Analysis of the effect of variable gravity on stationary convection in Rayleigh-Bénard convection for free-free, rigid-rigid and rigid-free boundary conditions

Abstract

In this research article Rayleigh-Bénard convection has been studied considering variable gravity. We analysed gravitational field variation for six different cases, namely, (i)f(z)=z^2-2z, (ii) f(z)=-z^2, (iii) f(z)=-z, (iv) f(z)=z, (v) f(z)=e^z and (vi) f(z)=log⁡(1+z). Galerkin type weighted residual method (GWRM) is used to derive mathematical expression for Rayleigh number (Stationary Convection), for all cases of gravitational field variation, considering free-free, rigid-rigid and rigid-free boundary conditions. It is observed that the system’s stability is influenced by both the gravitational field variation and the type of boundary conditions. Decreasing gravity tends to stabilize the system, while increasing gravity tends to destabilize it. Additionally, rigid boundaries help stabilize the convection process, while free boundaries make the system more prone to instability.