Zeitschrift für angewandte Mathematik und Physik ZAMP

, Volume 42, Issue 6, pp 943–959

Cooling of a composite slab in a two-fluid medium

Authors

  • R. K. Bera
    • Dept of MathematicsPresidency College
  • A. Chakrabarti
    • Dept of Applied MathematicsIndian Institute of Science
Original Papers

DOI: 10.1007/BF00944571

Cite this article as:
Bera, R.K. & Chakrabarti, A. Z. angew. Math. Phys. (1991) 42: 943. doi:10.1007/BF00944571

Abstract

A mixed boundary value problem associated with the diffusion equation that involves the physical problem of cooling of an infinite parallel-sided composite 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 speedv. Simple expressions are derived for the values of the sputtering temperatures of the slab at the points of contact with the respective layers, assuming the front layer of the fluid to be of finite width and the back layer 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.

Copyright information

© Birkhäuser Verlag 1991