Chaos in a triple diffusive system involving a viscoelastic fluid layer

The onset of double diffusive convection in a viscoelastic fluid layer

The stability of a horizontal layer of an electrically conducting, viscoelastic fluid (Oldroyd fluid) heated from below in the presence of a magnetic field is considered, on the assumption that both bounding surfaces are free. Linear stability theory is used to derive an eigenvalue system of sixth order, and an exact eigenvalue equation for a neutral instability is obtained. Critical Rayleigh numbers, wave numbers, and frequencies for the onset of instability are presented graphically as functions of the Chandrasekhar number for various values of the Prandtl number and the elastic parameters. It is shown that the effects which arise in consequence of the coupling between the magnetic field and the viscoelastic behaviour of a fluid are exceedingly complicated.

Capillary instability due to a shear stress on the free surface of a viscoelastic fluid layer

Viscoelastic fluids can be difficult to model due to the wide range of different physical behaviors that polymer melts can exhibit. One such feature is the viscous elastic boundary layer. We address the particular problem of a viscoelastic shear-dependent fluid flowing past a corner and investigate how the properties of the boundary layer change for a White-Metzner fluid. The boundary layer equations are derived and the upstream layer is matched with the far-field flow. It was found that if the fluid is sufficiently shear thinning then the viscoelastic boundary layer formulation fails due to the inertial forces becoming dominant. The depth of the boundary layer is controlled by the shear-thinning parameters. These effects are not a feature of other shear-thinning models, such as the Phan-Thien-Tanner model. This study provides insight in the different effects of some commonly used viscoelastic models in corner flows in the upstream boundary layer, the downstream boundary layer is not addressed.

The present paper considered the thermosolutal convection in a compressible Walters B' viscoelastic fluid layer heated and soluted from below in the presence of uniform rotation. Following the linearized stability theory and normal mode analysis, the dispersion relation is obtained. For the case of stationary convection, Walters B′ viscoelastic fluid behaves like a Newtonian fluid and compressibility, rotation and stable solute gradient have stabilizing effect on the system for G >1. Graphs have been plotted by giving numerical values to the parameters to depict the stability characteristics. The stable solute gradient, rotation and viscoelasticity introduce oscillatory modes in the system which were non-existent in their absence. The sufficient conditions for the non-existence of overstability are also obtained.

We have looked at how a rotating layer of viscoelastic (Walter’s B) fluid saturated porous medium heated from below is affected by a vertical DC electric field when it comes to the commencement of thermal convection. The technique calledGalerkin is used to solve the eigen value problem in a numerical manner. The viscoelastic fluid “Walter’s B” exhibits behavior similar to a standard Newtonian nanofluid when there is stationary convection. The stationary convection does not begin at the viscoelasticity criteria. The stationary convection occurrence for rigid rigid boundaries is obtained analytically. More stabilization is present in the system with increase in Ta and Da-1. Heat is more effectively transferred and convection is hastened when a DC electric field is present. It’s important to note that the specific application of electro-thermal convection in mining will depend on the geological and environmental conditions of the site, as well as the type of minerals or resources being extracted. The effectiveness and feasibility of such methods will also need to be carefully evaluated in each case.

The visco-elastic Ekman layer

Momentum boundary layer of viscoelastic second grade fluid taken into consideration with the effect of uniform transverse magnetic field and normal electric field also included in the analysis. Thermal boundary layer formed over the non-isothermal boundary wall, with viscous dissipation and Ohmic dissipation due to transverse magnetic field and electric field has been investigated. The highly non-linear momentum boundary layer equation and thermal boundary layer equation are converted into similarity equations and then solved numerically by employing fifth order Runge-Kutta-Fehlberg method with shooting.

Accurate solutions for viscoelastic boundary layer flow and heat transfer over stretching sheet

In this paper, the study the momentum and heat transfer characteristics in an incompressible electrically conducting non‐Newtonian boundary layer flow of a viscoelastic fluid over a stretching sheet. The partial differential equations governing the flow and heat transfer characteristics are converted into highly nonlinear coupled ordinary differential equations by similarity transformations.The resultant coupled highly nonlinear ordinary differential equations are solved by means of, homotopy analysis method (HAM) for constructing an approximate solution of heat transfer in magnetohydrodynamic (MHD) viscoelastic boundary layer flow over a stretching sheet with non‐uniform heat source.The proposed method is a strong and easy to use analytic tool for nonlinear problems and does not need small parameters in the equations. The HAM solutions contain an auxiry parameter, which provides a convenient way of controlling the convergence region of series solutions. The results obtained here reveal that the proposed method is very effective and simple for solving nonlinear evolution equations. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in physics. Copyright © 2012 John Wiley & Sons, Ltd.

English

Numerical modeling of fractional viscoelastic non-Newtonian fluids over a backward facing step – Buoyancy driven flow and heat transfer

Mathematical study of the small oscillations of a spherical layer of viscoelastic fluid about a rigid spherical core in the gravitational field

Energy transfer and turbulence structures in a zero-pressure gradient turbulent boundary layer of a drag-reducing viscoelastic solution were investigated using the direct numerical simulation (DNS) data with the Oldroyd-B and Giesekus models. This work is an extension of the first report, in which mean velocity profiles and turbulence statistics have been investigated. It is found that the contribution to turbulent kinetic energy transfer due to the polymer stress work term is not negligible for the Oldroyd-B model, whereas it is negligible for the Giesekus model. The polymer diffusion term for both the Oldroyd-B and Giesekus models is negligible. For the Oldroyd-B model, we can see that quasi-streamwise vortices are weakened and become larger in the streamwise direction, compared to Newtonian fluids. On the other hand, quasi-streamwise vortices for the Giesekus model are similar to those for Newtonian fluid.

When swimming in close proximity, some microorganisms such as spermatozoa synchronize their flagella. Previous work on swimming sheets showed that such synchronization requires a geometrical asymmetry in the flagellar waveforms. Here we inquire about a physical mechanism responsible for such symmetry breaking in nature. Using a two-dimensional model, we demonstrate that flexible sheets with symmetric internal forcing deform when interacting with each other via a thin fluid layer in such a way as to systematically break the overall waveform symmetry, thereby always evolving to an in-phase conformation where energy dissipation is minimized. This dynamics is shown to be mathematically equivalent to that obtained for prescribed waveforms in viscoelastic fluids, emphasizing the crucial role of elasticity in symmetry breaking and synchronization.