The flow of non-Newtonian fluids down inclines

Equipment units (e.g. tray column heaters) in many chemical engineering and mineral processing industries involve the flow of non-Newtonian fluids down inclined plates. When designing these equipment units the non-Newtonian fluid flows often are not fully understood and so the designs are not properly optimised. In this study the flow down a series of inclined plates was experimentally and numerically investigated to better understand the flow for various fluids and to validate a computational fluid dynamics (CFD) model.In the experimental rig there were a series of consecutive plates inclined at 45°. An optically clear polymer solution was used to simulate a yield pseudo-plastic material and allowed flow visualisation to be undertaken of the flow. The fluid film thickness was observed to decrease down the consecutive plates. Experiments were also carried out using a yield pseudo-plastic mineral slurry and the results were found to be qualitatively similar.An analytical model was developed to calculate the fluid film layer thickness on the first plate and a CFD model was used to compute the flow down a series of flat plates. The CFD model employed a homogeneous multiphase model and surface-sharpening algorithm. The CFD model accurately predicted the fluid film thicknesses and flow patterns. The validated CFD model can now be used with confidence as a design tool.     

Nonisothermal Couette flow of a non-Newtonian fluid under the action of a pressure gradient

Nonisothermal Couette flow has been studied in a number of papers [1–11] for various laws of the temperature dependence of viscosity. In [1] the viscosity of the medium was assumed constant; in [2–5] a hyperbolic law of variation of viscosity with temperature was used; in [6–8] the Reynolds relation was assumed; in [9] the investigation was performed for an arbitrary temperature dependence of viscosity. Flows of media with an exponential temperature dependence of viscosity are characterized by large temperature gradients in the flow. This permits the treatment of the temperature variation in the flow of the fluid as a hydrodynamic thermal explosion [8, 10, 11]. The conditions of the formulation of the problem of the articles mentioned were limited by the possibility of obtaining an analytic solution. In the present article we consider nonisothermal Couette flows of a non-Newtonian fluid under the action of a pressure gradient along the plates. The equations for this case do not have an analytic solution. Methods developed in [12–14] for the qualitative study of differential equations in three-dimensional phase spaces were used in the analysis. The calculations were performed by computer.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 26–30, May–June, 1981.     

Forced convective flow over a flat plate in non-Newtonian power law fluids

A new forced convection parameter

Boundary layer flow at a three-dimensional stagnation point in power-law non-Newtonian fluids

Similarity solutions for the three-dimensional flow and heat transfer of a power-law fluid near a stagnation point of an isothermal surface are presented. The results of the numerical integrations are given in tables and shown on graphs for some different values of the power-law index n, geometric parameter c, and the Prandtl number Pr. Whenever possible, these results are compared with available analytical solutions and found to be highly accurate.     

Nonisothermal polymeric fluids

The phase-space kinetic theory for polymeric liquid mixtures has been further developed for molecular models without internal constraints. The theory provides expressions for the mass, momentum, and energy fluxes, each of which may in general be influenced by concentration, velocity, and temperature gradients. To illustrate the use of these results, the thermal conductivity for a dilute polymer solution is derived; the FENE dumbbell model is used to describe the mechanical behavior of the polymer chains. The Hookean dumbbell results can be obtained by letting the finite extensibility parameter b tend to infinity.Dedicated to Prof. Dr. J. Meissner on the occasion of his retirement from the chair of Polymer Physics at the Eidgenössische Technische Hochschule (ETH) Zürich, Switzerland     

The stability of two concentric non-Newtonian fluids in circular pipe flow

The flow of two concentric non-Newtonian fluids, under constant pressure gradient in a circular tube, is studied by linear stability analysis. The viscosities of the two fluids are different and their dependence on shear stress is described by the Ellis model. It is found that the steady state flow can be unstable, depending on certain combinations of the values of physical parameters, to infinitesimal axisymmetric disturbances of large wavelengths, for any Reynolds number however small. The flow is predominantly stable if the inner fluid is more viscous and predominantly unstable if the outer fluid is more viscous. Stronger dependence of viscosity on shear stress can both stabilize and destabilize the flow. Interfacial tension is also destabilizing when the Weber number is small than about 10⁴.     

Behaviors of flow mechanisms and heat transfer of non-Newtonian fluids through a spinneret

This investigation examines non-Newtonian flow mechanisms and heat transfer characteristics for a micro spinneret. The working fluid, Polyethylene terephthalate (PET), is the raw material of micro fiber, and a large-scale experimental test model was designed to visualize the complex viscous flow system in the micro spinneret. To visualize the complex convective flow system, an experimental test model was constructed, using glycerin instead of PET. The related parameters of PET were compared with those of glycerin. The power law correlates the shear strain with PET viscosity at various temperatures. The pressure distribution along the flow direction was measured and the flow pattern was visualized using polyethylene (PE) powder of 20–40 m. Similar configurations were calculated for micro spinneret physical parameters to determine the thermal flow characteristics. The Reynolds number in the test model is not less than 10^–2. In the non-Newtonian PET working fluid of practical micro spinneret, flows with Re = 10⁴ to 10^–2 are in the same low Reynolds number flow regime. Therefore, the working fluid is expected to have the same flow characteristic. A numerical solution covering the range of approximately Re = 10^–4 at PET confirms that the flow characteristics of glycerin are constant for Re = 1.228 × 10^–2. The Peclet number in the test model can be adjusted to a value similar to that in the micro spinneret. The flow visualization was compared with that of the numerical solution, and the friction factor and Nusselt number in the micro spinneret were analyzed. Finally, numerical results and friction factor with various exit angles of micro spinneret in a triangular zone flow system were also summarized.     

On the dispersion of soluble matter in a channel flow of non-Newtonian fluid

Summary An analysis of the dispersion of a solute in Rivlin-Ericksen third-order fluid in a parallel plate channel is carried out. It is seen that the solute which is dispersed relative to a plane moving with the mean speed of the flow has its effective Taylor diffusion coefficient which decreases with increasing the non-Newtonian parameter With 1 table     

Heat transfer to non-Newtonian fluids in laminar flow through rectangular ducts

Heat transfer to non-newtonian fluids flowing laminarly through rectangular ducts is examined. The conservation equations of mass, momentum, and energy are solved numerically with the aid of a finite volume technique. The viscoelastic behavior of the fluid is represented by the Criminale-Ericksen-Filbey (CEF) constitutive equation. Secondary flows occur due to the elastic behavior of the fluid, and, consequently, heat transfer is strongly enhanced. It is observed that shear thinning yields negligible heat transfer enhancement effect, when compared with the secondary flow effect. Maximum heat transfer is shown to occur for some combinations of parameters. Thus, there are optimal combinations of aspect ratio and Reynolds numbers, which depend on the fluid's mechanical behavior. This result can be usefully explored in thermal designs of certain industrial processes.     

Attractors of non-Newtonian fluids

The existence of global attractors is demonstrated for the dynamical systems generated by motions of nonlinear bipolar and non-Newtonian viscous fluids and upper bounds are obtained for the Hausdorff and fractal dimensions of the attractors for the bipolar case.     

On the dispersion of a solute in oscillating flow of a non-Newtonian fluid in a channel

The paper presents an exact analysis of the dispersion of an immiscible solute in a non-Newtonian fluid (known as an incompressible second-order fluid which shows viscoelastic behaviour) flowing slowly in a parallel plate channel in the presence of a periodic pressure gradient. Using a generalized dispersion model which is valid for all times after the solute injection, the diffusion coefficients K _i (τ)(i=1,2,3,…) are obtained as functions of time τ in the case when the initial solute distribution is in the form of a slug of finite extent. The analysis leads to the novel result that K ₂(τ) (which is a measure of the longitudinal dispersion coefficient of the solute) has a steady part S in addition to a fluctuating part D ₂(τ) due to the pulsatility of the flow. It is found that S decreases with increase in the viscoelastic parameter M for given values of the amplitude λ and frequency ω of the pressure pulsation. On the other hand, it is found that at a fixed instant τ, the amplitude of D ₂(τ) increases with increase in M for given values of λ and ω. Further it is shown that at a given instant τ, the amplitude of D ₂(τ) decreases with increase in ω for given λ and M and the profile for D ₂(τ) becomes progressively flatter with increase in ω. Finally the axial distribution of the average concentration θ _m of the solute over the channel cross-section is determined at different instants after the solute injection for several values of M, λ and ω. The present study is likely to have important bearing on the problem of dispersion of tracers in blood flow through arteries.     

Nonisothermal model of asymmetric fluids

Several studies have been devoted to the investigation of the properties of fluid models with asymmetric stress tensors [1–5].In the following we consider the peculiarities of the Grad nonisothermal model [1]. It is shown that for the case of a nonuniform temperature field in a fluid in the general case there is an intersection of the thermal flux with the moment stress flux. Account for the flux intersection leads to change of the moment of momentum and specific entropy equations.In those cases when the physical characteristics of the medium in the flow region may be considered constant, the flux intersection may influence the fluid flow only through the boundary conditions.Thus, for example, the asymmetric moment stresses created by the temperature gradient will drive a fluid layer into motion if one of the layer surfaces is free.