We consider the flow of Eyring-Powell model fluid in the annulus between two cylinders whose viscosity depends upon the temperature. We consider the steady flow in the annulus due to the motion of inner cylinder and constant pressure gradient. In the problem considered the flow is found to be remarkedly different from that for the incompressible Navier-Stokes fluid with constant viscosity. An analytical solution of the nonlinear problem is obtained using homotopy analysis method. The behavior of pertinent parameters is analyzed and depicted through graphs.

The analysis of the behaviour of the fluid motion of the non-Newtonian fluids becomes much complicated and subtle as compared to Newtonian fluids due to the fact that non-Newtonian fluids do not exhibit the linear relationship between stress and strain. Rivlin and Ericksen [

The constitutive equation for a Cauchy stress in an Eyring-Powell model fluid is given by

Consider the steady flow of an Eyring-Powell model fluid with variable temperature dependent viscosity between coaxial cylinders. The motion is caused due to a constant pressure gradient and by the motion of the inner cylinder parallel to its length, whereas the outer cylinder is kept stationary. The heat transfer analysis is also taken into account. The dimensionless problem which can describe the flow is

Here the viscosity is expressed in the form

If

Here

In order to report the convergence of the obtained series solutions and the effects of sundry parameters in the present investigation we plotted Figures

Temperature profile for Reynolds’ model for different values of

Velocity profile for Reynolds’ model for different values of

Velocity profile for Reynolds’ model for different values of

Temperature profile for Reynolds’ model for different values of

Temperature profile for Vogel’s model for different values of

Velocity profile for Vogel’s model for different values of

Temperature profile for Vogel’s model for different values of

Velocity profile for Vogel’s model for different values of

Velocity profile for Vogel’s model for different values of

In this paper, we consider the flow of Eyring-Powell model fluid in the annulus between two cylinders whose viscosity depends upon the temperature. We discussed the steady flow in the annulus due to the motion of inner cylinder and constant pressure gradient. In the problem considered the flow is found to be remarkedly different from that for the incompressible Navier-Stokes fluid with constant viscosity. The behavior of pertinent parameters is analyzed and depicted through graphs. Using usual similarity transformations the governing equations have been transformed into non-linear ordinary differential equations. The highly non-linear problem is then solved by homotopy analysis method. Effects of the various parameters on velocity and temperature profiles are examined.

The authors declare that there is no conflict of interests regarding the publication of this paper.