Features:

• Three-parameter model
• Gives Newton's law for phi1 = 0 and power law for phi0 = 0
• For alpha>1, approaches Newton's law for small tau; for alpha<1, approaches Newton's law for large tau
• Useful for polymers, solutions of carboxymethylcellulose in water

Finding the velocity profile of a non-Newtonian fluid described by the Ellis model
 
 

Maple solution for velocity profile of Ellis fluid in pipe flow
 

Finding the temperature profile for the special case of "short contact times."  This means that heat does not penetrate very far into the fluid.  For forced convection heat transfer, the velocity profile is first found, which aids in finding the temperature profile.  In the energy balance, terms can be discarded that are not important in the vicinity of the wall.
 
 

Maple solution for Forced Convection Heat Transfer for Non-Newtonian Flow in Tubes - Short Contact Time