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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 620238, 11 pages
http://dx.doi.org/10.1155/2013/620238
Research Article

Analysis of Third-Grade Fluid in Helical Screw Rheometer

1Department of Mathematics, COMSATS Institute of Information Technology, Islamabad, Pakistan
2Department of Mathematics, Abdul Wali Khan University, Mardan, Pakistan
3Department of Mathematics, Pennsylvania State University, York Campus, York, PA 17 403, USA

Received 17 October 2012; Revised 4 March 2013; Accepted 20 March 2013

Academic Editor: Juan Torregrosa

Copyright © 2013 M. Zeb et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The steady flow of an incompressible, third-grade fluid in helical screw rheometer (HSR) is studied by “unwrapping or flattening” the channel, lands, and the outside rotating barrel. The geometry is approximated as a shallow infinite channel, by assuming that the width of the channel is large as compared to the depth. The developed second-order nonlinear coupled differential equations are reduced to single differential equation by using a transformation. Using Adomian decomposition method, analytical expressions are calculated for the the velocity profiles and volume flow rates. The results have been discussed with the help of graphs as well. We observed that the velocity profiles are strongly dependant on non-Newtonian parameter ( ), and with the increase in , the velocity profiles increase progressively, which conclude that extrusion process increases with the increase in . We also observed that the increase in pressure gradients in x- and z-direction increases the net flow inside the helical screw rheometer, which increases the extrusion process. We noticed that the flow increases as the flight angle increase.