The effects of natural convection during solidification : granular flow

Guenigault, Richard Alfred

Applied mathematics
August 1984

Thesis or dissertation

© 1984 Richard Alfred Guenigault. All rights reserved. No part of this publication may be reproduced without the written permission of the copyright holder.

It is a purpose of this thesis to present numerical results on the inward solidification of spheres and (horizontal) cylinders filled with liquid which is initially at a temperature above the fusion temperature. The changes in density within the liquid, due to temperature variations, induce a liquid motion by natural convection. There is a non-uniform heat transfer from the liquid to the solid phase producing a non- symmetrical inward moving solidification interface in the shape of a limacon of Pascal. The clegree of distortion in the front is dependent on the size of the (initial) Rayleigh number of the natural convective flow. Small time perturbation expansions are employed to calculate the thermal fields in both the liquid and solid phases, to obtain the stream function for the convective motion and to locate the non-uniform solidification front. Numerical results are presented graphically for both the sphere and the cylinder.

Another purpose of this thesis is to investigate the flow profiles of a granular material in a hopper. A simplified approximate analysis is presented for the transient flow. The equations governing the motion of the material in a two-dimensional hopper are solved and the results obtained are compared with those for the steady state flow. The use of this transient model in conjunction with experimental observation will be of use in practical applications.

Department of Applied Mathematics, The University of Hull
Sponsor (Organisation)
Science and Engineering Research Council (Great Britain)
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