Travelling-wave similarity solutions for an unsteady shear-stress-driven dry patch in a flowing film

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Abstract

We investigate unsteady flow of a thin film of Newtonian fluid around a symmetric slender dry patch moving with constant velocity on an inclined planar substrate, the flow being driven by a prescribed constant shear stress at the free surface of the film (which would be of uniform thickness in the absence of the dry patch). We obtain a novel unsteady travelling-wave similarity solution which predicts that the dry patch has a parabolic shape and that the film thickness increases monotonically away from the dry patch.
Original languageEnglish
Pages (from-to)975-980
Number of pages6
JournalSains Malaysina
Volume42
Issue number7
Publication statusPublished - 2013
EventProceedings of the 19th National Symposium on Science and Mathematics (Prosiding Simposium Kebangsaan Sains Matematik Ke 19, SKSM 19), 9th--11th November 2011, Universiti Teknologi Mara Pulau Pinang, Malaysia. - , Malaysia
Duration: 9 Nov 201111 Nov 2011

Keywords

  • thin-film flow
  • travelling-wave
  • similarity solutions
  • dry patch

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