The velocity and shear stress versus radial position are obtained for the laminar flow of a power-law fluid in a pipe. Pipe radius and applied pressure gradients can be set by the user. If you choose a power-law exponent, n, equal to 1 then a Newtonian fluid is recovered. Dilatant and pseudo-plastic fluids are obtained for n>1 and n<1, respectively. A non-Newtonian fluid has a viscosity that changes with the applied shear force.
For a Newtonian fluid (such as water), the viscosity is independent of how fast you are stirring it, but for a non-Newtonian fluid the viscosity is dependent. It gets easier or harder to stir faster for different types of non-Newtonian fluids. Different constitutive equations, giving rise to various models of non-Newtonian fluids, have been proposed in order to express the viscosity as a function of the strain rate. In power-law fluids, n is the power-law exponent and kappa is the power-law consistency index. Dilatant fluids correspond to the case where the exponent in the power-law constitutive equation is positive while pseudo-plastic fluids are obtained when n<1. We see that viscosity decreases with strain rate for n<1, which is the case for pseudo-plastic fluids, also called shear-thinning fluids. On the other hand, dilatant fluids are shear-thickening. If n=1, one recovers the Newtonian fluid behavior.
The user of the GUI application should be aware that good data for the power law exponent and consistency index must be used in order for the result to be correct.
For a treatment using Mathematica, please visit the following links:
I have learnt a lot from your codes. :-)
May i know which governing equation you have used. I was not able to get the governing equations. It would he helpful if u tell me the equation.
Yes Shaun is right there is an analytical solution to this problem. But there is no such solution for other constitutive equations such as Carreau model. So it is really worth studying in order to learn how to solve split boundary problems using the shooting method.
Another much ado about nothing! It's amazing to notice how some authors can make simple things very complicated. This kind of flow equation (steady flow of a power-law fluid in a pipe) can be solved analytically. Such a program should not contain fsolve nor ode45! Students, do not use this file! Program your own m.file and make it better!