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Numerical Modeling of an inclined thin Liquid Layer Flow Based on Generalized Boundary Conditions

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We study a one-sided mathematical model of flows of thin liquid layers with evaporation taken into account. The model is described by the Navier–Stokes and heat transfer equations with refined conditions at the interface. We obtain the evolution equation defining the position of the thermocapillary boundary and construct an algorithm for its numerical solution. We study the flow of a liquid layer over an inclined heated substrate at moderate Reynolds numbers. We show the effect of heating the substrate and the influence of an additional term on the flow pattern in comparison with the classical condition at the interface.

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Authors and Affiliations

  1. Altai State University, 61, Lenina Pr., Barnaul, 656049, Russia

    E. V. Laskovets

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  1. E. V. Laskovets
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Correspondence to E. V. Laskovets.

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JMS Source Journal International Mathematical Schools. Vol. 1. Advances in Pure and Applied Mathematics

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Laskovets, E.V. Numerical Modeling of an inclined thin Liquid Layer Flow Based on Generalized Boundary Conditions. J Math Sci 267, 501–510 (2022). https://doi.org/10.1007/s10958-022-06155-6

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  • DOI: https://doi.org/10.1007/s10958-022-06155-6

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