Abstract
Fluid flow through porous media in intricate geometries has been a fascinating and challenging area of study in applied mathematics and engineering. This area has immense significance in several sectors, such as petroleum, food processing, pharmaceuticals, groundwater flow, and nuclear reactors. This research investigates the behaviour of Newtonian fluids in a conduit filled with a permeable medium under combing and separating stream configurations. The finite element method with the Taylor-Galerkin/Pressure-Correction method is applied in the present study. The stream consists of two reversible setups and two unidirectional streams of linear fluids within a channel filled with porous materials, featuring a sudden gap. To obtain steady solutions, a time-dependent numerical approach is employed. The study examines the effect of intensifying inertia, porosity, and variations in flow rates.
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