ORIGINAL PAPER
On a Couple-Stress Rivlin-Ericksen Ferromagnetic Fluid Heated from Below with Varying Gravity, Rotation, Magnetic Field and Suspended Particles Flowing Through a Porous Medium
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D.A.V. College, Muzaffarnagar, Uttar Pradesh- 251001, India
Online publication date: 2022-06-14
Publication date: 2022-06-01
International Journal of Applied Mechanics and Engineering 2022;27(2):177-198
KEYWORDS
ABSTRACT
The thermal instability of a couple-stress Rivlin-Ericksen ferromagnetic fluid with varying gravity field, suspended particles, rotation and magnetic field flowing through a porous medium is investigated. The dispersion relation has been developed and solved analytically using the normal mode approach and linear stability theory. The effect of suspended particles, rotation, couple stress, permeability and magnetic field on the fluid layer has been investigated. For stationary conventions, it is found that suspended particles always have a destabilizing effect for λ>0 and a stabilizing effect for λ<0 and couple-stress, magnetic field and permeability of the medium have a stabilizing effect on the thermal instability under certain conditions. In the absence of the rotation couple-stress has a stabilizing effect if λ >0 and a destabilizing effect if λ<0. Rotation has a stabilizing effect if λ >0 and a destabilizing effect if λ<0. In the absence of rotation permeability has a stabilizing effect if λ<0 and a destabilizing effect if λ>0. Magnetisation always has a stabilizing effect (λ>0 or λ<0).
REFERENCES (27)
1.
Stokes V.K. (1966): Couple-Stresses in Fluids.– Physics of Fluids, vol.9, pp.1709-1715.
2.
Stokes V.K. (1984): Theories of Fluids with Microstructure.– Springer-Verleg, New-York.
3.
Walicki E. and Walicka A. (1999): Interia effect in the squeeze film of a couple-stress fluids in biological bearings.– Int. J. Appl. Mech. Engg., vol.4, pp.363-373.
4.
Chandrasekhar S. (1981): Hydrodynamic and Hydromagnetic Stability.– Dover Publication, New York.
5.
Sharma R.C. and Sharma S. (2001): On couple-stress fluid heated from below in porous medium.– Indian J. Phys., vol.75B, pp.59-61.
6.
Kumar Vivek and Kumar Sudhir (2010): On a couple-stress fluid heated from below in hydromagnetics, Applications and Applied Mathematics.– vol.05, No.2, pp.529-542.
7.
Sunil, Divya, Sharma R.C. and Sharma Veena (2003): Compressible couple-stress fluid permitted with suspended particles heated and soluted from below in porous medium.– Indian Journal of Pure & Applied Physics, vol.41, pp.602-611.
8.
Kumar K., Singh V., and Sharma S. (2017): Effect of horizontal magnetic field and horizontal rotation on thermosolutal stability of a dusty couple-stress fluid through a porous medium, a Brinkman model.– Journal of Applied Fluid Mechanics, vol.10, No.2, pp.681-692.
9.
Stanly W. and Dr. Vansthakumari R. (2017): A study of thermal stability on dusty couple-stress fluid in hydromagnetic field with rotation.– Science International, vol.5, No.2, pp.47-55.
10.
Sharma R.C. and Thakur K.D. (2000): On couple-stress fluid heated from below in porous medium in hydromagnetics.– Czechoslovak Journal of Physics, vol.50, pp.753-758.
11.
Sunil, Sharma R.C. and Singh M. (2002): On a couple-stress fluid heated from below in a porous medium in the presence of magnetic field and rotation.– J Porous Media, vol.5, No.2, pp.149-158.
12.
Mishra Pankaj and Kumar Dhirendra (2021): Magnetic field and rotation effect on thermal instability in an anisotropic couple-stress fluid saturated porous layer under presence of cross diffusion.– Journal of Physics, Conf. Ser., vol.1849, Article ID.012009, p.13.
13.
Rosenweigh R.E. (1985): Ferrohydrodyanamics.– Cambridge University Press, Cambridge J.
14.
Finlayson B.A. (1970): Convective instability of ferromagnetic fluids.– J. Fluid Mech.,vol.40, pp.753-767.
15.
Siddheswar P.G. (1993): Rayleigh Benard convection in a ferromagnetic fluids with Second Sound.– Japan Soc. Mag. Fluids, vol.32, pp.32-36.
16.
Siddheswar P.G. (1995): Convective Instability of ferromagnetic fluids bounded by fluid permeable magnetic boundaries.– J. Magnetism and Magnetic Material, vol.49, pp.148-150.
17.
Venkatasubramaniam S. and Kaloni P. N. (1994): Effect of rotation on the thermo convective instability of a horizontal layer of ferrofluids.– Int. J. Engg. Sci., vol.32, No.2, pp.237-256.
18.
Stiles P.J. and Kagan M. (1990): Thermo convective Instability of a horizontal layer of ferrofluid in a strong vertical magnetic field.– JMMM, vol.85, No.1-3, pp.196-198.
19.
Pant S., Bhagat N. and Kharayat H. (2016): The Effect of suspended particles and magnetic field on thermal in ferromagnetic fluid with varying gravitational field in porous medium.– IJAR, vol.4, pp.939-946.
20.
Bhagat N. and Pant S. (2016): The effect of rotation and magnetic field on the onset of thermal convection in dusty ferromagnetic fluid with varying gravitational field in porous medium.– Acta Ciencia Indica, vol.XLII No.M, pp.239-249.
21.
Nandian P.K., Pundir Rimple and Pundir S.K. (2020): Effect of dust particles on a rotating couple-stress ferromagnetic fluid heated from below.– IJSEAS, vol.6, No.4, pp.39-56.
22.
Nandian P.K., Pundir Rimple and Pundir S.K. (2020): Effect of dust particles on a rotating couple-stress ferromagnetic fluid heated from below in the presence of rotation and horizontal magnetic field saturating in a porous medium.– Compliance Engineering Journal, vol.11, No.10, pp.1-14.
23.
Rahul and Sharma Naveen (2021): Effect of rotation on thermal instability of couple-stress Rivlin Ericksen ferromagnetic fluid in presence of variable gravity field through porous medium.– Compliance Engineering Journal, vol.12, No.6, pp.65-85.
24.
Rahul and Sharma Naveen (2021): Effect of magnetic field on thermal instability of couple stress Rivlin-Ericksen ferromagnetic fluid with variable gravity field through porous medium.– Turkish Online Journal Of Qualitative Inquiry, vol.12, No.9, pp.3018-3035.
25.
Sharma Naveen and Rahul (2021): Effect of magnetic field on thermal instability of rotated couple stress Rivlin-Ericksen ferromagnetic fluid in the presence of variable gravity field through porous medium.– International Journal of Statistics and Reliability Engineering vol.8, No.2, pp.309-320.
26.
Rahul, Sharma Naveen and Sharma M.K. (2021): On a couple-stress Rivlin-Ericksen ferromagnetic fluid heating from below with varying gravity and suspended particles through a porous medium.– Journal of International Academy of Physical Sciences, vol.25, No.2, pp.279-295.
27.
Rahul and Sharma Naveen (2021): On a couple-stress Rivlin-Ericksen ferromagnetic fluid heating from below with varying gravity, rotation and suspended particles through a porous medium.– International Journal of Recent Scientific Research, vol.12, No.11C, pp.43639-43651.