International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 7, Pages 477-485

Cooling of a plate with general boundary conditions

F. D. Zaman1 and R. Al-Khairy2

1Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
2Department of Mathematics, Dammam College of Girls, Dammam, Saudi Arabia

Received 3 September 1997; Revised 21 October 1998

Copyright © 2000 F. D. Zaman and R. Al-Khairy. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider steady state temperature distribution in a homogeneous rectangular infinite plate the lower part of which is cooled by a fluid flowing at a constant velocity while the upper part satisfies the general mixed boundary conditions. The Wiener-Hopf method has been used to obtain the solution in the infinite series form and some special cases have been discussed.