Upper Limits to the Linear Growth Rate in Triply Diffusive Convection

In the present paper it is mathematically established that the linear growth rate of an arbitrary neutral or unstable oscillatory perturbation of growing amplitude in a triply diffusive fluid layer (with one of the component as heat with diffusivity κ) must lie inside a semicircle in the right half of the (P_r, P_i􀀅) - plane whose centre is at the origin and radius equals 􀀇√(|R􀀉| + R₁􀀋)􀀌 where R and R1 are the thermal Rayleigh number and concentration Rayleigh number with diffusivities κ and κ_1. Further, it is proved that this result is uniformly valid for quite general nature of the bounding surfaces.