scholarly journals Perturbation Methods to Analysis of Thermal, Fluid Flow and Dynamics Behaviors of Engineering Systems

2021 ◽  
Author(s):  
Gbeminiyi M. Sobamowo
Keyword(s):  
Fluid Flow ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Perturbation Methods ◽  
Thermal Contact ◽  
Engineering Systems ◽  
Regular Perturbation ◽  
Homotopy Perturbation ◽  
Thermal Fluid Flow ◽  
Nonlinear Elastic

This chapter presents the applications of perturbation methods such as regular and homotopy perturbation methods to thermal, fluid flow and dynamic behaviors of engineering systems. The first example shows the utilization of regular perturbation method to thermal analysis of convective-radiative fin with end cooling and thermal contact resistance. The second example is concerned with the application of homotopy perturbation method to squeezing flow and heat transfer of Casson nanofluid between two parallel plates embedded in a porous medium under the influences of slip, Lorentz force, viscous dissipation and thermal radiation. Additionally, the dynamic behavior of piezoelectric nanobeam embedded in linear and nonlinear elastic foundations operating in a thermal-magnetic environment is analyzed using homotopy perturbation method which is presented in the third example. It is believed that the presentation in this chapter will enhance the understanding of these methods for the real world applications.

scholarly journals The Approximate Solution of Fractional Fredholm Integrodifferential Equations by Variational Iteration and Homotopy Perturbation Methods

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Abdelouahab Kadem ◽  
Adem Kilicman
Keyword(s):  
Approximate Solution ◽  
Perturbation Method ◽  
Iteration Method ◽  
Homotopy Perturbation Method ◽  
Perturbation Methods ◽  
Variational Iteration Method ◽  
Integrodifferential Equations ◽  
Variational Iteration ◽  
Homotopy Perturbation ◽  
Constant Coefficients

Variational iteration method and homotopy perturbation method are used to solve the fractional Fredholm integrodifferential equations with constant coefficients. The obtained results indicate that the method is efficient and also accurate.

Homotopy perturbation method for MHD non-Newtonian Williamson fluid over exponentially stretching sheet with viscous dissipation and convective boundary condition

2019 ◽  
Vol 30 (11) ◽  
pp. 1950088 ◽  
Author(s):  
Khadijah M. Abualnaja
Keyword(s):  
Fluid Flow ◽  
Perturbation Method ◽  
Numerical Method ◽  
Homotopy Perturbation Method ◽  
Stretching Sheet ◽  
Fluid Temperature ◽  
Williamson Fluid ◽  
Homotopy Perturbation ◽  
Exponential Stretching ◽  
Special Cases

This research is aimed at presenting the two-dimensional steady fluid flow, represented by Williamson constitutive model past a nonlinear exponential stretching sheet theoretically. The system of ODEs describing the physical problem is successfully solved numerically with the help of the homotopy perturbation method (HPM). Special attention is given to study the convergence analysis of the proposed method. The influences of the physical governing parameters acting on the fluid velocity and the fluid temperature are explained with the help of the figures and tables. Further, the presented numerical method is employed to calculate both the rate of heat transfer and the drag force for the Williamson fluid flow. In particular, it is observed that both the Eckert number and the dimensionless convective parameter have the effect of enhancing the temperature of the stretching surface, while the inverse was noted for the dimensionless mixed convection parameter. Finally, the comparison with previous numerical investigations of other authors at some special cases which is reported here proves that the results obtained via homotopy perturbation method are accurate and the numerical method is reliable.

scholarly journals Homotopy perturbation method for motion of a spherical solid particle in plane couette fluid flow

2011 ◽  
Vol 61 (8) ◽  
pp. 2267-2270 ◽  
Author(s):  
M. Jalaal ◽  
M.G. Nejad ◽  
P. Jalili ◽  
M. Esmaeilpour ◽  
H. Bararnia ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Perturbation Method ◽  
Solid Particle ◽  
Homotopy Perturbation Method ◽  
Homotopy Perturbation ◽  
Spherical Solid Particle

scholarly journals Analytic approximate solutions for fluid flow in the presence of heat and mass transfer

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 259-264
Author(s):  
Adem Kılıcman ◽  
Yasir Khan ◽  
Ali Akgul ◽  
Naeem Faraz ◽  
Esra Akgul ◽  
...  
Keyword(s):  
Mass Transfer ◽  
Fluid Flow ◽  
Perturbation Method ◽  
Heat And Mass Transfer ◽  
Homotopy Perturbation Method ◽  
Approximate Solutions ◽  
Solution Procedure ◽  
Homotopy Perturbation ◽  
Present Solution ◽  
Linear Ode

This paper outlines a comprehensive study of the fluid-flow in the presence of heat and mass transfer. The governing non-linear ODE are solved by means of the homotopy perturbation method. A comparison of the present solution is also made with the existing solution and excellent agreement is observed. The implementation of homotopy perturbation method proved to be extremely effective and highly suitable. The solution procedure explicitly elucidates the remarkable accuracy of the proposed algorithm.

scholarly journals Mathematical Model and Solution for an Unsteady MHD Fourth Grade Fluid Flow over a Vertical Plate in a Porous Medium with Magnetic Field and Suction/Injection Effects

2020 ◽  
Vol 12 (4) ◽  
pp. 485-498
Author(s):  
O. J. Fenuga ◽  
S. J. Aroloye ◽  
S. O. Salawu
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Fluid Flow ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Fourth Grade ◽  
Governing Equations ◽  
Homotopy Perturbation ◽  
Grade Fluid ◽  
Fourth Grade Fluid

This work investigates the mathematical model and solution for an unsteady MHD fourth grade fluid flow over a vertical plate in a porous medium with the effects of the magnetic field and suction/injection parameters using Homotopy Perturbation Method. The flow is considered to satisfy the constitutive equations of fourth grade fluid flow model and because of the Homotopy Perturbation Method used, only the momentum equation with initial and boundary conditions are solved as governing equations. After initializing stability test, the convergence of the governing equations are observed graphically using the results of Homotopy Perturbation Method with the new analytical method used by Yurusoy in literature and there is a perfect agreement in results. The impact of dimensionless second, third and fourth grade parameters with the effects of magnetic field and suction/injection parameters on the velocity field are displayed graphically and discussed. Increase in suction parameter decreases the momentum boundary layer thickness while injection parameter enhances velocity distribution in the boundary layer. Magnetic field reduces velocity throughout the boundary layer because the Lorentz force which acts as retarding force reduces the boundary layer thickness.

scholarly journals Application of Perturbation Theory in Heat Flow Analysis

2021 ◽  
Author(s):  
Neelam Gupta ◽  
Neel Kanth
Keyword(s):  
Partial Differential Equations ◽  
Heat Flow ◽  
Differential Equations ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Perturbation Methods ◽  
Separation Of Variables ◽  
Flow Analysis ◽  
Partial Differential ◽  
Homotopy Perturbation

Many physical and engineering problems can be modeled using partial differential equations such as heat transfer through conduction process in steady and unsteady state. Perturbation methods are analytical approximation method to understand physical phenomena which depends on perturbation quantity. Homotopy perturbation method (HPM) was proposed by Ji Huan He. HPM is considered as effective method in solving partial differential equations. The solution obtained by HPM converges to exact solution, which are in the form of an infinite function series. Biazar and Eslami proposed new homotopy perturbation method (NHPM) in which construction of an appropriate homotopy equation and selection of appropriate initial approximation guess are two important steps. In present work, heat flow analysis has been done on a rod of length L and diffusivity α using HPM and NHPM. The solution obtained using different perturbation methods are compared with the solution obtained from most common analytical method separation of variables.

Analytical Approximations for Dry Friction-induced Stick-Slip and Pure-Slip Vibration Amplitudes of a Self-Excited SD Oscillator

2021 ◽  
Author(s):  
Junfeng Yan ◽  
Zehao Huang
Keyword(s):  
Perturbation Method ◽  
Friction Force ◽  
Dry Friction ◽  
Homotopy Perturbation Method ◽  
Perturbation Methods ◽  
Stick Slip ◽  
Homotopy Perturbation ◽  
Analytical Approximations ◽  
Sd Oscillator ◽  
Analytical Expressions

Abstract An analytical and numerical investigation into pure-slip and stick-slip oscillations induced by dry friction between a rigid mass linked by an inclined spring, modeled by the archetypal self-excited smooth and discontinuous (SD) oscillator, and the classical moving rigid belt, is presented. The friction force between surface contacts is modeled in the sense of Stribeck effect to formulate the friction model that the friction force firstly decreases and then increases with increasing relative sliding speed. Some perturbation methods are considered into this system for establishing the approximate analytical expressions of the occurring conditions, vibration amplitudes, and base frequencies of dry friction-induced stick-slip and pure-slip oscillations. For pure-slip oscillations, two different approaches are applied to analyze this self-excited SD oscillator. One of them is the homotopy perturbation method by constructing the nonlinear amplitude and frequency. Based on the multiple-scales homotopy perturbation method, a nonlinear equation for amplitude of the analytical approximate solution is constructed, which containing all parameters of problem. For stick-slip oscillations, the analytical approximations for amplitude and frequency are obtained by perturbation methods for finite time intervals of the stick phase, which is linked to the subsequent slip phase under the conditions of continuity and periodicity. The accuracy of analytical approximations is verified by the comparison between analytical approximations and numerical simulations. These analytical expressions are needed for gaining a deeper understanding of dry friction-induced pure-slip and stick-slip oscillations for the friction system with geometric nonlinearity.

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