Competition between stationary and oscillatory viscoelastic thermocapillary convection of a film coating a thick wall

Abstract

In this paper new results on linear viscoelastic thermal Marangoni convection are presented. The constitutive equation assumed is that of the Maxwell viscoelastic fluid. The competition between stationary and oscillatory convection is shown by means of plots of codimension-two points where the corresponding critical Marangoni numbers are the same. The variation of these points is investigated in a wide range of magnitudes of the thickness and thermal conductivity of the wall. Also, a discussion is given about the dependence they have on the Biot number of the fluid-atmosphere interface. Besides, it is shown how the range of the viscoelastic relaxation time corresponding to this points is modified by the Prandtl number.