On the Use of Rotating-Disk Geometry for Evaluating the Drag-Reducing Efficiency of Polymeric and Surfactant Additives

In this study we will examine the applicability of the flow induced by a rotating disk in evaluating the performance of polymeric and surfactant additives in reducing skin friction drag and effect of viscosity on drag reduction capability of polymeric and surfactant solutions. It is shown that these additives can dramatically reduce friction drag provided that the flow is occurring under turbulent conditions while they have no effect on Taylor instabilities. Based on the experimental data, a drag reduction in the range of 10% can be achieved with the effect becoming more pronounced the higher the Reynolds number

Dynamics of Microbubbles Oscillating in Rheopectic Fluids Subject to Acoustic Pressure Field

In the present work, the dynamics of a single spherical gas bubble surrounded by a rheopectic fluid obeying the Quemada model is numerically investigated while the bubble undergoes oscillatory motion due to acoustic forcing. The generalized form of the Rayleigh–Plesset equation has been used for studying bubble dynamics in Quemada fluids. The integro-differential equation representing the dynamics of the bubble is solved numerically using the finite-element method (FEM) and also the Gauss–Laguerre quadrature (GLQ) method. The effect of rheopexy number (Rx) and viscosity ratio (ξ) are then investigated over a wide range of working parameters. Numerical results show that the rheopectic behavior of the fluid surrounding the bubble can dramatically affect the bubble dynamics. It is predicted that for highly anti-thixotropic fluids, harmonics are affected so much so that the bubble may exhibit chaotic behavior. For instance, at Rx = 0.001 and ξ = 1/81, a one-micron-sized bubble may attain a size almost 30 times of its initial size. The general conclusion is that, in sonography, microbubbles dispersed in rheopectic fluids may indeed be considered as a potent ultrasound contrast agent provided that the fluid is just moderately anti-thixotropic otherwise its chaotic response might damage the adjacent tissues

On the Use of Hydrodynamic Instability Test as an Efficient Tool for Evaluating Viscoelastic Fluid Models

Abstract The so-called ''second-order'' rheological model has been of widespread use in studies related to viscoelastic fluids. The model, however, has been shown by Mathematics Subject Classification: 76E2

Newtonian Heating Effects of Oldroyd-B Liquid Flow with Cross-Diffusion and Second Order Slip

The current study highlights the Newtonian heating and second-order slip velocity with cross-diffusion effects on Oldroyd-B liquid flow. The modified Fourier heat flux is included in the energy equation system. The present problem is modeled with the physical governing system. The complexity of the governing system was reduced to a nonlinear ordinary system with the help of suitable transformations. A homotopy algorithm was used to validate the nonlinear system. This algorithm was solved via MATHEMATICA software. Their substantial aspects are further studied and reported in detail. We noticed that the influence of slip velocity order two is lower than the slip velocity order one

Linear stability of the flow of a second order fluid past a wedge

The linear stability analysis of Rivlin–Ericksen fluids of second order is investigated for boundary layer flows, where a semi-infinite wedge is placed symmetrically with respect to the flow direction. Second order fluids belong to a larger family of fluids called order fluids, which is one of the first classes proposed to model departures from Newtonian behavior. Second order fluids can model non-zero normal stress differences, which is an essential feature of viscoelastic fluids. The linear stability properties are studied for both signs of the elasticity number K, which characterizes the non-Newtonian response of the fluid. Stabilization is observed for the temporal and spatial evolution of two-dimensional disturbances when K > 0 in terms of increase of critical Reynolds numbers and reduction of growth rates, whereas the flow is less stable when K 0 and diminished when K < 0

Numerical study of chemical reaction effects in magnetohydrodynamic Oldroyd B oblique stagnation flow with a non-Fourier heat flux model

Reactive magnetohydrodynamic (MHD) flows arise in many areas of nuclear reactor transport. Working fluids in such systems may be either Newtonian or non-Newtonian. Motivated by these applications, in the current study, a mathematical model is developed for electrically-conducting viscoelastic oblique flow impinging on stretching wall under transverse magnetic field. A non-Fourier Cattaneo-Christov model is employed to simulate thermal relaxation effects which cannot be simulated with the classical Fourier heat conduction approach. The Oldroyd-B non-Newtonian model is employed which allows relaxation and retardation effects to be included. A convective boundary condition is imposed at the wall invoking Biot number effects. The fluid is assumed to be chemically reactive and both homogeneous-heterogeneous reactions are studied. The conservation equations for mass, momentum, energy and species (concentration) are altered with applicable similarity variables and the emerging strongly coupled, nonlinear non-dimensional boundary value problem is solved with robust well-tested Runge-Kutta-Fehlberg numerical quadrature and a shooting technique with tolerance level of 10−4. Validation with the Adomian decomposition method (ADM) is included. The influence of selected thermal (Biot number, Prandtl number), viscoelastic hydrodynamic (Deborah relaxation number), Schmidt number, magnetic parameter and chemical reaction parameters, on velocity, temperature and concentration distributions are plotted for fixed values of geometric (stretching rate, obliqueness) and thermal relaxation parameter. Wall heat transfer rate (local heat flux) and wall species transfer rate (local mass flux) are also computed and it is observed that local mass flux increases with strength of heterogeneous reactions whereas it decreases with strength of homogeneous reactions. The results provide interesting insights into certain nuclear reactor transport phenomena and furthermore a benchmark for more general CFD simulations

Numerical study of radiative Maxwell viscoelastic magnetized flow from a stretching permeable sheet with the Cattaneo–Christov heat flux model

In this article, the Cattaneo-Christov heat flux model is implemented to study non-Fourier heat and mass transfer in the magnetohydrodynamic (MHD) flow of an upper convected Maxwell (UCM) fluid over a permeable stretching sheet under a transverse constant magnetic field. Thermal radiation and chemical reaction effects are also considered. The nonlinear partial differential conservation equations for mass, momentum, energy and species conservation are transformed with appropriate similarity variables into a system of coupled, highly nonlinear ordinary differential equations with appropriate boundary conditions. Numerical solutions have been presented for the influence of elasticity parameter (), magnetic parameter (M2), suction/injection parameter (λ), Prandtl number (Pr), conduction-radiation parameter (Rd), sheet stretching parameter (A), Schmidt number (Sc), chemical reaction parameter (γ_c), modified Deborah number with respect to relaxation time of heat flux (i.e. non-Fourier Deborah number) on velocity components, temperature and concentration profiles using the successive Taylor series linearization method (STSLM) utilizing Chebyshev interpolating polynomials and Gauss-Lobatto collocation. The effects of selected parameters on skin friction coefficient, Nusselt number and Sherwood number are also presented with the help of tables. Verification of the STSLM solutions is achieved with existing published results demonstrating close agreement. Further validation of skin friction coefficient, Nusselt number and Sherwood number values computed with STSLM is included using Mathematica software shooting quadrature