**6. Acknowledgements**

The project was supported by the National Natural Science Foundation of China (10802099), Doctoral Fund of Ministry of Education of China (200804251520), and Natural Science Foundation of Shandong Province (ZR2009AQ006). The author also acknowledges the support from the Brain Korea 21 program at Seoul National University.

## **7. References**


**3** 

*Vietnam* 

**Incompressible Non-Newtonian Fluid Flows** 

A non-Newtonian fluid is a fluid whose flow properties differ in many ways from those of Newtonian fluids. Most commonly the viscosity of non-Newtonian fluids is not independent of shear rate or shear rate history. In practice, many fluid materials exhibits non-Newtonian fluid behavior such as: salt solutions, molten, ketchup, custard, toothpaste, starch suspensions, paint, blood, and shampoo etc. In a Newtonian fluid, the relation between the shear stress and the shear rate is linear, passing through the origin, the constant of proportionality being the coefficient of viscosity. In a non-Newtonian fluid, the relation between the shear stress and the shear rate is different, and can even be time-dependent. Therefore a constant coefficient of viscosity cannot be defined. In the previous parts of this book, the mechanics of Newtonian fluid have been mentioned. In this chapter, the common rheological models of non-Newtonian fluids are introduced and several approaches concerned with non-Newtonian fluid flows are considered. In addition, the solution of common non-Newtonian fluid flows in a circular pipe,

As above mentioned, a non-Newtonian fluid is one whose flow curve (shear stress versus shear rate) is nonlinear or does not pass through the origin, i.e. where the apparent viscosity, shear stress divided by shear rate, is not constant at a given temperature and pressure but is dependent on flow conditions such as flow geometry, shear rate, etc. and sometimes even on the kinematic history of the fluid element under consideration. Such materials may be

1. fluids for which the rate of shear at any point is determined only by the value of the shear stress at that point at that instant; these fluids are variously known as 'time

3. substances exhibiting characteristics of both ideal fluids and elastic solids and showing partial elastic recovery, after deformation; these are categorized as 'viscoplastic fluids'. Among the three groups, the time independent Non-Newtonian fluids are the most popular and easiest to handle in analysis. In this chapter, only this group of Non-Newtonian fluids

independent' , ' purely viscous' , 'inelastic' or 'generalized Newtonian fluids'); 2. more complex fluids for which the relation between shear stress and shear rate depends, in addition, upon the duration of shearing and their kinematic history; they

**1. Introduction** 

are considered.

annular and rectangular duct are presented.

**2. Classification of non-Newtonian fluid** 

conveniently grouped into three general classes:

are called 'time-dependent fluids', and finally,

Quoc-Hung Nguyen and Ngoc-Diep Nguyen *Mechanical Faculty, Ho Chi Minh University of Industry,* 

