Showing papers on "Second-order fluid published in 1972"

Nonlinear Stability of Plane Poiseuille Flow of Viscoelastic Liquids

Abstract: The stability of plane Poiseuille flow to infinitesimal perturbations was studied for the second order and Maxwell fluid rheological models. When the Deborah number based disturbance propagation is small the second order fluid is a consistent constitutive equation and the two models give identical results. This occurs for elasticity number (E) less than 5×10−4. At higher values of E the second order fluid cannot be used. The critical Reynolds number is a slowly decreasing function of E up to E≈10−4 and a rapidly decreasing function subsequently in the region where fluid relaxation effects become important. For a sufficiently elastic fluid the flow transition is governed by a new mode of the Orr‐Sommerfeld equation and differs qualitatively from that for a Newtonian liquid. The results suggest the likelihood of low Reynolds number instability in highly elastic liquids.

Non-torsional oscillations of a disc in rotating second order fluid

Abstract: This paper deals with the non-torsional oscillations of a disc in rotating second-order fluid. The disc and the fluid are initially in a state of rigid rotation and the non-torsional oscillations in its own plane are then imposed on the disc. The depth of penetration of the oscillations is increased due to the presence of the coefficient of visco-elasticity. It tends to infinity when the frequency of the oscillations is twice the angular velocity of rotation, meaning thereby that no equilibrium boundary layer exist. An initial value problem for two cases—(i) one disc bounding a semi-infinite mass of the fluid, (ii) two discs containing the fluid in between them is discussed. The classical Rayleigh layer for second-order fluid is derived as a particualr case and it is also found that steady Ekman layer is reached for large time.