Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 37
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Dholey, S. 2016. Magnetohydrodynamic unsteady separated stagnation-point flow of a viscous fluid over a moving plate. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 96, Issue. 6, p. 707.


    Pan, Mingyang Zheng, Liancun Liu, Fawang and Zhang, Xinxin 2016. Lie group analysis and similarity solution for fractional Blasius flow. Communications in Nonlinear Science and Numerical Simulation, Vol. 37, p. 90.


    Polyanin, Andrei D. and Zhurov, Alexei I. 2016. Parametrically defined nonlinear differential equations and their solutions: Applications in fluid dynamics. Applied Mathematics Letters, Vol. 55, p. 72.


    Polyanin, Andrei D. and Zhurov, Alexei I. 2016. Direct functional separation of variables and new exact solutions to axisymmetric unsteady boundary-layer equations. Communications in Nonlinear Science and Numerical Simulation, Vol. 31, Issue. 1-3, p. 11.


    Polyanin, Andrei D. and Zhurov, Alexei I. 2016. Functional and generalized separable solutions to unsteady Navier–Stokes equations. International Journal of Non-Linear Mechanics, Vol. 79, p. 88.


    Polyanin, Andrei D. and Zhurov, Alexei I. 2016. Non-isothermal flows of liquid metals and melts: Qualitative features, asymptotic models, problems, exact and approximate solutions. International Journal of Non-Linear Mechanics, Vol. 82, p. 104.


    Polyanin, Andrei D. and Zhurov, Alexei I. 2016. One-dimensional reductions and functional separable solutions to unsteady plane and axisymmetric boundary-layer equations for non-Newtonian fluids. International Journal of Non-Linear Mechanics, Vol. 85, p. 70.


    Dholey, S 2015. The boundary layers of an unsteady separated stagnation-point flow of a viscous incompressible fluid over a moving plate. Fluid Dynamics Research, Vol. 47, Issue. 3, p. 035504.


    Nandy, Samir Kumar Mahapatra, Tapas Ray and Pop, Ioan 2015. Unsteady separated stagnation-point flow over a moving porous plate in the presence of a variable magnetic field. European Journal of Mechanics - B/Fluids, Vol. 53, p. 229.


    Polyanin, A. D. 2015. Transformations, properties, and exact solutions of nonstationary axisymmetric boundary-layer equations. Theoretical Foundations of Chemical Engineering, Vol. 49, Issue. 4, p. 406.


    Polyanin, Andrei D. and Zhurov, Alexei I. 2015. Unsteady axisymmetric boundary-layer equations: Transformations, properties, exact solutions, order reduction and solution method. International Journal of Non-Linear Mechanics, Vol. 74, p. 40.


    Uddin, Md. Jashim Bég, O. A. Aziz, A. and Ismail, A. I. Md. 2015. Group Analysis of Free Convection Flow of a Magnetic Nanofluid with Chemical Reaction. Mathematical Problems in Engineering, Vol. 2015, p. 1.


    Zheng, Z.C. and Ghate, A.S. 2015. A solution of two-parameter asymptotic expansions for a two-dimensional unsteady boundary layer. Applied Mathematics and Computation, Vol. 270, p. 90.


    Lok, Y. Y. and Pop, I. 2014. Stretching or shrinking sheet problem for unsteady separated stagnation-point flow. Meccanica, Vol. 49, Issue. 6, p. 1479.


    Roşca, Alin V. Roşca, Natalia C. and Pop, Ioan 2014. Axisymmetric stagnation point flow and heat transfer towards a permeable moving flat plate with surface slip condition. Applied Mathematics and Computation, Vol. 233, p. 139.


    Dholey, S. and Gupta, A. S. 2013. Unsteady separated stagnation-point flow of an incompressible viscous fluid on the surface of a moving porous plate. Physics of Fluids, Vol. 25, Issue. 2, p. 023601.


    Fang, Tiegang and Jing, Wei 2013. Closed-form analytical solutions of flow and heat transfer for an unsteady rear stagnation-point flow. International Journal of Heat and Mass Transfer, Vol. 62, p. 55.


    Fang, Tiegang and Tao, Hua 2012. Unsteady viscous flow over a rotating stretchable disk with deceleration. Communications in Nonlinear Science and Numerical Simulation, Vol. 17, Issue. 12, p. 5064.


    Rohni, Azizah Mohd Ahmad, Syakila and Pop, Ioan 2012. Note on Cortell’s non-linearly stretching permeable sheet. International Journal of Heat and Mass Transfer, Vol. 55, Issue. 21-22, p. 5846.


    Fang, Tiegang Lee, Chia-fon F. and Zhang, Ji 2011. The boundary layers of an unsteady incompressible stagnation-point flow with mass transfer. International Journal of Non-Linear Mechanics, Vol. 46, Issue. 7, p. 942.


    ×
  • Journal of Fluid Mechanics, Volume 216
  • July 1990, pp. 537-559

Similarity solutions of the two-dimensional unsteady boundary-layer equations

  • Philip K. H. Ma (a1) and W. H. Hui (a1)
  • DOI: http://dx.doi.org/10.1017/S0022112090000520
  • Published online: 01 April 2006
Abstract

The method of Lie group transformations is used to derive all group-invariant similarity solutions of the unsteady two-dimensional laminar boundary-layer equations. A new method of nonlinear superposition is then used to generate further similarity solutions from a group-invariant solution. Our results are shown to include all the existing solutions as special cases. A detailed analysis is given to several classes of solutions which are also solutions to the full Navier–Stokes equations and which exhibit flow separation.

Copyright
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax