Melting heat transfer in the stagnation‐point flow of an upper‐convected Maxwell (UCM) fluid past a stretching sheet

The steady laminar boundary layer flow and heat transfer past a stretching sheet arre considered. Upper‐convected Maxwell (UCM) fluid is treated as a rheological model. The resulting nonlinear differential system is solved by homotopy analysis method (HAM). The influence of melting parameter (M), Prandtl number (Pr), Deborah number (β) and stretching ratio (A = a/c) on the velocity and temperature profiles is thoroughly examined. It is noticed that fields are effected appreciably with the variation of parameters. Furthermore, it is seen that the local Nusselt number is a decreasing function of melting parameter. Copyright © 2011 John Wiley & Sons, Ltd.     

横向载荷作用下轴向运动梁的屈曲失稳以及非线性振动特性

梁的轴向运动会诱发其产生横向振动并可能导致屈曲失稳,对结构的安全性和可靠性产生重大的影响。本文重点研究了横向载荷作用下轴向运动梁的屈曲失稳及横向非线性振动特性。基于Hamilton变分原理,建立了横向载荷作用下轴向运动梁的动力学方程,获得了梁的后屈曲构型。使用截断Galerkin法,将控制方程改写成Duffing方程的形式。用同伦分析方法确定载荷作用下轴向运动梁的非线性受迫振动的封闭形式的表达式。结果表明,后屈曲构型对轴向速度和初始轴向应力有明显的依赖性。通过同伦分析法得出非线性基频的显式表达式,获得了初始轴向力会影响非线性频率随初始振幅和轴向速度的线性关系。另外,轴向外激励的方向也会改变系统固有频率。     

Three-dimensional flow over a stretching surface in a viscoelastic fluid

This article looks at the hydrodynamic elastico-viscous fluid over a stretching surface. The equations governing the flow are reduced to ordinary differential equations, which are analytically solved by applying an efficient technique namely the homotopy analysis method (HAM). The solutions for the velocity components are computed. The numerical values of wall skin friction coefficients are also tabulated. The present HAM solution is compared with the known exact solution for the two-dimensional flow and an excellent agreement is found.     

Channel flow of a Maxwell fluid with chemical reaction

This work is concerned with the two-dimensional boundary layer flow of an upper-convected Maxwell (UCM) fluid in a channel with chemical reaction. The walls of the channel are porous. Employing similarity transformations the governing non-linear partial differential equations are reduced into non-linear ordinary differential equations. The resulting ordinary differential equations are solved analytically using homotopy analysis method (HAM). Expressions for series solutions are derived. The convergence of the obtained series solutions are shown explicitly. The effects of Reynold’s number Re, Deborah number De, Schmidt number Sc and chemical reaction parameter γ on the velocity and the concentration fields are shown through graphs and discussed.     

Numerical solutions of peristaltic flow of Williamson fluid with radially varying MHD in an endoscope

In this article we have studied the peristaltic motion of an incompressible Williamson fluid with constant and radially varying magnetohydrodynamics (MHD) in an endoscope. Using the low Reynolds and long wavelength assumptions, the equations of Williamson fluid model in simplified form are solved using (i) the HAM method and (ii) the Shooting method. The comparisons of both solutions have been found a very good agreement. Graphical results have been presented for various emerging parameters. © British Crown Copyright 2010/MOD. Reproduced with permission. Published by John Wiley & Sons, Ltd.     

Influence of thermophoretic diffusion of nanoparticles with Joule heating in flow of Maxwell nanofluid

The aspects of activation energy in magnetized Maxwell nanofluid flow with Brownian movement and thermophoretic diffusion have been elaborated here. Furthermore, Joule heating, variable conductivity and chemical reaction are scrutinized. The Buongiorno nanofluid thought is ratify to incorporate the importance of thermophoretic and Brownian diffusion. The attained ODEs have been solved via homotopic algorithm. The performance of operational variables is inspected. The Maxwell temperature field for Eckert number and variable conductivity factor have similar trend. The fluid concentration exaggerates for activation energy and decelerates for Brownian motion parameter. Furthermore, the brilliant outcomes attained and associated with possible existing prose accurately.     

Homotopy Solutions for a Generalized Second-Grade Fluid Past a Porous Plate

The flow of a second-grade fluid past a porous plate subject to either suction or blowing at the plate has been studied. A modified model of second-grade fluid that has shear-dependent viscosity and can predict the normal stress difference is used. The differential equations governing the flow are solved using homotopy analysis method (HAM). Expressions for the velocity have been constructed and discussed with the help of graphs. Analysis of the obtained results showed that the flow is appreciably influenced by the material and normal stress coefficient. Several results of interest are deduced as the particular cases of the presented analysis.     

Rotating flow of a third grade fluid in a porous space with Hall current

This study investigates the rotating magnetohydrodynamic (MHD) flow of a third-grade fluid in a porous space. Modified Darcy's law has been utilized for the flow modeling. The Hall effects are taken into consideration. The basic equations governing the flow are reduced to a highly nonlinear ordinary differential equation. This equation has been solved analytically by employing the homotopy analysis method (HAM). The effects of the various interesting parameters on the velocity distribution have been discussed.     

A new technique of using homotopy analysis method for solving high‐order nonlinear differential equations

In this paper, a new technique of homotopy analysis method (HAM) is proposed for solving high‐order nonlinear initial value problems. This method improves the convergence of the series solution, eliminates the unneeded terms and reduces time consuming in the standard homotopy analysis method (HAM) by transform the nth‐order nonlinear differential equation to a system of n first‐order equations. Second‐ and third‐ order problems are solved as illustration examples of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

Homotopy Solution for the Channel Flow of a Third Grade Fluid

The solution for the flow of a third grade fluid bounded by two parallel porous plates is given using homotopy analysis method (HAM). A comparison is made with the exact numerical solution for the various values of the physical parameters. It is found that a proper choice of the auxiliary parameter occurring in HAM solution gives very close results.