Symmetries of boundary layer equations of power-law fluids of second grade

Abstract

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.

Applications of Group Theoretical Methods to Non‐Newtonian Fluid Flow Models: Survey of Results

“…Fluids of Second Grade [27]. The only model available dealing with the flow of a power-law second-grade fluid and solved by employing the Lie group method was investigated by Pakdemirli et al [27].…”

“…The only model available dealing with the flow of a power-law second-grade fluid and solved by employing the Lie group method was investigated by Pakdemirli et al [27]. They derived the boundary layer equations for an incompressible power-law second-grade fluid.…”

“…The condition given in (32) is known as an invariant surface condition. Thus, the invariant solution of (27) is obtained by solving the invariant surface condition (32) together with (27). For (27) and (32) to be compatible, the th prolongation X [ ] of the generator X must be tangent to the intersection of and the surface Φ; that is,…”

“…If (32) is satisfied, then the operator X is called a nonclassical infinitesimal symmetry of the th order partial differential equation (27). For the case of two independent variables, and , two cases arise, namely.…”

A hybrid finite volume/finite element method for incompressible generalized Newtonian fluid flows on unstructured triangular meshes

“…The Power-Law model is commonly used to describe the behavior of non-Newtonian fluids [29][30][31]. The effective viscosity of the Power-Law fluid is given by…”