The dual integral equation method in hydromechanical systems release_dqy6mtantbcb5jx2fldzgg6liy

by N. I. Kavallaris, V. Zisis

Published in Journal of Applied Mathematics by Hindawi Limited.

2004   Volume 2004, p447-460

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<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$m$"><mml:mi>m</mml:mi></mml:math>th-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.
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