Feedback Control of Rayleigh Convection in Viscoelastic Maxwell Fluids

Control of Rayleigh convection in a viscoelastic Maxwell fluid is addressed here by considering a feedback from shadowgraphic visualizations. Here, a theoretical approach is made to the problem of the onset of convective motion through a source term in the lower thermal boundary condition. A numerical Galerkin technique is then used to study the linear hydrodynamic stability. Small relaxation times are considered for Prandtl numbers 1 and 10. Interesting results for the Rayleigh, the wavenumber, and the frequency of oscillations are presented along with discussion on the physical mechanism. In short, the linear hydrodynamic stability analysis states that suppression of convection may be favored.