Rayleigh and Marangoni convection and rheology are linked in the thermal convection of viscoelastic fluids to some recent technological applications. Such technology developments as the ones presented here undoubtedly shall be based on interdisciplinary projects involving not only rheology or fluid mechanics but several other disciplines. Three practical applications which use Rayleigh or Marangoni convection in their working principle are presented along with some technical details. This contribution focus mainly on the physical mechanism and the involved hydrodynamics of some lab and industrial applications. Finally, a short discussion on the role play by the convective mechanisms is given in order to provide integration of the exposed ideas.

The thermal boundary conditions have important effects on the hydrodynamics of a thermo-convective fluid layer. These effects are introduced through the Biot number under the Robin type boundary conditions. The thermal conductivity and thicknesses of the walls are key properties to bridge two known ideal situations widely studied: the fluid layer bounded by two insulating walls and the fluid layer bounded by two perfect thermal conducting walls. This chapter is devoted to the physical mechanisms involved in the thermal boundary conditions, its influence on the linear stability of the fluid layer and its implications with the pattern formation. A review of very important investigations on the subject is also given. The role of the thermal conductivities and thicknesses of the walls is explained with help of curves of criticality for the thermoconvection in a horizontal Newtonian fluid layer.