J Austral Math Soc Ser B 33 pp474--485, 1992.

Cooling of an infinite slab in a two-fluid medium

R. K. Bera and A. Chakrabarti

Abstract

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.

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Authors

R. K. Bera

Department of Mathematics, Presidency College, Calcutta-700 073, India.

A. Chakrabarti

Department of Applied Mathematics, Indian Institute of Science, Bangalore-560 012, India.