Phenomenological behavior of multipolar viscous fluids
Phenomenological behavior of multipolar viscous fluids
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DOI：
10.1090/qam/1178435
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发表时间：
1992
影响因子：
0.8
通讯作者：
H. Bellout;F. Bloom;J. Necas
中科院分区：
文献类型：
--
作者：
H. Bellout;F. Bloom;J. Necas
A constitutive theory is formulated to describe the flow of viscous fluids: the theory of multipolar fluids exhibits nonlinear relations among the stress tensors and spatial derivatives of the velocity of order greater than one and is compatible with the basic principles of continuum mechanics and thermodynamics. For an isothermal, incompressible, dipolar fluid the velocity profiles for various steady flows, such as proper Poiseuille flow in a circular pipe, are computed; the results are compared with the velocity profiles obtained from the steady Navier-Stokes equations through an application of the Prandtl boundary-layer theory. Introduction. The physical theory of multipolar fluids was delineated in the papers of Necas and Silhavy [1] and Bleustein and Green [2] and follows the general ideas of Green and Rivlin [3], [4]; the theory is compatible with the principles of thermodynamics, as well as with the principle of material frame indifference. The formulation in [2] is somewhat different than the presentation in [1] dealing as it does only with the special case of a dipolar fluid but allowing for the presence of dipolar inertia terms in the constitutive theory which are not present in [1], As formulated in [1] and [2], the theory takes into account the possibility of nonlinear relations between the various stress tensors and spatial derivatives of the velocity vector. In [2] only a special example of a flow of linear dipolar viscous fluid was studied; for viscous, heat conducting, compressible fluids, with the assumption of linear relations between the relevant stress tensors and spatial derivatives of the velocity vector, a rigorous mathematical proof of the global existence in time of solutions to associated initialboundary value problems may be established, the basic theorems being contained in Received February 6, 1991. 1991 Mathematics Subject Classification. Primary 76, 35.
