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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

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2019

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Vol. 23, nr 1

138--143

EN

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.

2

Effect of soret and temperature dependent viscosity on thermohaline convection in a ferrofluid saturating a porous medium

Sekar R., Raju K.

International Journal of Applied Mechanics and Engineering

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2014

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Vol. 19, no. 2

321--336

EN

Soret driven ferrothermoconvective instability in multi-component fluids has a wide range of applications in heat and mass transfer. This paper deals with the theoretical investigation of the effect of temperature dependent viscosity on a Soret driven ferrothermohaline convection heated from below and salted from above subjected to a transverse uniform magnetic field in the presence of a porous medium. The Brinkman model is used in the study. It is found that the stationary mode of instability is preferred. For a horizontal fluid layer contained between two free boundaries an exact solution is examined using the normal mode technique for a linear stability analysis. The effect of salinity has been included in magnetization and density of the fluid. The critical thermal magnetic Rayleigh number for the onset of instability is obtained numerically for sufficiently large values of the buoyancy magnetization parameter M1 using the method of numerical Galerkin technique. It is found that magnetization and permeability of the porous medium destabilize the system. The effect of temperature dependent viscosity stabilizes the system on the onset of convection.

3

Effect of temperature-dependent viscosity on ferroconvection in a porous medium

Ramanathan A., Muchikel N.

International Journal of Applied Mechanics and Engineering

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2006

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Vol. 11, no 1

93-104

EN

The effect of temperature-dependent viscosity on the threshold of ferroconvective instability in a porous medium is studied using the Brinkman model. It is found that the stationary mode of instability is preferred to the oscillatory mode. The critical values of the magnetic Rayleigh number marking the onset of ferroconvection are obtained using the Galerkin technique. It is found that the effect of magnetization is to destabilize the system and so is the effect of temperature-dependent viscosity. The porous medium is found to have a stabilizing influence on the onset of convection. The problem is important in energy conversion devices involving ferromagnetic fluids as working media.

4

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

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2003

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Vol. 8, no 3

413-424

EN

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.