Study of weakly nonlinear double‐diffusive magnetoconvection under concentration modulation

Abstract

This article explains the heat and mass transfer of electrically conducting Newtonian fluid in double‐diffusive magnetoconvective flow. We have considered two infinite horizontal plates at a constant distance apart under the concentration‐modulated boundary condition. A constant magnetic field is considered in vertically upward directions, which generates an induced magnetic field. We have used the weakly nonlinear analysis to obtain the heat and mass transfer rate using the Ginzburg–Landau equation. The software MATHEMATICA is used to determine the solution of the Ginzburg–Landau equation by inbuilt function. The effects of physical parameters that occurred in the study on the Nusselt number and Sherwood number have been examined graphically. Modulation has a negligible effect on the threshold value of the thermal Rayleigh number, that is, on stationary convection. Moreover, it was found that the Chandrasekhar number, magnetic‐Prandtl number, amplitude of modulation, and frequency of modulation are proportional to the heat and mass transports.