The present paper deals with a weak nonlinear theory of double-diffusive magnetoconvection in an electrically conducting Newtonian liquid, confined between two horizontal surfaces, under a constant vertical magnetic field, and subjected to imposed time-periodic thermal boundaries. The temperature of both walls is varied time periodic in this case. The 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. Effect of various parameters on the heat and mass transport is discussed extensively. It is found that the effect of magnetic field is to stabilize the system. Further, it is also notified that the heat and mass transport can be controlled by suitably adjusting the external parameters of the system. 1. Introduction Double-diffusive convection is an important fluid dynamics phenomenon that involves motions driven by two different density gradients diffusing at different rates. In double-diffusive convection, the buoyancy force is affected not only by the difference of temperatures but also by the difference of concentration of the fluid. An example of double-diffusive 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, fluid flows around shrouded heat-dissipation fins, migration of moisture through air contained in fibrous insulations, grain storage system, the dispersion of contaminants through water saturated soil, crystal P growth, solidification of binary mixtures, and the underground disposal of nuclear wastes. Therefore, much work has also been done on double-diffusive convection in an electrically conducted fluid 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 field. The study of double-diffusive magnetoconvection has recently drawn the attention of astrophysicists, geophysicists, oceanographers, engineers, and a host of others [4, 5]. The study of magnetoconvection in an electrically conducting horizontal fluid layer was motivated by astrophysical and geophysical applications; relate in some or the other way to the problems concerning the external constraints like
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