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.
Highlights
Pulsating flows abound in many areas of engineering fluid dynamics
An early study of pulsatile hydrodynamics was reported by Richardson and Tyler [4] who studied the alternating aerodynamic flow regimes in the vicinity of the entry region of pipes under periodic pressure differences
These studies were all concerned with purely fluid regimes. It has been documented for some time that porous materials often occur in industrial operations and can be used to achieve hydrodynamic control of key processes
Summary
Pulsating flows abound in many areas of engineering fluid dynamics. Pressure surges in pipelines, cavitation in hydraulic systems [1], pumping of slurries and foodstuffs [2] etc. Much later Uchida [6] considered oscillatory boundary layer flow regimes in pulsating pipe flows These analyses provide classical benchmarks for more modern numerical studies, as documented by Schlichting [7]. Other Newtonian studies of pulsating pipe flows include those by Ishii [9], Yakhot et al [10] and most recently by Blyth and Pozrikidis [11] who studied numerically the influence of pulsatile flow on gas column stability These studies were all concerned with purely fluid regimes. In the present study we consider the pulsatile non-Newtonian flow in a Darcy-Forchheimer porous medium channel using a bi-viscosity rheological flow model described by Nakamura and Sawada [16]. The present model may be applied to filtration processes in chemical engineering processes
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