Numerical Modeling of Laminar Casson Fluid Flow in Eccentric Annular Entrance Regions
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Authors: A. M. ATEIA AND O. H. GALAL
DOI: 10.46793/KgJMat2610.1663A
Abstract:
The laminar flow of an incompressible Casson fluid in the entrance region of an eccentric annulus was analyzed numerically. Such asymmetric annular structures are critical in applications like drilling, heat exchangers and biomedical simulations. The Casson fluid model, which is relevant for biological (e.g., blood), industrial (e.g., drilling fluids) and environmental (e.g., mudflows) systems, was investigated using the Finite Difference Method (FDM) with variable mesh size. The Navier-Stokes equations in bipolar coordinates were solved to calculate pressure gradients and axial velocities for varying radius ratios S, relative eccentricities e and yield stress values τD. The results for the entrance region, which were validated against the literature on fully developed flow, showed an accuracy of 97.89% to 99.68%. The entrance region pressure gradient exceeded the fully developed zone by 6.16 to 50.52 times, while the axial velocity ranged from 43.75% to 53.65% of its fully developed value. These findings underscore the importance of entrance region dynamics in engineering design.
Keywords:
Non-Newtonian flow, variable mesh size, eccentric annulus, Casson fluid, entrance region.
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