Finite element solutions for non-Newtonian pulsatile flow in a non-Darcian porous medium conduit

Bhargava, Rama, Takhar, Harmindar S., Rawat, S., Bég, Tasveer A. and Bég, O. Anwar (2007) Finite element solutions for non-Newtonian pulsatile flow in a non-Darcian porous medium conduit. Nonlinear analysis: modelling and control, 12 (3). pp. 317-327. ISSN 1392-5113

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Abstract

The present analysis is motivated by the need to elucidate with more accuracy and sophistication the hydrodynamics of non-Newtonian flow via a channel containing a porous material under pulsating pressure gradient. A one-dimensional transient rheological model for pulsating flow through a Darcy-Forcheimmer porous channel is used. A modified Casson non-Newtonian constitutive model is employed for the transport fluid with a drag force formulation for the porous body force effects. The model is transformed and solved using a finite element numerical technique. Rheological effects are examined using a β parameter which vanishes in the limit (Newtonian flow). Velocity profiles are plotted for studying the influence of Reynolds number, Darcy number, Forchheimer number and the β (non-Newtonian) parameter. The channel considered is rigid with a pulsatile pressure applied via an appropriate pressure gradient term. The model finds applications in industrial filtration systems, pumping of polymeric fluids etc.