, can be adopted to control the pandemic of COVID-19. This article sheds light on the dynamical behaviors of nonlinear COVID-19 models based on two methods: the homotopy perturbation method (HPM)… More >

Farnaz Ismail¹, Mubashir Qayyum^{2, *}, Syed Inayat Ali Shah¹

CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.3, pp. 825-845, 2020, DOI:10.32604/cmes.2020.011073

Abstract Modeling and analysis of thin film flow with respect to magneto hydro dynamical effect has been an important theme in the field of fluid dynamics, due to its vast industrial applications. The analysis involves studying the behavior and response of governing equations on the basis of various parameters such as thickness of the film, film surface profile, shear stress, liquid velocity, volumetric flux, vorticity, gravity, viscosity among others, along with different boundary conditions. In this article, we extend this analysis in fractional space using a homotopy based scheme, considering the case of a Non-Newtonian Pseudo-Plastic fluid for lifting and drainage… More >

Diptiranjan Behera¹, S. Chakraverty²

CMES-Computer Modeling in Engineering & Sciences, Vol.104, No.3, pp. 211-225, 2015, DOI:10.3970/cmes.2015.104.211

Abstract This paper presents the numerical solution of a viscoelastic continuous beam whose damping behaviours are defined in term of fractional derivatives of arbitrary order. Homotopy Perturbation Method (HPM) is used to obtain the dynamic response with respect to unit impulse load. Obtained results are depicted in term of plots. Comparisons are made with the analytic solutions obtained by Zu-feng and Xiao-yan (2007) to show the effectiveness and validation of the present method. More >

Linjun Wang¹, Xu Han², Youxiang Xie³

CMES-Computer Modeling in Engineering & Sciences, Vol.82, No.3&4, pp. 179-194, 2011, DOI:10.32604/cmes.2011.082.179

Abstract In this paper, a new homotopy perturbation method (IHPM) is presented and suggested to solve an ill-posed problem of multi-source dynamic loads reconstruction. We propose a stable and reliable modification, and obtain a new regularization method, then employ it to find the exact solution for the multi-source dynamic load identification problem. Also, this present method only needs easy computations rather than successive integrations. Finally, the performances of two numerical examples are given. Comparisons are performed between the original homotopy perturbation method (HPM) and IHPM. The results verify that the present method is very simple and effective. More >