Showing papers on "Second-order fluid published in 2002"

Drop deformation for non-Newtonian fluids in slow flows

Abstract: The problem of a single drop immersed in a flowing immiscible fluid is here investigated for non-Newtonian fluids in slow, steady-state flows. The two materials are assumed to be second-order simple fluids, hence effects of constitutive elasticity are included in the analysis. A perturbative approach is used to obtain the complete analytic solution, including the drop shape, up to second order in the imposed deformation rate of the external flow. The adopted perturbation method differs from the classical one adopted for the Newtonian case, as it makes use of rotational invariance to obtain from the start a workable tensorial representation of the pressure and velocity fields, and of the drop deformation.

The Rayleigh–Stokes problem for heated second grade fluids

Abstract: The temperature distribution in a second grade fluid subject to a linear flow on a heated flat plate and within a heated edge is determined using the simple and double Fourier sine transforms. At rest, it is the same both for a second grade fluid and for a Newtonian one.

Decay of a potential vortex and propagation of a heat wave in a second grade fluid

Abstract: The propagation of a heat wave in an incompressible second grade fluid within the context of a potential vortex is studied. The solutions for the Newtonian fluid can be obtained from those for fluids of second grade as a limiting case.

Orientation of symmetric bodies falling in a second-order liquid at nonzero reynolds number

Abstract: We study the steady translational fall of a homogeneous body of revolution around an axis a, with fore-and-aft symmetry, in a second-order liquid at nonzero Reynolds (Re) and Weissenberg (We) numbers. We show that, at first order in these parameters, only two orientations are allowed, namely, those with a either parallel or perpendicular to the direction of the gravity g. In both cases the translational velocity is parallel to g. The stability of the orientations can be described in terms of a critical value Ec for the elasticity number E = We/Re, where Ec depends only on the geometric properties of the body, such as size or shape, and on the quantity (Ψ1 + Ψ2)/Ψ1, where Ψ1 and Ψ2 are the first and second normal stress coefficients. These results are then applied to the case when the body is a prolate spheroid. Our analysis shows, in particular, that there is no tilt-angle phenomenon at first order in Re and We.

Unsteady non-linear convection in a second-order fluid

Abstract: Linear and weakly non-linear analyses of convection in a second-order fluid is investigated. The Rivlin–Ericksen constitutive equation is considered to give viscoelastic correction to the momentum equation. The linear and non-linear analyses are, respectively, based on the normal mode technique and truncated representation of Fourier series. The linear theory reveals that the critical eigenvalue is independent of viscoelastic effects and the principle of exchange of stabilities holds. An autonomous system of differential equations representing cellular convection arising in the non-linear study is solved numerically. The non-linear analysis reveals that finite amplitudes have random behaviour. The effect of viscoelasticity on the non-linear solutions is analysed by considering different projections in the phase-space. Also, the transient behaviour concerning the variations of the Nusselt number with time has been investigated. The onset of chaotic motion is also discussed in this paper.

Study on Thin Film Lubrication With Second-Order Fluid

Abstract: The basic lubrication equations are deduced from the original second-order fluid constitutive equations. Two examples of lubrication, a plane inclined slider and a journal bearing, are calculated respectively. The Reynolds boundary conditions are used in the calculation of the journal bearing. In this calculation, it is found that the load carrying capacities of the slider and the journal bearing are of different tendencies with the increase of the Deborah number. Furthermore, the results show that with the decrease of the film thickness, the increase of the normal stress of second-order fluid is greater than that of Newtonian fluid. Finally, it is found that the distribution of the normal stress changes significantly at a certain thickness.