Analysis of Third-Grade Fluid in Helical Screw Rheometer
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 (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>β</mml:mi></mml:mrow><mml:mo>~</mml:mo></mml:mover></mml:mrow></mml:math>), and with the increase in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>β</mml:mi></mml:mrow><mml:mo>~</mml:mo></mml:mover></mml:mrow></mml:math>, the velocity profiles increase progressively, which conclude that extrusion process increases with the increase in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>β</mml:mi></mml:mrow><mml:mo>~</mml:mo></mml:mover></mml:mrow></mml:math>. 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.