Finite Element Solution of Thermal Gee-Lyon Flows in a Circular Tube
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Date
2016-05
Authors
Aimambet, Narken
Journal Title
Journal ISSN
Volume Title
Publisher
Nazarbayev University School of Science and Technology
Abstract
The goal of this project is to calculate the temperature distribu-
tion of certain pressure-driven non-Newtonian
ows inside a circular tube.
The rheology under consideration is the type in which the shear stress is an
implicit function of the shear rate de ned as the inverse function of an odd
function. The
uid velocity in the tube is approximated by the steady state
velocity pro le along the tube length and the viscosity is assumed to be
independent of the temperature. The velocity pro le is computed by using
Mathematica's build-in ODE solver semi-analytically. The corresponding
steady state temperature pro le at tube length is then calculated taking
into account of heat source generated by shear rate from the
uid
ow by
solving an ODE. The temperature distribution from the entrance to the fully
developed region is then approximated numerically by using the axisymmet-
ric linear triangular nite elements. Material and geometric constants and
data for extrusion of chemical Lucite through the tube in literature are used
for the numerical example. Comparison of the numerical result with the
industrial experimental result is made at a point along the central axis of
the tube.
Description
Keywords
Research Subject Categories, Non-Newtonian fluid, finite element method, temperature distribution, extrusion
Citation
Narken Aimambet. 2016. Finite Element Solution of Thermal Gee-Lyon Flows in a Circular Tube. Department of Mathematics, Nazarbayev University, Astana, Kazakhstan. http://nur.nu.edu.kz/handle/123456789/1566