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Developing mathematical theories of the physical world: Open Access research on fluid dynamics from Strathclyde

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Non-isothermal thin-film flow on a stationary or rotating cylinder

Duffy, B.R. and Wilson, S.K. (2007) Non-isothermal thin-film flow on a stationary or rotating cylinder. In: Proceedings of the 10th UK national conference on heat transfer. International Society of Coating Science and Technology, Corning.

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Abstract

We investigate steady two-dimensional °ow of a thin ¯lm of °uid with temperature-dependent vis-cosity on a uniformly heated or cooled horizontal cylinder, which may be stationary or rotating about its axis. We show that increasing (decreasing) the ambient temperature has the e®ect of making the ¯lm thinner (thicker). For °ow on a rotating cylinder we determine the critical mass Mc beyond which a continuous solution is not possible. Also we show that at large Biot number the ¯lm thickness (but not the °uid velocity) can be obtained from that in the isothermal case by a simple re-scaling