^{1, 2}

^{1, 2}

^{3, 4}

^{1}

^{1}

^{2}

^{3}

^{4}

Boundary layer equations are derived for the Sisko fluid. Using Lie group theory, a symmetry analysis of the equations is performed. A partial differential system is transferred to an ordinary differential system via symmetries. Resulting equations are numerically solved. Effects of non-Newtonian parameters on the solutions are discussed.

Due to the inadequacy of Newtonian fluid model which predicts a linear relationship between the shear stress and velocity gradient, many non-Newtonian fluid models were proposed to explain the complex behavior. Usually, the stress constitutive relations of such models inherit complexities which lead to highly nonlinear equations of motion with many terms. To simplify the extremely complex equations, one alternative is to use boundary layer theory which is known to effectively reduce the complexity of Navier-Stokes equations and reduce drastically the computational time. Since there are many non-Newtonian models and new models are being proposed continuously, boundary layer theory for each proposed model also appears in the literature. It is beyond the scope of this work to review vast literature on the boundary layers of non-Newtonian fluids. A limited work on the topic can be found in [

In this work, boundary layer theory is developed for the Sisko fluid, a non-Newtonian fluid model which combines the features of viscous and power law models. A complete symmetry analysis of the boundary layer equations is presented. Using one of the symmetries, the partial differential system is transformed into an ordinary differential system. The resulting ordinary differential system is numerically solved by a finite difference algorithm. Effect of non-Newtonian parameters on the velocity profiles is shown in the graphs.

As a non-Newtonian model, Sisko [

The Cauchy stress tensor for Sisko fluid is

The classical boundary conditions for the problem are

Lie group Theory is employed in search of symmetries of the equations. Details of the theory can be found in [

Usually boundary conditions put much restriction on the symmetries which may lead to removal of all the symmetries. In our case, however, some of the symmetries remain stable after imposing the boundary conditions. For nonlinear equations, the generators should be applied to the boundaries and boundary conditions also [

Selecting parameter “

Equation (

Effect of

Effect of

There is an increase in

Effect of

Effect of

On the contrary, a reverse effect is observed for power index

Effect of power index

Effect of power index

Boundary layer equations of Sisko fluid derived for the first time. Lie group theory is applied to the equations. Equations admit two finite parameter Lie group transformations and an infinite parameter Lie group transformation. The infinite parameter Lie group transformation is not stable with respect to usual boundary layer conditions. Using the scaling symmetry which is one of the finite parameter transformations, the partial differential system is transferred into an ordinary differential system. Resulting ordinary differential system is solved numerically using a finite difference scheme. Effects of non-Newtonian parameters on the boundary layers are discussed in detail. It is found that an increase in the parameters

This work is completed during mutual short visits of T. Hayat to Turkey and M. Pakdemirli to Pakistan. Funding supports of TUBITAK of Turkey and HEC of Pakistan are highly appreciated.