Browsing by Author "Khalique C.M."

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    Boundary layer equations and stretching sheet solutions for the modified second grade fluid
    (2007) Aksoy Y.; Pakdemirli M.; Khalique C.M.
    A modified second grade non-Newtonian fluid model is considered. The model is a combination of power-law and second grade fluids 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. The boundary layer equations are derived from the equations. Symmetries of the boundary layer equations are calculated using Lie Group theory. For a special power law index of m = -1, the principal Lie algebra extends. Using one of the symmetries, the partial differential system is transferred to an ordinary differential system. The ordinary differential equations are numerically integrated for the stretching sheet boundary 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. The shear stress on the boundary is also calculated. © 2007 Elsevier Ltd. All rights reserved.
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    Symmetries of boundary layer equations of power-law fluids of second grade
    (2008) Pakdemirli M.; Aksoy Y.; Yürüsoy M.; Khalique C.M.
    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. © 2008 The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH.