Dual Series Equations to Solve the Laplace Equation with Mixed Boundary Conditions

A solution of the Laplace equation in cylindrical coordinates is presented for a bounded cylinder with the known height and radius which is subject to inhomogeneous mixed boundary conditions of the third and second kinds on the surface. On the other surface, unmixed boundary conditions of the first...

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Published inJournal of engineering physics and thermophysics Vol. 96; no. 6; pp. 1460 - 1467
Main Author Hoshan, N. A.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.11.2023
Springer
Springer Nature B.V
Subjects
Boundary conditions
Classical Mechanics
Complex Systems
Cylindrical coordinates
Engineering
Engineering Thermodynamics
Fredholm equations
Heat and Mass Transfer
Industrial Chemistry/Chemical Engineering
Integral equations
Integral transforms
Laplace equation
Thermodynamics
dual series equations
mixed boundary conditions
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ISSN1062-0125
1573-871X
DOI10.1007/s10891-023-02814-w

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Summary:A solution of the Laplace equation in cylindrical coordinates is presented for a bounded cylinder with the known height and radius which is subject to inhomogeneous mixed boundary conditions of the third and second kinds on the surface. On the other surface, unmixed boundary conditions of the first or second kind are given. Through separation of variables, the Hankel integral transform, and the dual series equations, the solution of the mixed problem is reduced to solving the Fredholm integral equation of the second kind.
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ISSN:1062-0125
1573-871X
DOI:10.1007/s10891-023-02814-w