Journal of Applied Mathematics
Volume 2004 (2004), Issue 6, Pages 447-460
doi:10.1155/S1110757X04407153
The dual integral equation method in hydromechanical systems
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.
Abstract
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.