IJCRR - 6(9), May, 2014
Pages: 11-17
Print Article
Download XML Download PDF
THERMO-MAGNETIC CONVECTION OF AN OLDROYDIAN FLUID THROUGH A BRINKMAN POROUS MEDIUM
Author: Anand Kumar, Rajan Singh
Category: General Sciences
Abstract:Objective: The objective in the present investigation is to study the effect of magnetic field on thermal convection of an Oldroydian viscoelastic fluid through a Brinkman porous medium. Methods: The normal mode method is used to obtain the dispersion relation. Conclusions: For the case of stationary convection, Oldroydian viscoelastic fluid behaves like an ordinary Newtonian fluid and medium permeability and medium porosity have destabilizing effects on the system whereas the magnetic field and Darcy-Brinkman number have stabilizing effects on the system. It is also found that the modes may be oscillatory and non-oscillatory and the principle of exchange of stabilities is valid under certain condition.
Keywords: Stability, Magnetic Field, Brinkman Porous Medium.
Full Text:
INTRODUCTION
The problem of the onset of convection in a horizontal layer of Newtonian fluid heated from below under varying assumptions of hydrodynamics and hydromagnetics has been discussed in detail by Chandrasekhar (1981).A porous medium is defined as a material consisting of a solid matrix with an interconnected void.A comprehensive and detailed study of thermal convection through various porous mediums has been given by Nield andBejan (2006). Tissues can be treated as a porous medium as it is composed of dispersed cells separated by connective voids which allow for flow of nutrients, minerals, etc. There are several evidences, both theoretical and experimental, which suggest that the Darcy’s equation gives inadequate resultsof the hydrodynamic conditions particularly near the boundaries of a porous medium. The DarcyBrinkman equation, which takes into account the boundary effects, has been employed in recent years in biomedical hydrodynamic studies (Khaled and Vafai, 2003). An experimental demonstration by Toms and Strawbridge (1953) reveals that a dilute solution of methyl methacrylate in n-butyl acetate behaves in accordance with the theoretical model of Oldroyd fluid (1958).Sharma (1975) studied the stability of a layer of an electrically conducting Oldroyd fluid in the presence of a magnetic field and found that the magnetic field has a stabilizing influence.Sharma and Sunil (1994) considered the thermal instability of an Oldroydian viscoelastic fluid permeated with suspended particles in hydromagnetics in a porous medium and concluded that for the case of stationary convection, magnetic field has a stabilizing effect whereas medium permeability and suspended particles have destabilizing effects on the system. Kumar et al. (2013) investigated theoretically the influences of dust particles, variable gravity and magnetic field of an Oldroydian Viscoelastic fluid through a Brinkman Porous Medium. The purpose of the present study is to investigate the problem of the onset of stability of an Oldroydian viscoelastic fluid through a Brinkman porous medium in hydromagnetics.
RESEARCH METHODOLOGY
The following Research Methodology is adopted for the proposed Research paper: ? Identification of the problem
FORMULATION OF THE PROBLEM
Consider an infinite horizontal layer of an Oldroydian viscoelastic fluid bounded by the planes z=0 and z=d in a porous medium of porosity ? and medium permeability 1 k . The fluid layer is acted on by a uniform vertical magnetic field H (0, 0, H). The governing equations of motion and continuity for anOldroydian viscoelastic fluid are defined as:? Collection and study of related literature ? Mathematical formulation of the problem ? Stability analysis and use of normal mode method ? Interpretation of results ? Conclusion
References:
EFERENCES
1. Chandrasekhar, S.C. (1981). Hydrodynamic and Hydromagnetic Stability, Dover Publication, New York.
2. Khaled, A.R.A. and Vafai, K. (2003). The role of porous media in modeling flow and heat transfer in biological tissues. Int. J. Heat Mass Transfer, Vol.46, pp.4989-5003.
3. Kumar, K., Singh, V. and Sharma, S. (2013). Stability of an Oldroydian Viscoelastic Fluid Permeated with Suspended Particles through a Brinkman Porous Medium with variable gravity field in Hydromagnetics, American Journal of fluid Dynamics, Vol. 3, 3, pp. 58- 66. doi: 10.5923/j.ajfd.20130303.02
4. Nield, D.A. and Bejan, A. (2006). Convection in porous media. Springer, New-York.
5. Oldroyd J.G. (1958). Non-Newtonian effects in steady motion of some idealized elasticviscous liquids, Proc. Royal Soc. London, A 245, pp. 278-297.
6. Sharma R.C. (1975). Thermal instability in a viscoelastic fluid in hydromagnetics, Acta Phys. Hung., Vol. 38, pp. 293-298.
7. Sharma R.C. and Sunil. (1994). Thermal instability of Oldroydian viscoelastic fluid with suspended particles in hydromagnetics in porous medium, Polymer Plastics Technology and Engineering, Vol. 33, Issue 3, pp. 323- 339.
8. Toms B.A. and Strawbridge D.J. (1953). Elastic and viscous properties of dilute solutions of polymethyl methacrylate in organic liquids, Trans. Faraday Soc., Vol. 49, pp. 1225-1232.
|