zbMATH — the first resource for mathematics

A class of exact solutions for the flow of a micropolar fluid. (English) Zbl 0609.76006
The flow of a micropolar fluid in an orthogonal rheometer is considered. It is shown that an infinite number of exact solutions characterizing asymmetric motions are possible. The expressions for pressure in the fluid, the components of the forces and couples acting on the plates are obtained. The effect of microrotation on the flow is brought out by considering numerical results for the case of coaxially rotating disks.

MSC:
 76A05 Non-Newtonian fluids 76U05 General theory of rotating fluids 35Q99 Partial differential equations of mathematical physics and other areas of application 76M99 Basic methods in fluid mechanics
Full Text:
References:
 [1] Berker, R., A new solution of the Navier-Stokes equation for the motion of a fluid contained between two parallel plates rotating about the same axis, Archiwum mechaniki stosowanej, 31, 265-280, (1979) · Zbl 0415.76026 [2] Berker, R., An exact solution of the Navier-Stokes equation: the vortex with curvilinear axis, Int. J. engng sci., 20, 217-230, (1982) · Zbl 0487.76039 [3] Berker, R., (), 1-384 [4] Huilgol, R.R., On the properties of the motion with constant stretch history occurring in the Maxwell rheometer, Trans. soc. rheol., 13, 513-536, (1969) [5] Rajagopal, K.R., On the flow of a simple fluid in an orthogonal rheometer, Arch. rail mech. anal., 79, 39-47, (1982) · Zbl 0513.76002 [6] Rajagopal, K.R.; Wineman, A., Flow of a BKZ fluid in an orthogonal rheometer, J. rheol., 27, 509-516, (1983) · Zbl 0535.76004 [7] Rao, A.Ramachandra; Rao, P.Raghupathi, MHD flow of a second grade fluid in an orthogonal rheometer, Int. J. engng sci., 23, 1387-1395, (1985) · Zbl 0575.76109 [8] Eringen, A.C., Theory of micropolar fluids, J. math. mech., 16, 1-18, (1966) · Zbl 0145.21302 [9] Cowin, S.C., The theory of polar fluids, Adv. appl. mech., 14, 279-347, (1974) · Zbl 0293.76003 [10] Guram, G.S.; Anwar, M., Steady flow of a micropolar fluid due to a rotating disk, J. engng math., 13, 223-234, (1979) · Zbl 0398.76030 [11] Guram, G.S.; Kamal, M.Anwar, Steady forced flow of a micropolar fluid against a rotating disk, Int. J. engng sci., 22, 813-821, (1984) · Zbl 0551.76042 [12] Abbott, T.N.G.; Walters, K., Rheometrical flow systems. part 2, theory for orthogonal rheometer, including an exact solution of the Navier-Stokes equations, J. fluid mech., 40, 205-213, (1970) · Zbl 0184.52102
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.