Journal of Applied Mathematics
Volume 2004 (2004), Issue 6, Pages 447-460

The dual integral equation method in hydromechanical systems

N. I. Kavallaris and V. Zisis

Department of Mathematics, Faculty of Applied Mathematics and Physics, National Technical University of Athens, Zografou Campus, Athens 15780, Greece

Received 26 July 2004

Copyright © 2004 N. I. Kavallaris and V. Zisis. 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.


Some hydromechanical systems are investigated by applying the dual integral equation method. In developing this method we suggest from elementary appropriate solutions of Laplace's equation, in the domain under consideration, the introduction of a potential function which provides useful combinations in cylindrical and spherical coordinates systems. Since the mixed boundary conditions and the form of the potential function are quite general, we obtain integral equations with mth-order Hankel kernels. We then discuss a kind of approximate practicable solutions. We note also that the method has important applications in situations which arise in the determination of the temperature distribution in steady-state heat-conduction problems.