Lie group analysis of creeping flow of a second grade fluid

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 bring 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. (C) 2001 Elsevier Science Ltd. All rights reserved.