Hostname: page-component-8448b6f56d-qsmjn Total loading time: 0 Render date: 2024-04-19T07:55:37.675Z Has data issue: false hasContentIssue false
  • English
  • Français

Cooling of an infinite slab in a two-fluid medium

Published online by Cambridge University Press:  17 February 2009

R. K. Bera  and
A. Chakrabarti
R. K. Bera
Affiliation:
Department of Mathematics, Presidency College, Calcutta-700 073, India.
A. Chakrabarti
Affiliation:
Department of Applied Mathematics, Indian Institute of Science, Bangalore-560 012, India.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A mixed boundary-valued problem associated with the diffusion equation, that involves the physical problem of cooling of an infinite slab in a two-fluid medium, is solved completely by using the Wiener-Hopf technique. An analytical solution is derived for the temperature distribution at the quench fronts being created by two different layers of cold fluids having different cooling abilities moving on the upper surface of the slab at constant speed. Simple expressions are derived for the values of the sputtering temperatures of the slab at the points of contact with the respective layers, assuming one layer of the fluid to be of finite extent and the other of infinite extent. The main problem is solved through a three-part Wiener-Hopf problem of a special type, and the numerical results under certain special circumstances are obtained and presented in the form of a table.

Type
Research Article
Information
The ANZIAM Journal , Volume 33 , Issue 4 , April 1992 , pp. 474 - 485
Copyright
Copyright © Australian Mathematical Society 1992

References

[1] Caflish, R. E. and Keller, J. B., “Quench front propagation”, Nuclear Engineering and Design 65 (1981) 97–102.CrossRefGoogle Scholar
[2] Chakrabarti, A., “The sputtering temperatures of a cooling cylindrical rod with an insulated core”, Applied Scientific Research 43 (1986) 107–113.CrossRefGoogle Scholar
[3] Chakrabarti, A., “Cooling of a composite slab”, Applied Scientific Research 43 (1986) 213–225.CrossRefGoogle Scholar
[4] Chakrabarti, A., “A simplified approach to a three-part Wiener-Hopf probleme arising in diffraction theory”, Math. Proc. Camb. Phil. Soc. 102 (1987) 371.CrossRefGoogle Scholar
[5] Evans, D. V., “A note on the cooling of a cylinder entering a fluid”, IMA J. of Applied Mathematics 33 (1984) 49–54.CrossRefGoogle Scholar
[6] Jones, D. S., Electromagnetic theory (Pergamon, London, 1964).Google Scholar
[7] Levine, H., “On a mixed boundary value problem of diffusion type”, Applied Scientific Research 39 (1982) 261–276.CrossRefGoogle Scholar
[8] Noble, B., Methods based on the Winer-Hopf technique (Pergamon, London, 1958).Google Scholar