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Analytical solution of magnetohydrodynamic sink flow

Analytical solution of magnetohydrodynamic sink flow
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摘要 An analytical solution to the famous Falkner-Skan equation for the magnetohydrodynamic （MHD） flow is obtained for a special case, namely, the sink flow with a velocity power index of-1. The solution is given in a closed form. Multiple solution branches are obtained. The effects of the magnetic parameter and the wall stretching parameter are analyzed. Interesting velocity profiles are observed with reversal flow regions even for a stationary wall. These solutions provide a rare case of the Falkner-Skan MHD flow with an analytical closed form formula. They greatly enrich the analytical solution for the celebrated Falkner-Skan equation and provide better understanding of this equation. An analytical solution to the famous Falkner-Skan equation for the magnetohydrodynamic （MHD） flow is obtained for a special case, namely, the sink flow with a velocity power index of-1. The solution is given in a closed form. Multiple solution branches are obtained. The effects of the magnetic parameter and the wall stretching parameter are analyzed. Interesting velocity profiles are observed with reversal flow regions even for a stationary wall. These solutions provide a rare case of the Falkner-Skan MHD flow with an analytical closed form formula. They greatly enrich the analytical solution for the celebrated Falkner-Skan equation and provide better understanding of this equation.
作者 章骥 方铁钢 钟永芳
机构地区 Mechanical and Aerospace Engineering Department School of Engineering
出处 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2011年第10期1221-1230,共10页 应用数学和力学（英文版）
关键词 similarity solution Falkner-Skan equation stretching surface magnetohydrodynamic （MHD） analytical solution sink flow similarity solution, Falkner-Skan equation, stretching surface, magnetohydrodynamic （MHD）, analytical solution, sink flow
分类号 O361.3 [理学—流体力学]
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参考文献32

  • 1Falkner, V. M. and Skan, S. W. Some approximate solutions of the boundary layer equations. Phil. Mag., 12, 865-896 (1931).
  • 2Hartree, D. R. On an equation occurring in Falkner and Skan's approximate treatment of the equations of the boundary layer. Mathematical Proceedings of the Cambridge Philosophical Society, 33(2), 223-239 (1937).
  • 3Weyl, H. On the differential equation of the simplest boundary-layer problems. Ann. Math., 43, 381-407 (1942).
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  • 6Stewartson, K. Further solutions of the Falkner-Skan equations. Proceedings of the Cambridge Philosophical Society, Mathematical and Physical Sciences, 50, 454-465 (1954).
  • 7Libby, P. A. and Liu, T. M. Further solutions of the Falkner-Skan equation. AIAA J., 5, 1040-1042 (1967).
  • 8Zaturska, M. B. and Banks, W. H. H. A new solution branch of the Falkner-Skan equation. Acta Mechanica, 152, 197-201 (2001).
  • 9Schlichting, H. and Bussmann, K. Exakte losungen furdie laminare grenzschicht mit absaugung und ausblasen. Schriften Deutschen Akademiedre Luftfahrtforschung Series B, 7(2), 25-69 (1943).
  • 10Nickel, K. Eine einfache abschatzung fur grenzschichten. Ing.-Arch. Bd., 31, 85-100 (1962).
Applied Mathematics and Mechanics(English Edition)
2011年 第10期

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