Lie group analysis of creeping flow of a second grade fluid

Yürüsoy M., Pakdemirli M., Noyan Ö.

International Journal of Non-Linear Mechanics, vol.36, no.6, pp.955-960, 2001 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 6
  • Publication Date: 2001
  • Doi Number: 10.1016/s0020-7462(00)00060-3
  • Journal Name: International Journal of Non-Linear Mechanics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.955-960
  • Keywords: creeping flow, Lie groups, second grade fluid
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

The two-dimensional equations of motion for the slowly flowing second grade fluid are written in cartesian coordinates neglecting the inertial terms. By employing Lie group analysis, the symmetries of the equations are calculated. The Lie algebra consists of four finite parameter Lie group transformations, one being the scaling symmetry and the others being translations. Two different types of solutions are found using the symmetries. Using the translations in x and y coordinates, an exponential type of exact solution is constructed. For the scaling symmetry, the outcoming ordinary differential equations are more involved and only a series type of approximate solution is presented. Finally, some boundary value problems are discussed. © 2001 Elsevier Science Ltd.