On rotatory hydro magnetic multicomponent convection

The present paper mathematically establishes that the ‘principle of the exchange of stabilities’ for Rotatoryhydromagnetic multicomponent convection is valid in the regime (R_1 σ)/(2τ_1^2 π^4)+(R_2 σ)/(2τ_2^2 π^4)+⋯+(R_(n-1) σ)/(2τ_(n-1)^2 π^4)+T_a/π^4 +(Qσ_1)/π^2 ≤1, where R_1, R_2,…, R_(n-1) are the Rayleigh numbers for the n-1 concentration components, τ_1, τ_2…, τ_(n-1) are the Lewis numbers for the n-1 concentration components, Q is the Chandrasekhar number, T_a is the Taylor number, σ is the thermal Prandtl number and σ_1 is the magnetic Prandtl number. When the complement of this sufficient condition holds good, oscillatory motions of neutral or growing amplitude can exist, and thus it is important to derive upper bounds for the complex growth rate of such motions when atleast one of the boundaries is rigid so that exact solutions of the problem in closed form are not obtainable. Thus as a second problem bounds for the complex growth rate are also obtained. It is further proved that the results obtained herein are uniformly applicable for rigid surfaces which may be insulating or perfectly conducting.