Showing papers on "Second-order fluid published in 2008"

Erratum to: Unsteady flow of an Oldroyd-B fluid induced by the impulsive motion of a plate between two side walls perpendicular to the plate

Abstract: Exact solutions for the unsteady flow of an Oldroyd-B fluid produced by a suddenly moved plane wall between two side walls perpendicular to the plane are established by means of the Fourier sine transforms The similar solutions for Maxwell, Newtonian and second grade fluids, performing the same motion, appear as limiting cases of the solutions obtained here In the absence of the side walls, the solutions corresponding to the motion over an infinite suddenly moved plate are also obtained as the limiting cases Finally, for comparison, the velocity field in the middle of the channel and the shear stress at the bottom wall are plotted for different values of the material constants

Two spheres in a free stream of a second-order fluid

Abstract: The forces acting on two fixed spheres in a second-order uniform flow are investigated. When α1+α2=0, where α1 and α2 are fluid parameters related to the first and second normal stress coefficients, the velocity field for a second-order fluid is the same as the one predicted by the Stokes equations while the pressure is modified. The Stokes solutions given by Stimson and Jeffery [Proc. R. Soc. London, Ser. A 111, 110 (1926)] for the case when the flow direction is along the line of centers and Goldman et al. [Chem. Eng. Sci. 21, 1151 (1966)] for the case when the flow direction is perpendicular to the line of centers are utilized and the stresses and the forces acting on the particles in a second-order fluid are calculated. For flow along the line of centers or perpendicular to it, the net force is in the direction that tends to decrease the particle separation distance. For the case of flow at arbitrary angle, unequal forces are applied to the spheres perpendicularly to the line of centers. These forces ...

Second Order Fluid Models with General Boundary Behaviour

Abstract: A crucial property of second order fluid models is the behaviour of the fluid level at the boundaries. Two cases have been considered: the reflecting and the absorbing boundary. This paper presents an approach for the stationary analysis of second order fluid models with any combination of boundary behaviours. The proposed approach is based on the solution of a linear system whose coefficients are obtained from a matrix exponent. A practical example demonstrates the suitability of the technique in performance modeling.

Effect of Second Sound on the Onset of Rayleigh-Benard Convection in a Coleman - Noll Fluid

Abstract: This paper deals with linear stability analysis of the effects resulting from the substitution of the classical Fourier law by the non-classical Maxwell - Cattaneo law in Rayleigh - Benard convection in second order fluid is studies. Coleman-Noll constitutive equaion is used to give a viscoelastic correction. The eigenvalue is obtained for free - free isothernal boundary combination. The classical approach predicts an infinite speed for the propagation of heat. The present non-classical theory involves a wave type heat transport (SECOND SOUND) and does not suffer from the physically unacceptable drawback of infinite heat propagation speed. It is found that the results are noteworthy at short times and the critical eigenvalues are less than the classical ones.

Analysis of perturbed flows of a second-order fluid using a 1D hierarchical model

Abstract: The aim of this paper is to analyze the un- steady flow of a non-Newtonian incompressible second-order fluid in a straight rigid axisymmetric tube with circular cross- section of constant radius. To study this problem, we use the 1D nine-director Cosserat theory approach which reduces the exact three-dimensional equations to a system depending only on time and on a single spatial variable. From this one- dimensional system we obtain the relationship between mean pressure gradient and volume flow rate over a finite section of the tube. Attention is focused on some numerical simulation of steady/unsteady flows for specific mean pressure gradient and on the analysis of perturbed flows.

Conservation of energy of non-Newtonian media for the Rayleigh-Stokes problem

Abstract: The energetic balance of the Rayleigh–Stokes problem for Newtonian-, second grade- and Maxwell fluids is studied for different initial and boundary conditions. We get the solutions of the differential equations by Fourier sine transform or by series expansion. The result for the kinetic energy Ekin, the dissipation Φ and the power of the shear stresses at the wall L are important for nature and technology.

Numerical simulations of a second-order fluid with normal stress coefficients depending on the shear rate

Abstract: We analyze the unsteady flow of an incompressible generalized second-order fluid in a straight rigid tube, with circular cross-section of constant radius, where the normal stress coefficients depend on the shear rate by using a power law model. The full 3D unsteady model is simplified using a one-dimensional hierarchical approach based on the Cosserat theory related to fluid dynamics, which reduces the exact three-dimensional equations to a system depending only on time and on a single spatial variable. From this new system we obtain the relationship between mean pressure gradient and volume flow rate over a finite section of the tube. Attention is focused on some numerical simulation under constant mean pressure gradient and on the analysis of perturbed flows.

Perturbed flows of a second-order fluid in a uniform straight tube

Abstract: The aim of this paper is to analyze the perturbed flows of a non-Newtonian incompressible second-order fluid in a straight rigid axisymmetric tube with circular cross-section of constant radius. To study this problem, we use the 1D nine-director Cosserat theory approach which reduces the exact three-dimensional equations to a system depending only on time and on a single spatial variable. From this one-dimensional system we obtain the relationship between mean pressure gradient and volume flow rate over a finite section of the tube. Attention is focused on some numerical simulation of steady/unsteady flows on the analysis of perturbed flows.