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Choudhary, Shalu
- The Effect of Temperature and Pressure Dependent Viscosity on Thermal Convection in a Rotating Couple-Stress Fluid Saturating a Porous Medium: A Nonlinear Stability Analysis
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Authors
Shalu Choudhary
1,
Sunil
1
Affiliations
1 Department of Mathematics, National Institute of Technology, Hamirpur, (H.P.) 177005, IN
1 Department of Mathematics, National Institute of Technology, Hamirpur, (H.P.) 177005, IN
Source
Research Journal of Science and Technology, Vol 5, No 1 (2013), Pagination: 55-64Abstract
A conditional nonlinear stability threshold for rotating in a couple-stress fluid heated from below saturating a porous media with temperature and pressure dependent viscosity is exactly the same as the linear instability boundary. This optimal result is important because it shows that linearized instability theory has captured completely the physics of the onset of convection. Then the effect of couple stress parameter , variable dependent viscosity , medium permeability , Taylor number and Darcy- Brinkman number on the onset of convection are also analyzed.Keywords
Couple-stress fluid, Temperature and Pressure Dependent Viscosity, Porous Medium, Medium Permeability, Rotation, Porosity.
References
- Adams, R. (1975). Sobolev Spaces, Academic Press, New York.
- Chandrasekhar, S. (1981). Hydrodynamic and Hydromagnetic Stability, New York, Dover.
- Galdi, G.P. and Padula, M. (1990). A new approach to energy theory in the stability of fluid motion, Arch. Ration. Mech. Analysis, 110, 187-28.
- Galdi, G. P. and Straughan ,B. (1985). A nonlinear analysis of the stabilizing effect of rotation in the bénard problem, Proc. Roy. Soc. London A, 402, 257-283.
- Hardy G. H., Littlewood, J. E. and Polya, G. (1994). Inequalities, Cambridge University Press, Cambridge.
- Joseph, D.D. (1965). On the stability of the Boussinesq equations, Arch. Ration. Mech. Analysis, 20,59-71.
- Joseph, D. D. (1966). Nonlinear stability of the Boussinesq equations by the method of energy,Arch. Ration. Mech. Analysis, 22, 163-184.
- Laun, H. M. (2003). Pressure dependent viscosity and dissipative heating in capillary rheometry of polymer melts, Rheol Acta, 42, 295-308.
- Mulone, G. and Rionero, S. (2003). Necessary and sufficient conditions for nonlinear stability in the magnetic Bénard proble,. Arch. Rat. Mech. Anal., 166, 197-218.
- Nield, D. A. and Bejan, A. (2006). Convection in Porous Media, Springer, New York.
- Orr, W. McF. (1907). Stability or instability of the steady motions of a perfect liquid, Proc. Roy. Irish. Acad. Sect., A 27, 69-138.
- Qin, Y. and Kaloni, P. N. (1995). Nonlinear stability problem of a rotating porous layer, Q. Appl. Math., 53, 129-142.
- Rajagopal, K. R., Saccomandi, G. and Vergori, L. (2009a). On the Oberbeck-Boussinesq approximation in fluids with pressuredependent viscosities, Nonlinear Anal. Real Word Appl., 10, 1139-1150.
- Rajagopal, K. R., Saccomandi, G. and Vergori, L. (2009b). Stability analysis of the Rayleigh-Bènard convection for a fluid with temperature and pressure dependent viscosity, ZAMP, 60, 739-755.
- Rajagopal, K. R., Saccomandi, G. and Vergori, L. (2011). Stability analysis of the Rayleigh-Bènard convection in a porous medium, ZAMP, 60, 149-160.
- Serrin, J. (1959). On the stability of viscous fluid motions, Arch. Ration. Mech. Analysis, 3, 1-13.
- Straughan, B. (1998). Explosive Instabilities in Mechanics, Springer, Berlin, Germany.
- Straughan, B.(2004).The Energy Method, Stability and Nonlinear Convection, Springer Verlag, New York.
- Straughan, B. (2001). A sharp nonlinear stability threshold in rotating porous convection, Proc. Roy. Soc. Lond., A 457, 87-93.
- Stokes, V.K. (1966). Couple stresses in fluids, Phys. Fluids., 9, 1709-1715.
- Stokes, G. G. (1845). On the theories of the internal friction of fluids in motion, and motion of elastic solids, Trans. Camb. Phil. Soc., 8, 287-305.
- Sunil and Mahajan, A. (2008). A nonlinear stability analysis for rotating magnetized ferrofluid heated from below, Appl. Math. Comp., 204, 299-310.
- Sunil and Mahajan, A. (2009). A nonlinear stability analysis for rotating magnetized ferrofluid heated from below saturating a porous medium, ZAMP, 60, 344-362.
- Sunil, Devi, R. and Mahajan, A. (2011). Global stability for thermal convection in a couple-stress fluid, Int. Commun. Heat Mass Trans., 38, 938-942.
- Sunil, Choudhary, S. and Bharti, P. K. (2012). Global stability for thermal convection in a couple-stress fluid saturating a porous medium with temperature and pressure dependent viscosity, Int. J. Appl. Mech. Engg. 17, 583-602.
- Vadasz, P. (1998). Free convection in rotating porous media, Transport Phenomena in Porous Media, 285- 312.