COUPLED BUOYANCY AND THERMOCAPILLARY CONVECTION IN A VISCOELASTIC MAXWELL FLUID

Linear coupled buoyancy and thermocapillary instabilities (the Benard-Marangoni problem) in a Maxwell viscoelastic fluid layer heated from below are studied. As the principle of exchange of stability is no longer valid, both stationary and oscillatory solutions are considered. It is shown that beyond a critical value of the relaxation time, the instability appearing in a fluid layer with a free upper surface subject to a temperature-dependent surface tension takes the form of oscillations. The critical temperature difference between the lower and upper surfaces is determined as a function of the Prandtl number and the relaxation time. The instability thresholds are graphically represented on 'Nield's diagrams' where the critical Marangoni number is given versus the Rayleigh number. At high Prandt] numbers discontinuities in the solutions are displayed for some specific values of the fluid layer thickness. It is also observed that for some range of variation of the parameters, thermocapillarity has an unusual stabilizing effect.