Thin-film Flows on Cylinders
Thin-film Flows on Cylinders

Author: George Adam Leslie

Publisher:

Published: 2012

Total Pages: 0

ISBN-13:

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Three different problems concerning thin- film flows on horizontal cylinders are studied. Firstly, steady two-dimensional gravity-driven flow with prescribed volume flux of a thin lm of Newtonian fluid with temperature-dependent viscosity (i.e. thermoviscous flow) over a uniformly heated or cooled stationary horizontal cylinder is studied. Numerical results along with asymptotic solutions in appropriate limits are presented giving an insight into the effects of thermoviscosity and heat transfer at the free surface. Next, we consider steady two-dimensional flow of a prescribed load (mass) of Newtonian uid with temperature-dependent viscosity on a uniformly heated or cooled rotating horizontal cylinder. The existence of a critical solution with a critical load above which no solutions exist is found, and both this critical solution and the case of prescribed subcritical load are studied in detail, with both numerical and asymptotic solutions presented. In particular, it is found that back ow (i.e. flow counter to the direction of rotation) occurs within a certain region of parameter space (back ow never occurs in the corresponding isothermal problem). Finally, the steady isothermal ow of a symmetric thin slowly-varying rivulet of a non-perfectly wetting Newtonian fluid on either the outside or the inside of a uniformly rotating horizontal cylinder is considered. Numerical and asymptotic solutions in appropriate limits are presented and it is found that rivulet flow on a rotating cylinder gives rise to a critical solution similar in nature to the critical solution found for the classical two-dimensional problem. We also show that back flow occurs within a particular region of parameter space.

Computational Analysis of Polymer Processing
Computational Analysis of Polymer Processing

Author: J.R.A. Pearson

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 351

ISBN-13: 9400966342

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Large, fast, digital computers have been widely used in engineering practice and their use has had a large impact in many fields. Polymer processing is no exception, and there is already a substantial amount of literature describing ways in which processes can be analysed, designed or controlled using the potentialities of modern computers. The emphasis given varies with the application, and most authors tend to quote the results of their calculations rather than describing in any detail the way the calculations were undertaken or the difficulties experienced in carrying them out. We aim to give here as useful and connected an account as we can of a wide class of applications, for the benefit of scientists and engineers who find themselves working on polymer processing problems and feel the need to undertake such calculations. The major application we have in mind is the simulation of the dynamics ofthe various physical phenomena which arise in a polymer process treated as a complex engineering system. This requires that the system be reasonably well represented by a limited number of relatively simple subprocesses whose connections can be clearly identified, that the domi nant physical effects relevant to each subprocess can be well defined in a suitable mathematical form and that the sets of equations and boundary conditions developed to describe the whole system can be successfully discretised and solved numerically.