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Potentials and Green's Functions in Micropolar Fluid Theory
Author(s) -
Ramkissoon H.,
Majumdar S. R.
Publication year - 1980
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19800600505
Subject(s) - mathematics , mathematical analysis , matrix (chemical analysis) , ordinary differential equation , flow (mathematics) , mathematical proof , boundary value problem , surface (topology) , singular integral , compressibility , harmonic , harmonic function , green s , integral equation , differential equation , physics , geometry , mechanics , materials science , quantum mechanics , composite material
The system of coupled differential equations characterizing the slow, steady, incompressible flow of micropolar fluid is examined. Integral representations for the velocity vector and the microrotation vector are obtained by utilizing the fundamental singular solutions corresponding to a concentrated force and a concentrated couple. The very form of these integral representations suggests the introduction of surface potentials of single and double layers. The properties of these potentials are stated in various theorems without detailed proofs since they behave much like the ordinary harmonic potentials. Matrix Green's functions are then constructed with the aid of the fundamental singular solutions. By making use of the integral representations, formal solutions to two types of boundary value problems are generated in terms of integrals which include given body forces, surface data and these matrix Green's functions.