Chia Wang

Publication Date


Document Type


Degree Name

M.S. (Master of Science)

Legacy Department

Department of Mechanical Engineering


Fluid dynamics


The Navier-Stokes equations are widely accepted as the basis for the study of laminar flow of Newtonian fluids. For non-Newtonian fluid, the stress-rate of strain relationship has been represented by a number of simple models such as the power-law. However, none of these simple models can truly represent the fluid behavior over the whole range of the rate of strain. Therefore, in this study, a viscosity function is employed which is based on a curve fitted to actual experimental data of a 0.1% aqueous polyacrylamide solution. The flow simulation results are therefore expected to represent actual laminar flow of non-Newtonian fluids having such a viscosity relationship. In this thesis, velocity, shear rate, and viscosity distributions for Newtonian and non-Newtonian fluids are numerically calculated using the finite difference method for flow in rectangular ducts. Velocity profiles for fully developed flow of Newtonian fluid through rectangular ducts are also calculated by infinite series solutions and approximate simple algebraic equations available in the literature. Agreement between infinite series solutions and approximate simple algebraic equations is very good over most of the cross section, but not in the regions very close to the corners. Velocity profiles for non-Newtonian fluid with the power-law model and an actual viscosity function obtained by a curve fit through measured data are also calculated. Results of the two profiles are compared between themselves and with the results obtained by a procedure developed by Schechter. The special cases of power-law viscosity and constant viscosity (Newtonian) are also calculated for comparison. Wherever possible, the results are compared with those of other researchers. The numerical program can be further improved by developing appropriate non-uniform grids and further improvement of numerical program regarding mapping of grid points during iteration procedure.


Includes bibliographical references (pages 103-104)


xvii, 158 pages




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