Problems involving heat transfer with change of phase

Beckett, Peter Michael

Applied mathematics
April 1971

Thesis or dissertation

© 1971 Peter Michael Beckett. All rights reserved. No part of this publication may be reproduced without the written permission of the copyright holder.

In Part I, two-dimensional laminar film condensation is investigated on the basis of boundary layer theory. The case of flow past a semi-infinite flat plate, which is aligned parallel to a uniform mainstream with velocity Um*(x)=Uo*, is discussed by means of a perturbation analysis for both small and large rates of cooling at the surface. Predictions, for this similar solution of the boundary layer equations, are compared with exact numerical solutions in the case of steam-water condensation. The perturbation analysis is then extended to non-similar flows and results for steam-water condensation are compared with numerical solutions obtained using the Hartree-Womersley method. The cases Um*(x)=Uo* sin(x/z) and Um*(x)=Uo* (1- 1/8 x/c) are used for comparison. The numerical solutions are also studied to discuss separation in these condensation problems.

Part II is devoted to the solidification of a cylindrical bar, initially at fusion temperature, when the outer surface temperature is lowered below fusion. The governing equations are solved numerically to obtain accurate results for the solidification process and. in addition a power series in the non-dimensional time is developed. Terms of this series are found both analytically and numerically. Interest surrounds the radius of convergence of such a series because of the similarity between the movements of the solidification front and the growth of the boundary layer for flow through a cylinder.

Department of Applied Mathematics, The University of Hull
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