International Journal of Mathematics and Computational Science
Articles Information
International Journal of Mathematics and Computational Science, Vol.1, No.5, Oct. 2015, Pub. Date: Jun. 17, 2015
A Mathematical Theorem in Triply-Diffusive Convection
Pages: 227-233 Views: 1248 Downloads: 696
Authors
[01] Hari Mohan, Department of Mathematics, ICDEOL, Himachal Pradesh University, Summer Hill Shimla-5, India.
[02] Pardeep Kumar, Department of Mathematics, ICDEOL, Himachal Pradesh University, Summer Hill Shimla-5, India.
Abstract
A mathematical analysis of the governing equations of triply diffusive fluid layer with one of the components as heat with diffusivity κ, prescribes upper limit for the complex growth rate of oscillatory motions of neutral or growing amplitude in such a manner that it naturally culminates in sufficient conditions precluding the non- existence of such motions. Further, the results derived herein are uniformly valid for quite general nature of bounding surfaces.
Keywords
Triply Diffusive Convection, Rayleigh Numbers, Lewis Number, Prandtl Number
References
[01] Brandt, A., Fernando H.J.S. (1996). Double Diffusive Convection .American Geophysical Union Washington, DC.
[02] Stern, M .E. (1960). The Salt Fountain and Thermohaline Convection. Tellus. vol 12, 172.
[03] Veronis, G. (1965) On Finite Amplitude Instability in Thermohaline Convection, J. Mar. Res. vol. 23, 1.
[04] Banerjee, M. B.,Katoch D.C.,Dube G.S., Banerjee K. (1981) Bound for linear growth rate of a perturbation in Thermohaline Convection. Proc. Roy. Soc. London, Ser. AVol.378,301.
[05] Gupta, J.R. Sood, S.K., Bhardwaj, U.D. (1986).On the characterization of nonoscillatory motions in rotatory hydromagnetic thermohaline convection. Indian J. Pure and Appl. Math. vol 17,100.
[06] Mohan, H., Anjula. (2001). On the limitations of the linear growth rate in Veronis and Stern’s Thermohaline Convections. Indian J. Pure and Appl. Math. vol.32 (11), 1659- 1666.
[07] Mohan, H. (2010). Bound for the Complex Growth Rate in Thermosolutal Convection Coupled with Cross-diffusion. Application and Applied Mathematics-An International Journal (AAM).vol. 5(10), 1428.
[08] Griffiths, R.W. (1979).The Influence of a third Diffusing Component upon the onset of Convection. J. Fluid Mech. vol. 92,659.
[09] Turner, J.S., Multicomponent Convection, Ann. Rev. Fluid Mech. 1985; 17:11-44p.
[10] Pearlstein, A.J., Harris, R.M., Terrones (1989).The onset of Convective Instability in a Triply Diffusive Fluid Layer .J. Fluid Mech. vol .202, 443.
[11] Lopez, A.R., Romero, L.A., Pearlstein, A.J. (1990).Effect of rigid boundaries on the onset of Convective Instability in a Triply Diffusive Fluid Layer. Physics of Fluids.vol.2 (6), 897.
[12] Terrones, G. (1993). Cross-diffusion Effects on the Stability Criteria in a Triply- diffusive System. Phys. Fluids. vol. A5. 2172.
[13] Ryzhkov, I., I., Shevtsova, V.M. (2007). On Thermal Diffusion and Convection in Multicomonent Mixtures with Application to the Thermo gravitational Column. Phys. Fluids. vol. 19, 1.
[14] Ryzhkov, I., I., Shevtsova, V.M. (2009). Long Wave Instability of a Multicomponent Fluid Layer with the Soret Effect. Phys. Fluids. vol. 21. 1.
[15] Rionero, S. (2013a).Triple Diffusive Convection in Porous Media.Act Mech.vol.224, 447.
[16] Rionero, S. (2013b). Multicomponent Diffusive –Convective Fluid motions in Porous Layers ultimately boundedness, absence of subcritical Instability, and global nonlinear stability for any number of salts. Phys Fluids. vol. 25, 1.
[17] Zhao, M., Wang, S., Zhang, Q. (2013). Onset of Triply Diffusive Convection in a Maxwell Fluid Saturated Porous Layer. Applied Mathematical Modelling. vol. 38, 2352.
[18] Shivkumara, I.S., Kumar, S.B.N. (2013) Bifurcation in Triply Diffusive Couple Stress Fluid Systems. International Journal of Engineering Research and Applications. vol. 3 (6), 372.
[19] Shivkumara, I.S., Kumar, S.B.N. (2014). Linear and Weakly Nonlinear Triple Diffusive Convection in a Couple Stress Fluid Layer. International Journal of Heat and Mass Transfer.vol.68, 542.
[20] Schultz, M.H. (1973) Spline Analysis, Prentice-Hall, Englewood Cliffs, N.J.
600 ATLANTIC AVE, BOSTON,
MA 02210, USA
+001-6179630233
AIS is an academia-oriented and non-commercial institute aiming at providing users with a way to quickly and easily get the academic and scientific information.
Copyright © 2014 - 2017 American Institute of Science except certain content provided by third parties.