Lei Liu

Publication Date


Document Type


First Advisor

Payvar, Parviz

Degree Name

M.S. (Master of Science)

Legacy Department

Department of Mechanical Engineering


Non-Newtonian fluids; Laminar flow


Laminar flows of Newtonian and non-Newtonian fluids through rectangular ducts are numerically investigated in this thesis. The objective of this thesis is to find a suitable constitutive equation that can effectively model viscoelastic fluids. Constitutive equations represent the rheological behavior of a fluid. In order to describe the secondary flow and the heat transfer enhancement of laminar viscoelastic flow through non-circular ducts, the Criminale-Erickson-Fibley (CEF) constitutive equation, which takes the normal stress difference into account, is employed to model a broad category of fluids. Based on the CEF model, a set of simplified non-dimensional governing equations are derived, where power law is used for both apparent viscosity and the second normal stress coefficient. The numerical procedure for three-dimensional parabolic flow is employed, where the momentum equations in the cross-stream directions are solved by the SIMPLER algorithm given by Patankar. Numerical results for hydrodynamically developed flow, hydrodynamically developing flow, thermally developed flow as well as simultaneously developing flow are reported based on Newtonian, purely viscous and viscoelastic fluids. It is illustrated that the numerical results agree well with the available analytical solutions. It is also shown that the CEF model effectively describes the rheological phenomena of viscoelastic fluids.


Includes bibliographical references (pages [79]-80)


80 pages




Northern Illinois University

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