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Integral Representations in Couple Stress Theory of Fluids
Author(s) -
Ramkissoon H.
Publication year - 1979
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.19790590903
Subject(s) - mathematics , reciprocity (cultural anthropology) , representation (politics) , mathematical analysis , boundary value problem , stress functions , surface integral , integral equation , differential (mechanical device) , compressibility , physics , mechanics , politics , political science , law , thermodynamics , psychology , social psychology
The system of differential equations characterizing the slow, steady, incompressible flow of couple stress fluids is examined. Integral representation for the velocity vector is obtained with the aid of a constructed fundamental singular solution and a derived reciprocity theorem. The very form of this integral representation suggests the introduction of potentials whose properties are stated. Matrix Green's functions are then introduced and the formal solutions to two types of boundary value problems are expressed by integral representations involving these functions, given body forces and surface data.