For Newtonian Fluid, the equations are as follows:

where:

u is the velocity in the x direction

delta P is the pressure drop over length L

mu(o) is the constant viscosity of Newtonian fluid

du/dy is the shear rate

After rearranging, the set of equations above are equivalent to those follows:

And with the new set of initial conditions:

These equations can be solved by either Shooting method or Finite Difference method.

Since the polymer fluid is Non-Newtonian, which indicates that the viscosity is no longer constant. The equations associated are:

where: lambda, b, c are parameters, and other symbols are defined as above

The Shooting method and Finite Difference method mentioned above can be modified to solve the equations for Non-Newtonian fluid.