A Series Solution of the Unsteady Von Kármán Swirling Viscous Flows

Xu, Hang; Liao, Shijun

doi:10.1007/s10440-006-9076-8

Cited by 17 publications

(20 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This fact has been confirmed by Abbasbandy [21], Sajid and Hayat [22] and Hayat and Sajid [23]. In recent years, the HAM has been successfully employed to solve many types of problems in science and engineering [21,[24][25][26][27][28][29][30][31][32][33][34][35][36]. Very recently, Song and Zhang [37] applied HAM to solve fractional KdVBurgers-Kuramoto equation.…”

Section: Introductionmentioning

confidence: 79%

Series Solutions of Systems of Nonlinear Fractional Differential Equations

et al. 2008

View full text Add to dashboard Cite

Differential equations of fractional order appear in many applications in physics, chemistry and engineering. An effective and easy-to-use method for solving such equations is needed. In this paper, series solutions of the FDEs are presented using the homotopy analysis method (HAM). The HAM provides a convenient way of controlling the convergence region and rate of the series solution. It is confirmed that the HAM series solutions contain the Adomian decomposition method (ADM) solution as special cases.

show abstract

Section: Introductionmentioning

confidence: 79%

Series Solutions of Systems of Nonlinear Fractional Differential Equations

et al. 2008

View full text Add to dashboard Cite

show abstract

“…The homotopy analysis method (HAM) was proposed by Liao [12,13,14,15]. This method has been successfully applied in many problems such as fluid flow and heat transfer problems [1,16,17,18]. The HAM and its modifications contain a certain auxiliary parameterh, which provides us with a simple way to adjust and control the convergence region and rate of convergence of the series solution.…”

Section: Introductionmentioning

confidence: 99%

A novel technique based on the homotopy analysis method to solve the first kind Cauchy integral equations arising in the theory of airfoils

Araghi¹,

Noeiaghdam²

2016

Journal of Interpolation and Approximation in Scientific Comput

View full text Add to dashboard Cite

In this paper, a new efficient and applicable method in order to solve the first kind Cauchy integral equation is presented. For this purpose, this integral equation is converted to the second kind, then the homotopy analysis method is applied to solve the obtained integral equation. Also, the convergence of the proposed method is proved. Several applicable examples are presented which are appeared in the theory of airfoils in fluid mechanics. By plotting thē h-curves, we show the convergence region of the examples and the tables of absolute errors for different values ofh and x are tabulated.

show abstract

“…Ever since, this method has been widely employed to many problems of fluid flow and heat transfer, cf. [17,23,29]. Some recent developments of HAM include the new technique of the homotopy analysis method (nHAM), the spectral homotopy analysis method (SHAM), the Tau and homotopy analysis method (THAM) and the optimal HAM.…”

Section: Introductionmentioning

confidence: 99%

Heat flux performance in a porous medium embedded Maxwell fluid flow over a vertically stretched plate due to heat absorption

Noor

Haq

Abbasbandy

et al. 2016

J. Nonlinear Sci. Appl.

View full text Add to dashboard Cite

Heat absorption and thermal radiation effects in a non-Newtonian fluid on a vertical stretching sheet with suspended particles are considered. The nonlinear partial differential equations are reduced to nonlinear ordinary differential equations via similarity approach. The equations are further solved using shooting-RK4 method and validated with homotopy-Padé solutions. Comparison between previous and present results revealed agreement up to five significant figures. The influence of various parameters on the flow velocity, temperature and concentration are examined. The profiles of reduced skin friction coefficient, Nusselt number and Sherwood number against selected parameters are sketched and discussed. Streamlines of the flow for different Maxwell parameters are visualized too. It is proclaimed that the heat flux of the flow is uplifted as value of either heat absorption or thermal radiation is multiplied. c 2016 All rights reserved.Keywords: Maxwell, thermophoresis, homotopy-Padé, shooting, heat absorption, thermal radiation. 2010 MSC: 35Q30, 76D10, 80A20. IntroductionBased on the law of conservation of energy in physics, energy is an entity that cannot be originated nor demolished but it can be transferred or transformed into diverse forms via medias around. A body * Corresponding author Email address: drfadiya@um.edu.my (N. F. M. Noor)Received 2016-02-05 Noor, et al., J. Nonlinear Sci. Appl. 9 (2016), 2986 2987 that posses energy experiences a proportional change in mass/momentum to satisfy Einstein's mass-energy equivalence [2] for static objects or energy-momentum equivalence for dynamic objects. Absorption is one of normal mechanisms of how a particular energy can be converted into another form. Energy absorption has wide applications in heat exchanger systems of automotive, machinery and reactor, metal suspension in bridge and building constructions, in material reactions such as laser and nuclear, in automated anti icing and retractor systems, and in shock absorber systems especially for permanent crash control, security and transportation safety barriers design and manufacturing. Thermophoresis is a phenomenon of suspended micro sized particles migration in a non-isothermal gas towards declining thermal gradient direction [9,10,13,22]. Thermophoretic velocity and force are experienced by the particles as a result of temperature differences [11,14]. Being an effective tool for collecting particles on surfaces surrounding by low temperature environment, it has abundance applications such as in microelectronics control clean room, modification of chemical/material depositions, air circulation and sampling of aerosol particles, formation in heat exchangers and particles removal from combustion systems of exhaust gases [24]. Thermophoresis is also an important mechanism in the study of semi-conductor technology especially in MHD energy generation system operations as well as in controlled high-quality wafer production [24]. A pioneer study on the nature of thermophoresis in the behavior of a lami...

show abstract

A Series Solution of the Unsteady Von Kármán Swirling Viscous Flows

Cited by 17 publications

References 42 publications

Series Solutions of Systems of Nonlinear Fractional Differential Equations

Series Solutions of Systems of Nonlinear Fractional Differential Equations

A novel technique based on the homotopy analysis method to solve the first kind Cauchy integral equations arising in the theory of airfoils

Heat flux performance in a porous medium embedded Maxwell fluid flow over a vertically stretched plate due to heat absorption

Contact Info

Product

Resources

About