Abstract
A layer of compressible, rotating, elastico-viscous fluid heated & soluted from below is considered in the presence of vertical magnetic field to include the effect of Hall currents. Dispersion relation governing the effect of viscoelasticity, salinity gradient, rotation, magnetic field and Hall currents is derived. For the case of stationary convection, the Rivlin-Erickson fluid behaves like an ordinary Newtonian fluid. The compressibility, stable solute gradient, rotation and magnetic field postpone the onset of thermosolutal instability whereas Hall currents are found to hasten the onset of thermosolutal instability in the absence of rotation. In the presence of rotation, Hall currents postpone/hasten the onset of instability depending upon the value of wavenumbers. Again, the dispersion relation is analyzed numerically & the results depicted graphically. The stable solute gradient and magnetic field (and corresponding Hall currents) introduce oscillatory modes in the system which were non-existent in their absence. The case of overstability is discussed & sufficient conditions for non-existence of overstability are derived.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. O. Ajadi,A note on the unsteady flow of dusty-viscous fluid between two parallel plates, J. Appl. Math. and Computing18(2) (2005), 393–403.
P. K. Bhatia and J. M. Steiner,Convective instability in a rotating viscoelastic fluid layer, Z. Angew. Math. Mech.52 (1972), 321–327.
S. Chandrasekhar,Hydrodynamic and Hydromagnetic Stability, Dover Publication, New York, 1981.
J. E. Dunn and K. R. Rajagopal,Fluids of differential type: Critical review and thermo- dynamic analysis, Int. J. Engg. Sci.33(5) (1995), 689–729.
A. S. Gupta,Hall effects on thermal instability, Rev. Roum. Math. Pures Appl.12 (1967), 665–677.
U. Gupta,Proceedings of 50th congress of ISTAM (an international meet), IIT Kharag- pur (2005), 133-141.
K. Halder,Application of Adomian’s approximation to blood flow through arteries in the presence of magnetic field, J. Appl. Math. & Computing12(2) (2003), 267–279.
D. D. Joseph,Stability of fluid motions, Springer-Verlag, Berlin,I, II, 1976.
A. K. Joshi, Acta Ciencia Indica,24 (1976), 377.
J. G. Oldroyd,Non-Newtonian effects in steady motion of some idealized elastico-viscous liquids, Proc. Roy. Soc. (London),A245 (1958), 278.
K. R. Rajagopal, M. Ruzicka and A. R. Srinivasa,On the Oberbeck-Boussinesq approxi- mation, J. Math. Models Methods Appl. Sci.6(8) (1996), 1157–1167.
S. L. Rathna,Flow of a particular class of non-Newtonian fluids near a rotating disc, Z. Angew. Math. Mech.42 (1962), 231–237.
R. S. Rivlin and J. L. Erickson,Stress deformation relations for isotropic materials, Ra- tional Mech. Anal.4 (1955), 323–329.
K. C. Sharma and U. Gupta,Hall effects on thermosolutal instability of a rotating plasma, IL Nuovo Cimento12D(12) (1990), 1603–1610.
R. C. Sharma and P. Kumar,Thermal instability of Rivlin-Erickson elastico-viscous fluid in presence of uniform rotation, Z. Naturforch.51a (1997), 821–824.
R. C. Sharma and U. Gupta,Thermal instability of compressible fluids with Hall currents and suspended particles in porous medium, Int. J. Engg. Sci.,31(7) (1993), 1053–1060.
A. Sherman and G. W. Sutton,Magnetohydrodynamics, Illinois, Northwestern Univ. Press, Evanston, 1962.
E. A. Spiegal and G. Veronis,On the Boussinesq approximation for a compressible fluid, Astrophys. J.131 (1960), 442.
Sunil, Y. D. Sharma and P. K. Bharti,Thermosolutal instability of compressible Rivlin- Erickson fluid with Hall currents, Int. J. Applied Mech. Engg.10(2) (2004), 329–343.
G. Veronis,On finite amplitude instability in thermohaline convection J. Marine Re- search23 (1965), 1–17.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gupta, U., Sharma, G. On Rivlin-Erickson elastico-viscous fluid heated and soluted from below in the presence of compressibility, rotation and hall currents. J. Appl. Math. Comput. 25, 51–66 (2007). https://doi.org/10.1007/BF02832338
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02832338