Heat and Mass Transfer of Triple Diffusive Convection in a Rotating Couple Stress Liquid Using Ginzburg-Landau Model
A nonlinear study of triple diffusive convection in a rotating couple stress liquid has been analysed. It is performed to study the effect of heat and mass transfer by deriving Ginzburg-Landau equation. Heat and mass transfer are quantified in terms of Nusselt number and Sherwood numbers, which are obtained as a function of thermal and solute Rayleigh numbers. The obtained Ginzburg-Landau equation is Bernoulli equation, and it has been elucidated numerically by using Mathematica. The effects of couple stress parameter, solute Rayleigh numbers, and Taylor number on the onset of convection and heat and mass transfer have been examined. It is found that the effects of couple stress parameter and Taylor number are to stabilize the system and to increase the heat and mass transfer.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1340112Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 775
 A. J. Pearlstein, R. D. Harris and G. Terrones, “The onset of convective instability in a triply diffusive fluid layer,” J. Fluid Mech., vol. 202, pp. 443-465, 1989.
 R. A. Lopez, L. A. Romero and A. J. Pearlstein, “Effect of rigid boundaries on the onset of convective instability in a triply diffusive fluid layer,” Phys. Fluids A, vol. 2, pp. 897, 1990.
 R. Sumithra, “Exact solution of triple diffusive Marangoni-convection in a composite layer,” Int. J. Engg. Research and Tech., vol. 1, no. 5, pp. 1-13, 2012.
 S. Rionero, “Triple diffusive convection in porous media,” Acta Mech., vol. 224, pp. 447–458, 2013.
 Sameena Tarannum and S. Pranesh, “Triple diffusive convection in Oldroyd-B liquid,” IOSR J. Math., vol. 12, no. 4, pp. 7-13, 2016.
 S. Chandrasekhar, “Hydrodynamic and hydromagnetic stability,” Oxford: Clarendon Press, 1961.
 V. K. Stokes, “Couple stress in fluids,” Phys. Fluids, pp. 1079-1715, 1966.
 P. G. Siddheshwar and S. Pranesh, “An analytical study of linear and non-linear convection in Boussinesq-Stokes suspensions,” Int. J. Non-Linear Mech., pp. 165-172, 2004.
 I. S. Shivakumara, S. Sureshkumar and N. Devaraju, “Effect of Non-Uniform Temperature Gradients on the Onset of Convection in a Couple-Stress Fluid-Saturated Porous Media,” J. Applied Fluid Mech., vol. 5, pp. 49-55, 2012.
 S. Pranesh and Sameena Tarannum, “Linear and weakly non-linear stability analyses of double-diffusive electro-convection in a micropolar fluid,” IOSR J. Math., vol. 11, no. 6(1), pp. 44-70, 2015.
 P. G. Siddheshwar, “A series solution for the Ginzburg-Landau Equation with a time-periodic coefficient,” Appl. Math. vol. 3, pp. 542-554, 2010.