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. Th...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.展开更多
The path equation describing the minimum drag work first proposed by Pakdemirli is reconsidered （Pakdemirli, M. The drag work minimization path for a fly- ing object with altitude-dependent drag parameters. Proceedin...The path equation describing the minimum drag work first proposed by Pakdemirli is reconsidered （Pakdemirli, M. The drag work minimization path for a fly- ing object with altitude-dependent drag parameters. Proceedings of the Institution of Mechanical Engineers, Part C, Journal of Mechanical Engineering Science 223（5）, 1113- 1116 （2009））. The Lie group theory is applied to the general equation. The group classi- fication with respect to an altitude-dependent arbitrary function is presented. Using the symmetries, the group-invariant solutions are determined, and the reduction of order is performed by the canonical coordinates.展开更多
文摘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.
文摘The path equation describing the minimum drag work first proposed by Pakdemirli is reconsidered （Pakdemirli, M. The drag work minimization path for a fly- ing object with altitude-dependent drag parameters. Proceedings of the Institution of Mechanical Engineers, Part C, Journal of Mechanical Engineering Science 223（5）, 1113- 1116 （2009））. The Lie group theory is applied to the general equation. The group classi- fication with respect to an altitude-dependent arbitrary function is presented. Using the symmetries, the group-invariant solutions are determined, and the reduction of order is performed by the canonical coordinates.
