### A semi-circle theorem in couple-stress fluid in the presence of rotation

#### Abstract

*T*is the Taylor number and

_{A}*F*is the couple-stress parameter, which prescribes the upper limits to the complex growth rate of arbitrary oscillatory motions of growing amplitude in a rotatory couple-stress fluid heated from below. Further, It is established that the existence of oscillatory motions of growing amplitude in the present configuration, depends crucially upon the magnitude of the non-dimensional number , in the sense so long as , no such motions are possible, and in particular PES is valid.

#### Full Text:

PDF#### References

Banyal, A. S. and Khanna, M., (2012), Bounds for Growth Rate of Perturbations in Couple-Stress Fluid in the Presence of Rotation, Global J. of Pure and Appld. Scis. & Tech., Vol. 2, Issue 2, pp. 24-31.

Chandrasekhar, S. (1981). Hydrodynamic and Hydromagnetic Stability, Dover Publication

Sharma, R. C., Prakash, K. and Dube, S. N. (1976). Effect of suspended particles on the onset of Bénard convection in hydromagnetics, J. Math. Anal. Appl., USA, Vol. 60 pp. 227-35.

Scanlon, J. W. and Segel, L. A. (1973). Some effects of suspended particles on the onset of Bénard convection, Phys. Fluids. Vol. 16, pp. 1573-78. CrossRef

Stokes, V. K. (1966). Couple-stress in fluids, Phys. Fluids, Vol. 9, pp. 1709-15. CrossRef

Walicki, E. and Walicka, A. (1999). Inertial effect in the squeeze film of couple-stress fluids in biological bearings, Int. J. Appl. Mech. Engg., Vol. 4, pp. 363-73.

Sharma, R. C. and Thakur, K. D. (2000). Couple stress-fluids heated from below in hydromagnetics, Czech. J. Phys., Vol. 50, pp. 753-58. CrossRef

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.

Sharma, R. C., Sunil, Sharma, Y. D. and Chandel, R. S. (2002). On couple-stress fluid permeated with suspended particles heated from below, Archives of Mechanics, 54(4) pp. 287-298.

Sharma, R. C. and Sharma, M. (2004). Effect of suspended particles on couple-stress fluid heated from below in the presence of rotation and magnetic field, Indian J. pure. Appl. Math., Vol. 35(8), pp. 973-989.

Sunil, Sharma, R. C. and Chandel, R. S. (2004). Effect of suspended particles on couple-stress fluid heated and soluted from below in porous medium, J. of Porous Media, Vol. 7, No. 1 pp. 9-18. CrossRef

Kumar, P. and Singh, M. (2008), Magneto thermosolutal convection in a couple-stress fluid, Ganita Sandesh (india), Vol. 21(2).

Singh, M. and. Kumar, P. (2009), Rotatory thermosolutal convection in a couple-stress fluid, Z. Naturforsch, 64a, 7(2009).

Kumar, V. and Kumar, S. (2011). On a couple-stress fluid heated from below in hydromagnetics, Appl. Appl. Math., Vol. 05(10), pp. 1529-1542.

Sunil, Devi, R. and Mahajan, A. (2011), Global stability for thermal convection in a couple stress-fluid, Int. comm. Heat and Mass Transfer, 38, pp. 938-942. CrossRef

Pellow, A., and Southwell, R. V. (1940). On the maintained convective motion in a fluid from below. Proc. Roy. Soc. London A 176, 312-43. CrossRef

Banerjee, M. B., Katoch, D. C., Dube, G. S. and Banerjee, K. (1981). Bounds for growth rate of perturbation in thermohaline convection. Proc. R. Soc. A378, 301-04.

Banerjee, M. B., and Banerjee, B. (1984). A characterization of nonoscillatory motions in magnetohydronamics. Ind. J. Pure & Appl Maths., 15(4), 377-382.

Gupta, J. R., Sood, S. K., and Bhardwaj, U. D. (1986). On the characterization of nonoscillatory motions in rotatory hydromagnetic thermohaline convection, Indian J. pure appl. Math., 17(1) pp. 100-107.

Banyal, A. S., (2011) A characterization of non-oscillatory motions in couple-stress fluid in the presence of suspended particles (2011), J. Comp. and Math. Scis. (JCMS), Vol. 2 (3), pp. 537-545.

Schultz, M. H. (1973). Spline Analysis, Prentice Hall, Englewood Cliffs, New Jersy.

Banerjee, M. B., Gupta, J. R. and Prakash, J. (1992). On thermohaline convection of Veronis type, J. Math. Anal. Appl., Vol. 179, No. 2 pp. 327-334. CrossRef

DOI: http://dx.doi.org/10.1260/1750-9548.6.4.403

Copyright (c) 2016 The International Journal of Multiphysics