Research Article Weak Nonlinear Double-Diffusive Magnetoconvection in a Newtonian Liquid under Temperature Modulation B. S. Bhadauria and Palle Kiran Department of Applied Mathematics, School for Physical Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow 226 025, India Correspondence should be addressed to B. S. Bhadauria; mathsbsb@yahoo.com Received 22 February 2014; Accepted 15 June 2014; Published 6 July 2014 Academic Editor: Yurong Liu Copyright © 2014 B. S. Bhadauria and P. Kiran. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Te present paper deals with a weak nonlinear theory of double-difusive magnetoconvection in an electrically conducting Newtonian liquid, confned between two horizontal surfaces, under a constant vertical magnetic feld, and subjected to imposed time-periodic thermal boundaries. Te temperature of both walls is varied time periodic in this case. Te disturbances are expanded in terms of power series of amplitude of convection, which is assumed to be small. Using nonautonomous Ginzburg-Landau equation, the Nusselt and Sherwood numbers obtained analytically and studied heat and mass transport in the system. Efect of various parameters on the heat and mass transport is discussed extensively. It is found that the efect of magnetic feld is to stabilize the system. Further, it is also notifed that the heat and mass transport can be controlled by suitably adjusting the external parameters of the system. 1. Introduction Double-difusive convection is an important fuid dynamics phenomenon that involves motions driven by two diferent density gradients difusing at diferent rates. In double- difusive convection, the buoyancy force is afected not only by the diference of temperatures but also by the diference of concentration of the fuid. An example of double-difusive convection is seen in oceanography, lakes, underground water, atmospheric pollution, chemical processes, laboratory experiments, modeling of solar ponds [1], electrochemistry, magma chambers and sparks [2], Fernando and Brandt[3], formation of microstructure during the cooling of molten metals, fuid fows around shrouded heat-dissipation fns, migration of moisture through air contained in fbrous insu- lations, grain storage system, the dispersion of contaminants through water saturated soil, crystal P growth, solidifca- tion of binary mixtures, and the underground disposal of nuclear wastes. Terefore, much work has also been done on double-difusive convection in an electrically conducted fuid layer because of its natural occurrence as mentioned above applications. Convection in planetary cores, stellar interiors, and Earth’s metallic core occurs in the presence of strong magnetic feld. Te study of double-difusive magnetocon- vection has recently drawn the attention of astrophysicists, geophysicists, oceanographers, engineers, and a host of others [4, 5]. Te study of magnetoconvection in an electrically con- ducting horizontal fuid layer was motivated by astrophysical and geophysical applications; relate in some or the other way to the problems concerning the external constraints like rotation or magnetic feld operative on double-difusive systems, in particular by observation of sunspots [6]. Tompson [7] and Chandrasekhar [8] were the frst to study the magnetoconvection in horizontal fuid layer. Lortz [9] was the frst to study the efect of magnetic feld on double- difusive convection. His object was to clarify some of the mathematical aspects of stability criterion [10] but his analysis is silent about the detailed study of stability analysis. Stommel et al. [11] explained that the difusion is generally a stabilizing factor in a single-component fuid. But in the case of two- component system it can act to release the potential energy in the component that is the heaviest at the top and make the system unstable. Gotoh and Yamada [12] studied the problem of magnetoconvection in a horizontal layer of magnetic fuid Hindawi Publishing Corporation International Journal of Engineering Mathematics Volume 2014, Article ID 296216, 14 pages http://dx.doi.org/10.1155/2014/296216