Effect of Rotation and Suspended Particles on the Stability of an Incompressible Walters’ (Model B′) Fluid Heated from Below Under a Variable Gravity Field in a Porous Medium
Abstract
The effect of rotation and suspended particles on the stability of an incompressible Wal- ters’ (model B′) fluid heated from below under a variable gravity field in a porous medium is considered. By applying a normal mode analysis method, the dispersion relation has been derived and solved numerically. It is observed that the rotation, gravity field, suspended par- ticles, and viscoelasticity introduce oscillatory modes. For stationary convection, the rotation has a stabilizing effect and suspended particles are found to have a destabilizing effect on the system, whereas the medium permeability has a stabilizing or destabilizing effect on the system under certain conditions. The effect of rotation, suspended particles, and medium permeability has also been shown graphically.Keywords:
Walters’ (model B′) fluid, rotation, suspended particles, variable gravity field, porous mediumReferences
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2. Lapwood E.R., Convection of a fluid in a porous medium, Proc. Camb. Phil. Soc., 44, 508–519, 1948.
3. Linden P.F., Salt fingers in a steady shear flow, Geophysics Fluid Dynamics, 6, 1–27, 1974.
4. Lister C.R.B., On the thermal balance of a mid ocean ridge, Geophysics. J. Roy. Astr. Soc., 26, 515–535, 1972.
5. Pradhan G.K., Samal P.C., Thermal instability of a fluid layer under variable body forces, J. Math. Anal. Appl., 122, 487–498, 1987.
6. Rana G.C., Kango S.K., Effect of rotation on thermal instability of compressible Walters’ (model B’) elastico-viscous fluid in porous medium, JARAM, 3, 44–57, 2011.
7. Scanlon J.W., Segel L.A., Effect of suspended particles on onset of Be’nard convection, Phys. Fluids, 16, 1573–78, 1973.
8. Sharma R.C., Thermal instability of viscoelastic fluid in hydromagnetics, Acta Physica Hungarica, 38, 293–298, 1975.
9. Sharma R.C., Sunil, Thermal instability of an Oldroydian viscoelastic fluid with suspended particles in hydromagnetics in porous medium, J. of Polymer Plastic Technology and Engineering, 33, 323–339, 1994.
10. Sharma V., Rana G.C., Thermal instability of a Walters’ (model B′) elastico-viscous fluid in the presence of variable gravity field and rotation in porous medium, J. NonEquilib. Thermodyn., 26, 31–40, 2001.
11. Sharma V., Rana G.C., Thermosolutal instability of a Walters’ (model B′) elasticoviscous rotating fluid in the presence of magnetic field and variable gravity field in porous medium, Proc. Nat. Acad. Sci. INDIA, 73, 93–111, 2003.
12. Sharma V., Gupta S., Effect of rotation on thermal convection of micropolar fluids in the presence of suspended particles, Arch. Mech., 60, 403–419, 2008.
13. Stomel H., Fedorov K.N., Small scale structure in temperature and salinity near Timor and Mindanao, Tellus, 19, 306–325, 1967.
14. Walters K., The solution of flow problems in the case of materials with memory, J. Mecanique, 1, 469–778, 1962.
15. Wooding R.A., Rayleigh instability of a thermal boundary layer in flow through a porous medium, J. Fluid Mech., 9, 183–192, 1960.
