The velocity field of second-order Rivlin-Ericksen fluid between two parallel porous plates rotating around two different axes but with the same angular velocity.

*(English)*Zbl 1210.76184Summary: The steady state velocity field of an incompressible, second-order Rivlin-Ericksen fluid between two parallel, planar porous plates rotating around different axes at same angular velocity is analyzed. In addition to the rotating flow between two plates, there exists another flow of the same fluid between two plates which is perpendicular to plates. Since the distance between the plates is very small if compared to the dimensions of the plates, the dimensions of the plates are assumed to be infinite. The paper differs from the existing relevant literature by the assumption of a non-vanishing normal stress module: \(\alpha _{1} + \alpha _{2} \neq 0\). The porous character of plates and the non-linearity of the fluid increase the order of the differential equation (it increases up to the fourth-order). By obtaining the exact solution of the problem using kinematic parameters it has been tried to bring a new aspect to researches in the same field.

##### MSC:

76S05 | Flows in porous media; filtration; seepage |

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\textit{N. A. Unverdi}, Int. J. Eng. Sci. 38, No. 8, 939--955 (2000; Zbl 1210.76184)

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##### References:

[1] | Abbot, T.N.G.; Walters, K., Rheometrical flow systems, part 2. theory for the orthogonal rheometer, including an exact solution of the navier – stokes equations, J. fluid mech., 40, 205, (1970) · Zbl 0184.52102 |

[2] | Berker, R., An exact solution of the navier – stokes equation, the vortex with curvilinear axis, Internat. J. engrg. sci., 20, 217, (1982) · Zbl 0487.76039 |

[3] | Berker, R., A new solution of the navier – stokes equation for the motion of a fluid contained between two parallel planes rotating about the same axis, Arch. mech. stos., 31, 265, (1979) · Zbl 0415.76026 |

[4] | R. Druot, Sur Un Cas D’integration Des Equation Du Mou. Vement D’un Fluide Incompressible Du Deuxieme Ordre, C.R Acad., Sci. Paris, 265A (1967) 300 |

[5] | Rajagopal, K.R.; Gupta, A.S., Flow and stability of a second grade fluid between two parallel rotating plates about non-coincident axes, Internat. J. engrg. sci., 19, 1401, (1981) · Zbl 0469.76003 |

[6] | Rajagopal, K.R., The flow of a second-order fluid between rotating parallel plates, J. non-Newtonian fluid mech., 9, 185, (1981) · Zbl 0476.76008 |

[7] | Kaloni, P.N., Several comments on the paper some remarks on useful theorems for second-order fluid, J. non-Newtonian fluid mech., 36, 1, (1990) |

[8] | Wagner, M.H., Analysis of time dependent non-linear stress growth data for shear and elongational flow of a low density branched polyethylene line melt, Rheol. acta., 15, 133, (1976) |

[9] | Currie, P.K., Constitutive equations for polymer melts predicted by Doi-edwards and curtiss-bird kinetic theory models, J. non Newtonian fluid mech., 11, 53, (1982) · Zbl 0492.76003 |

[10] | Knight, D.G., Flow between eccentric disks rotating at different speeds: inertia effects, Z. angew. math. phys., 31, 309, (1980) · Zbl 0425.76026 |

[11] | Rajagopal, K.R., A class of exact solution to the navier – stokes equations, Internat. J. engrg. sci., 22, 451, (1984) · Zbl 0531.76033 |

[12] | Elcrat, A.R., On one flow between a rotating disk and a porous disk, Arc. rational mech. anal., 73, 63, (1980) · Zbl 0422.76018 |

[13] | R.K. Bhatnagar, Secondary flow of an elasticoviscous fluid between two coaxial cones having the same vortex and rotating about a common axis, Proc. Nat. Acad. Sci. India 39 (1969) 107 · Zbl 0236.76003 |

[14] | Rao, A.R.; Kasivishwanathan, S.R., On exact solution of the unsteady navier – stokes equation the vortex with instantaneous curvilinear axis, Internat. J. engrg. sci., 25, 337, (1987) · Zbl 0609.76021 |

[15] | Rajagopal, K.R.; Gupta, A.S., An exact solution for the flow of a non-Newtonian fluid past an infinite porous plate, Meccanica, 19, 158, (1984) · Zbl 0552.76008 |

[16] | K.R. Rajagopal, P.N. Kaloni. Some remarks on boundary conditions for flows of fluids of the different type, Continuum Mechanics and its Applications, Hemisphere, Washington, DC, 1989, pp. 935-941 |

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