For a purely viscous non-Newtonian fluid (not viscoelastic), you use exactly the same form of equation as for a Newtonian fluid (see Bird, Stewart, and Lightfoot), except that you represent the viscosity as a function of the 2nd invariant of the rate of deformation tensor. There is a form of this functionality that gives the same behavior as a power law fluid for simple shear flows.ccrook said:How does one setup the stress tensor for a non-Newtonian fluid? I know that for any fluid the normals should be the pressure and for a power law fluid the shear stress in the direction of flow is related by K(du/dy)^n. Does this mean that all other components are 0 for a symmetric pipe or rectangular duct?
A stress tensor for non-Newtonian fluid is a mathematical representation of the internal forces and stresses that exist within a non-Newtonian fluid. It describes how the fluid responds to applied forces, taking into account its non-Newtonian behavior.
The main difference between these two types of stress tensors is that a stress tensor for non-Newtonian fluid takes into account the non-linear relationship between stress and strain, whereas a stress tensor for Newtonian fluid assumes a linear relationship. This means that the stress tensor for non-Newtonian fluid is more complex and can vary depending on the type of non-Newtonian behavior exhibited by the fluid.
The stress tensor is important for understanding the behavior of non-Newtonian fluids because it allows us to predict and analyze how these fluids will respond to external forces. This is crucial for many industrial and scientific applications, such as in the design of pipelines, pumps, and other fluid systems.
The stress tensor for non-Newtonian fluid is typically calculated using a constitutive equation, which relates the stress tensor to the strain tensor and other variables such as temperature, pressure, and shear rate. The specific form of the constitutive equation will depend on the type of non-Newtonian behavior exhibited by the fluid.
Yes, the stress tensor for non-Newtonian fluid can change over time, especially if the fluid is subject to varying external forces or if its properties (such as temperature or composition) change. This is why it is important to consider the time-dependent behavior of non-Newtonian fluids when studying their stress tensors.