Upper Limits to the Complex Growth Rates in Triply Diffusive Convection in Porous Medium

The paper mathematically establishes that the complex growth rate (p_r,p_i ) of an arbitrary neutral or unstable oscillatory perturbation of growing amplitude, in a triply diffusive fluid layer in porous medium (Darcy Model) with one of the components as heat with diffusivity , must lie inside a semicircle in the right- half of the (p_r,p_i)-plane whose centre is origin and radius equals √(R₁+<R₂)σ where R₁ and R₂ are the Raleigh numbers for the two concentration components with diffusivities k₁ and k₂ (with no loss of generality, k > k₁> k₂ ) and is the Prandtl number. Further, it is proved that above result is uniformly valid for quite general nature of the bounding surfaces.