2214 N-Sの式誘導の際の4階等方性テンソルのポリアディクスによる記述について(G05-3 解析モデルと解析手法,G05 流体工学)  [in Japanese] 2214 Description of Isotropic Tensor of Rank 4 for Navier-Stokes Equation using Polyadics  [in Japanese]

This paper describes the isotropic tensor of rank 4 in three-dimensional space using polyadic algebra. The isotropic tensor of rank 4 appears in the relation between strain and stress for the well-known Navier-Stokes equation. When the deformation of viscous fluid is assumed to be slight and isotropic, the isotropic tensor of rank 4, that is Cijkl, is reconfirmed explicitely to be described as C_<ijkl>=Aδ_<ij>δ_<kl>+Bδ_<ik>δ_<jl>+Cδ_<il>δ_<jk>, where δ denotes the Kronecker delta. A, B and C denote the constants due to fiuid properties. In this case the polyadics is newly found to be suitable for the description of the rotation of the orthogonal curvilinear coordinates. The polyadics may be useful to describe the fluid properties further for microhydrodynamics and non-Newtonian fluid flow.