Topographically Controlled Marangoni-Rayleigh-Bénard Convection in Liquid Metals

Marcello Lappa,Wasim Waris,Aydin Sayar

doi:10.3390/fluids6120447

Abstract

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.

Highlights

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The ability of the algorithm to reproduce the critical value of the Marangoni number needed for the onset of classical MB convection has been verified through correlation with available data obtained using the LSA approach
Some additional insights into the considered problem are sought through comparison with ‘companion problems’, not necessary linked to thermal convection driven by buoyancy of Marangoni effects

Summary

Introduction

Many materials pass through a liquid state and the properties that they display in the final solid state often depend on the convective phenomena that are established in their liquid state This concept applies to a variety of manufacturing and materials science applications. Whilst there are a plethora of materials that are of industrial relevance and importance due to the related technological applications and impact on world’s societies, silicon and other semiconductor materials have attracted a significant increasing interest especially during the late 20th and early 21st century. This interest partly stems from the abundance of these materials (especially silicon) on the surface of our planet

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Results

Conclusion