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Electrohydrodynamic instability of a rotating Walters’ (model B’) fluid in a porous medium: Brinkman model

Rana G. C., Chand R., Sharma Veena

Mechanics and Mechanical Engineering

2019

Vol. 23, nr 1

138--143

In this study, the instability of Walters’ (model B’) viscoelastic fluid in a Darcy-Brinkman-Boussinesq system heated from below saturating a porous medium in electrohydrodynamics is considered. By applying the linear stability analysis and normal modes, the dispersion relations accounting for the effect of Prandtl number, electric Rayleigh number, Darcy number, Brinkman-Darcy number, Taylor number and kinematic viscoelasticity parameter is derived. The effects of electric Rayleigh number, Darcy number, Brinkman-Darcy number and Taylor number on the onset of stationary convection have been investigated both analytically and graphically.

Hydrodynamic squeeze-film characteristic in porous annular disks using the Brinkman model

Lin J. R., Liao W. H.

International Journal of Applied Mechanics and Engineering

2003

Vol. 8, no 3

413-424

Based on the Brinkman model (BM) with the assumption that the pressure gradient across the porous region is an unknown function, the effects of viscous shear stresses upon the squeezing-film motion in porous annular disks are considered. Using the Brinkman equations and applying the continuity conditions at the interface for the velocities, shear stresses and pressures, two coupled modified Reynolds equations governing the squeeze-film pressure are obtained. The film pressure equation is solved and applied to evaluate the load-carrying capacity and the height-time relationship. According to the results obtained, the BM predicts quite a different squeezing action to those derived by the slip-flow model (SFM) and the Darcy model (DM). Comparing with the SFM, the viscous shear effects of the BM increase the load-carrying capacity and the response time. But, these trends are reversed as compared to the DM. On the whole, the effects of viscous shear stresses are more pronounced for moderate-value permeability parameters and a higher-value radius ratio. A design example for porous annular disks is also illustrated for engineering applications.