Introducing Non-Newtonian Fluid Mechanics Computations with Mathematica in the Undergraduate Curriculum


  • Housam Binous National Institute of Applied Sciences and Technology


We study four non-Newtonian fluid mechanics problems using Mathematica®. Constitutive equations describing the behavior of power-law, Bingham and Carreau models are recalled. The velocity profile is obtained for the horizontal flow of power-law fluids in pipes and annuli. For the vertical laminar film flow of a Bingham fluid we determine the velocity profile. Both problems involve the use of the shooting techniques because they have split boundary conditions. Since Mathematica permits symbolic computations, we determine analytical expressions of volumetric flow rates for pipe flow of the Bingham and power-law fluids. We use the built-in optimization command of Mathematica, FindMinimum, in order to find the non-Newtonian fluid model from representative data of flow rates measured under different applied pressure gradients in a horizontal pipe. These pedagogic problems are used to introduce the field of non-Newtonian fluid mechanics to students at the National Institute of Applied Sciences in Tunis. The Mathematica® notebooks are available from the corresponding author upon request or at Wolfram Research.

Author Biography

Housam Binous, National Institute of Applied Sciences and Technology

Housam Binous is a full-time faculty member at the National Institute of Applied Sciences and Technology in Tunis. He earned a Diptome d'ingenieur in biotechnology from the Ecole des Mines de Paris and a Ph.D. in chemical engineering from the University of California at Davis. His research interests include the application of computers in chemical engineering.






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