Symmetries of boundary layer equations of power-law fluids of second grade. (English) Zbl 1257.76097
Summary: A modified power-law fluid of second grade is considered. The model is a combination of power-law and second grade fluid in which the fluid may exhibit normal stresses, shear thinning or shear thickening behaviors. The equations of motion are derived for two dimensional incompressible flows, and from which the boundary layer equations are derived. Symmetries of the boundary layer equations are found by using Lie group theory, and then group classification with respect to power-law index is performed. By using one of the symmetries, namely the scaling symmetry, the partial differential system is transformed into an ordinary differential system, which is numerically integrated under the classical boundary layer conditions. Effects of power-law index and second grade coefficient on the boundary layers are shown and solutions are contrasted with the usual second grade fluid solutions.
MSC:
| 76M60 | Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics |
| 76A05 | Non-Newtonian fluids |
Software:
LIEReferences:
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