Topographically Controlled Marangoni-Rayleigh-Bénard Convection in Liquid Metals

Convection induced in a layer of liquid with a top free surface by a distribution of heating elements at the bottom can be seen as a variant of standard Marangoni–Rayleigh–Bénard Convection where in place of a flat boundary at constant temperature delimiting the system from below, the underlying thermal inhomogeneity reflects the existence of a topography. In the present work, this problem is investigated numerically through solution of the governing equations for mass, momentum and energy in their complete, three-dimensional time-dependent and non-linear form. Emphasis is given to a class of liquids for which thermal diffusion is expected to dominate over viscous effects (liquid metals). Fixing the Rayleigh and Marangoni number to 104 and 5 × 103, respectively, the sensitivity of the problem to the geometrical, kinematic and thermal boundary conditions is investigated parametrically by changing: the number and spacing of heating elements, their vertical extension, the nature of the lateral boundary (solid walls or periodic boundary) and the thermal behavior of the portions of bottom wall between adjoining elements (assumed to be either adiabatic or at the same temperature of the hot blocks). It is shown that, like the parent phenomena, this type of thermal flow is extremely sensitive to the specific conditions considered. The topography can be used to exert a control on the emerging flow in terms of temporal response and patterning behavior.