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Pseudo-steady state solutions for solidification in a wedge

Pseudo-steady state solutions for solidification in a wedge
Pseudo-steady state solutions for solidification in a wedge
Polubarinova-Kochina's analytical differential equation method is used to determine the pseudo-steady-state solution to problems involving the freezing (solidification) of wedges of liquid which are initially at their fusion temperature. In particular, we consider four distinct problems for wedges which are: freezing with the same constant boundary temperature, freezing with the same constant boundary heat fluxes, freezing with distinct constant boundary temperatures and freezing with distinct constant fluxes at the boundaries. For the last two problems, a Heun's differential equation with an unknown singularity is derived, which in both cases admits a particularly elegant simple solution for the special case when the wedge angle is ?. The moving boundaries obtained are shown pictorially.
0272-4960
109-121
Hoang, H.V.
75f64698-a5a0-41dc-b98e-2446d8ca6c5e
Hill, J.M.
db5454da-7690-4928-bb9d-46bd6dbcad00
Dewynne, J.N.
976c17bf-544b-4c7d-a757-0c806555d724
Hoang, H.V.
75f64698-a5a0-41dc-b98e-2446d8ca6c5e
Hill, J.M.
db5454da-7690-4928-bb9d-46bd6dbcad00
Dewynne, J.N.
976c17bf-544b-4c7d-a757-0c806555d724

Hoang, H.V., Hill, J.M. and Dewynne, J.N. (1998) Pseudo-steady state solutions for solidification in a wedge. IMA Journal of Applied Mathematics, 60 (2), 109-121. (doi:10.1093/imamat/60.2.109).

Record type: Article

Abstract

Polubarinova-Kochina's analytical differential equation method is used to determine the pseudo-steady-state solution to problems involving the freezing (solidification) of wedges of liquid which are initially at their fusion temperature. In particular, we consider four distinct problems for wedges which are: freezing with the same constant boundary temperature, freezing with the same constant boundary heat fluxes, freezing with distinct constant boundary temperatures and freezing with distinct constant fluxes at the boundaries. For the last two problems, a Heun's differential equation with an unknown singularity is derived, which in both cases admits a particularly elegant simple solution for the special case when the wedge angle is ?. The moving boundaries obtained are shown pictorially.

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Published date: 1998

Identifiers

Local EPrints ID: 29342
URI: http://eprints.soton.ac.uk/id/eprint/29342
ISSN: 0272-4960
PURE UUID: aa2114fd-8540-4e39-9a9d-04ba1c4c1141

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Date deposited: 13 Mar 2007
Last modified: 15 Mar 2024 07:30

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Contributors

Author: H.V. Hoang
Author: J.M. Hill
Author: J.N. Dewynne

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