Weakly nonlinear instability analysis of triple diffusive convection under internal heat generator and modulated boundaries

Abstract

A nonlinear instability analysis of triple diffusive convection under the time-dependent heat and mass transfer boundary conditions in the presence of internal heat source is evaluated in this study. On various physical parameters, the momentary behavior of both Sherwood and Nusselt number profiles is examined. In the geometry, we have considered two parallel infinite horizontal plates acting gravity vertically downward z-direction. By using the weakly nonlinear analysis, the Ginzburg–Landau equation is generated for the rate of heat and mass transport. Here, we have considered the temperature and concentration of two solutes. The temperature and first concentration of the solute at the lower plate are higher than the upper plate, while the second concentration of the solute at the upper plate is higher compared to that of the lower plate. According to the different modulation, we have considered four cases based on the phase angle of the modulations. The convective heat and mass transports are measured as a function of the Nusselt number (Nu) and Sherwood number (Sh1 and Sh2) for both the concentration. From the results, it is found that the first Lewis number increases all the considered profiles, while Ri increases the Nusselt number profile only. The principal discovery elucidated by this article resides in the observation that the internal heat source, subject to modulated boundaries, maintains the convective instability if different solutes are used from both ends.