Nonlinear double-diffusive convection with local heat and solute sources

Effects of local heat and solute sources on nonlinear double diffusive convection has been investigated. These sources introduce three new parameters. Dependence of the horizontal cells' size, critical solute Rayleigh number, and heat and solute fluxes on these new parameters is determined. In particular, it is found that local sources can significantly reduce the horizontal cells' size. For the case where the strength of the local solute source is insignificant, the preferred horizontal flow cross-section pattern is found to be squares. On the other hand, if the strength of the local solute source is significant, then hexagons become the preferred pattern when flow amplitude epsilon exceeds a critical value. However, both squares and hexagons can be stable for an even higher value of epsilon. The convective motion is upward at the center of the hexagonal cells if a solute sink acts on the flow. When a solute source acts on the flow, downward motion at the cells' center will occur. Furthermore, the local solute source is also found to be able to provide finite amplitude instability.