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Thermocapillary convection due to imposed interfacial heating in the presence of magnetic field

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Abstract

Marangoni convection arises when the surface tension of the fluid varies spatially due to accompanying temperature gradients along the interface, which can occur in various ways. In the case of nonuniform surface heat fluxes imposed due to incident beams from power sources, Marangoni convection can be induced within heated liquid pools formed during melting in a number of material-processing applications. In this work, we develop a physical model and study the thermocapillary flow generated due to an imposed surface heat flux with a specified spatial variation. Furthermore, we incorporate the effect of applying a magnetic field to investigate its influence on the structure of such unique class of surface tension-driven flows. New similarity solutions are developed for the thermocapillary convection due to an imposed interfacial heat flux variation specified as \(\mathop q\nolimits _0 \mathop x\nolimits ^{n + 1} \), where x is the surface coordinate and \( \mathop q\nolimits _0 \) is a parameter representing the magnitude of the incident power. Numerical results are obtained and the structure of the Marangoni convection for various sets of the characteristic parameters, such as the power-law exponent n, Prandtl number Pr and a magnetic interaction parameter M, are studied. In particular, it is found that with the increasing n, i.e., considering sharper variations in the surface heat flux profiles, the Marangoni convection is promoted. Conversely, with the increasing M, the magnitudes of the thermocapillary convection velocity are decreased, thereby demonstrating the damping effect of the magnetic field.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Colorado Denver, 1200 Larimer street, Denver, Colorado, 80217, USA

    Farzaneh Hajabdollahi & Kannan N. Premnath

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  1. Farzaneh Hajabdollahi
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  2. Kannan N. Premnath
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Correspondence to Farzaneh Hajabdollahi.

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Hajabdollahi, F., Premnath, K.N. Thermocapillary convection due to imposed interfacial heating in the presence of magnetic field. J Eng Math 108, 37–52 (2018). https://doi.org/10.1007/s10665-017-9903-0

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  • DOI: https://doi.org/10.1007/s10665-017-9903-0

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