Laminar Flow Of Viscoelastic Fluids Research Articles

THE FLOW OF DUSTY VISCO-ELASTIC FLUID BETWEEN TWO PARALLEL FLAT PLATES.

The flow of dusty visco-elastic fluid between two parallel plates when the lower plate is at rest and the upper one begins oscillating harmonically in its own plane is considered because of its growing importance in various technical problems in modern applied science. In this paper, we would like to consider the laminar flow of visco-elastic fluid containing uniformly small solid particles between two infinitely extended parallel plates when the lower plate is at rest and the upper one begins oscillating harmonically in its own plane. The analytical expressions for velocity fields of fluid and dust particles are obtained which are in elegant forms. The effects of elastic elements in the fluid, the mass concentration, and the relaxation time of dust particles on the velocity profiles are studied in detail. The skin friction at the lower plate wall and the total volume flow in between the plates are also obtained.

Thermal boundary layer of laminar flow of dilute polymer solution

The thermal boundary layer flow is a canonical flow with characteristics that are present in most natural and industrial convection flows. An approximate self-similar solution is proposed for the first time for the thermal boundary layer of steady laminar flow of viscoelastic fluids, described by the finitely extensible nonlinear elastic constitutive equation with Peterlin's closure (FENE-P model). This semi-analytical thermal solution is obtained by performing an order of magnitude analysis and ensuing simplifications of the governing equations by assuming that the fluid properties are independent of temperature therefore decoupling the flow governing equations from the energy equation. The effects of viscoelasticity quantified with the Weissenberg number based on the streamwise coordinate (x) (Wix) up to Wix=1 and viscous dissipation (results are presented for Brinkman numbers between -40 and +40) on thermal boundary layer characteristics are investigated comprehensively for both constant wall temperature and constant wall heat flux. At low elasticity levels (Wix<0.01) the solution exhibits a global self-similar behavior in which flow and thermal quantities collapse on the corresponding Newtonian curves, and the polymer characteristics show a unique behavior if adequately normalized. However, by increasing flow elasticity the unique self-similar behavior of the approximate solution is lost, with the elasticity dependent results exhibiting local variations. In addition, the effects of elasticity are intensified by viscous dissipation. For the present study cases, it is observed that elasticity may change Nusselt numbers by more than 8%, and the thermal boundary layer thickens by up to 10%.

Viscoelastic dream pipe with triangular pressure gradient wave form for substantial enhancement of heat transfer

A theoretical investigation is carried out to analyse the combined effects of oscillation and conjugation on the enhancement of heat transfer in laminar flow of viscoelastic fluids (CPyCl/NaSal) flowing in a circular tube with thermally conducting walls. The fluid flow is induced by a triangular pressure gradient wave form. Closed-form solutions for the momentum and heat equations are presented. The effects of influential parameters such as the wall thermal conductivity (ks), wall thickness (ε), fluid thickness, Womersley number (α), Deborah number and Prandtl number on the effective thermal diffusivity (κe) are examined. Several maxima occur in κe where the fluid flow exhibits a resonant behavior. In the viscous regime, κe increases with increasing ks and ϵ only up to the optimum value of α. In the elastic regime, the effect of conjugation on κe is saturated. The highest heat flux is achieved by the viscoelastic fluids with sinusoidal pressure gradient wave form when the walls are thermally insulated and this maximum heat flux (6.53 × 1011 W/m2) is 2968 times higher than the next highest value (2.2 × 108 W/m2) achieved by the Newtonian fluids with triangular pressure gradient wave form with thermally conducting walls. The present study demonstrates that viscoelastic fluids are preferable to Newtonian fluids and further triangular pressure gradient wave form is preferable when the walls are thermally conducting and sinusoidal pressure gradient wave form is preferable when the walls are thermally insulated.

Flow Characterization of Viscoelastic Fluids around Square Obstacle

This study focuses on the computational implementation of structured non-uniform finite volume method for the 2-D laminar flow of viscoelastic fluid past a square section of cylinder in a confined channel with a blockage ratio 1/4 for Re = 10-4, 5, 10 and 20. Oldroyd-B model (constant viscosity with elasticity) and the PTT model (shear-thinning with elasticity) are the constitutive models considered. In this study effects of the elasticity and inertia on the drag coefficients and stress fields around the square cylinder are obtained and discussed in detail. With an increase elasticity, drag coefficients get smaller due to stronger shear thinning effects for PTT fluid, however, the drag coefficients show slightly enhancement for the Oldroyd-B fluid.

Hydrodynamics and heat transfer in a laminar flow of viscoelastic fluid in a flat slot channel

Results of the numerical study of hydrodynamics and heat transfer in a laminar flow of viscoelastic fluid in a flat slot channel are presented in the present paper. The model of nonlinear viscoelastic fluid of Phan-Thien—Tanner is used to describe the viscoelastic properties of fluid. The solution to the stated problem by software package “COMSOL Multiphysics” is considered. The method of solution is verified, and results are compared with data of the other authors. It is determined that in the flow of viscoelastic fluid in a flat slot channel, the maximal contribution of heating due to dissipation is approximately 7–8 %.

Investigation of the viscoelastic flow and species diffusion in a porous channel with high permeability

In this study, effect of mass transfer on laminar flow of viscoelastic fluid in a porous channel with high permeability medium is investigated. The viscoelastic model used in this work is the upper convected Maxwell (UCM) model. Applying the similarity transformation, the governing partial equations are converted to ordinary differential equations. The problem is studied by a hybrid technique based on Differential Transformation Method (DTM) and iterative Newton’s method (INM). Also a numerical solution is done to validate the present analytical method. The effects of active parameters such as Darcy number (Da), transpiration Reynolds number (ReT) Deborah number (De) and Schmidt number (Sc) on the both velocity components and concentration function are discussed in this work. The results indicate that the stream function increases for large Deborah and Darcy numbers. The axial velocity is initially decreased by increasing the Deborah number but then increased while approaching the upper channel wall.

Heat transfer asymptote in laminar flow of non-linear viscoelastic fluids in straight non-circular tubes

The fully developed thermal field in constant pressure gradient driven laminar flow of a class of non-linear viscoelastic fluids with instantaneous elasticity in straight pipes of arbitrary contour ∂D with constant wall flux is investigated. The non-linear fluids considered are constitutively represented by a class of single mode, non-affine constitutive equations. The driving forces can be large. Asymptotic series in terms of the Weissenberg number Wi are employed to expand the field variables. A continuous one-to-one mapping is used to obtain arbitrary tube contours from a base tube contour ∂D 0. The analytical method presented is capable of predicting the velocity and temperature fields in tubes with arbitrary cross-section. Heat transfer enhancement due to shear-thinning is identified together with the enhancement due to the inherent elasticity of the fluid. The latter is to a very large extent the result of secondary flows in the cross-section but there is a component due to first normal stress differences as well. Increasingly large enhancements are computed with increasing elasticity of the fluid as compared to its Newtonian counterpart. Order of magnitude larger enhancements are possible even with slightly viscoelastic fluids. The coupling between inertial and viscoelastic non-linearities is crucial to enhancement. Isotherms for the temperature field are discussed for non-circular contours such as the ellipse and the equilateral triangle together with the behavior of the average Nusselt number Nu, a function of the Reynolds Re, the Prandtl Pr and the Weissenberg Wi numbers. Analytical evidence for the existence of a heat transfer asymptote in laminar flow of viscoelastic fluids in non-circular contours is given for the first time. Nu becomes asymptotically independent from elasticity with increasing Wi, Nu = f( Pe, Wi) → Nu = f( Pe). This asymptote is the counterpart in laminar flows in non-circular tubes of the heat transfer asymptote in turbulent flows of viscoelastic fluids in round pipes. A different asymptote corresponds to different cross-sectional shapes in straight tubes. The change of type of the vorticity equation governs the trends in the behavior of Nu with increasing Wi and Pe. The implications on the heat transfer enhancement is discussed in particular for slight deviations from Newtonian behavior where a rapid rise in enhancement seems to occur as opposed to the behavior for larger values of the Weissenberg number where the rate of increase is much slower. The asymptotic independence of Nu from elasticity with increasing Wi is related to the extent of the supercritical region controlled by the interaction of the viscoelastic Mach number M and the Elasticity number E, which mitigates and ultimately cancels the effect of the increasingly strong secondary flows with increasing Wi to level off the enhancement. The physics of the interaction of the effects of the Elasticity E, viscoelastic Mach M, Reynolds Re and Weissenberg Wi numbers on generating the heat transfer enhancement is discussed.

Study for Stratified Laminar Flow of Viscoelastic Fluids.

A numerical work is conducted in order to verify the phenomena which are observed in experiments for a Y-type junction of two laminar flow layers of a viscoelastic and Newtonian fluid with a relatively high-speed stratification, where the inertia of flows can not be neglected. A numerical technique based on Simplified Arbitrary Lagrangian-Eulerian (SALE) method is used for simulating a behavior of time-dependent interfacial stratified fluids. In comparison with experimental results, it is revealed that the present scheme predicts the wavy interfacial surface phenomena that can occur in the stratified flow geometry with a viscoelastic fluid at a specific combination of the Reynolds number and the Deborah number.

Laminar flow of viscoelastic fluids in rectangular ducts with heat transfer: A finite element analysis

A numerical study on the laminar flow and heat transfer behavior of viscoelastic fluids in rectangular ducts is conducted using the finite element approach. A Criminale-Ericksen-Fibley relation is applied to describe the viscoelastic character of the fluid, and a hydrodynamically and thermally fully developed flow with the H1 thermal boundary condition is considered. The finite element procedure employed yields essentially mesh-independent predictions with a fairly moderate computational effort. Computed results are presented and discussed in terms of the secondary flow field, the temperature field, the friction factor and the Nusselt number. In particular it is shown that the presence of a secondary flow markedly alters the temperature field and results in a substantial heat transfer enhancement with all duct aspect ratios considered.

Heat transfer enhancement in laminar flow of viscoelastic fluids through rectangular ducts

Heat transfer enhancement in laminar flow of viscoelastic fluids through rectangular ducts

Dividing Flow Properties of Newtonian Fluid and Viscoelastic Fluid. 2nd Report. Flow Patterns and Energy Losses in Two-Dimensional Steady Laminar Flow of Viscoelastic Fluid.

In the first report, the dividing flow properties of Newtonian fluid in two-dimensional steady laminar flow were presented. In this report, the flow patterns and the enrgy losses of the viscoelastic fluid (separan solution) are shown. In the dividing flow of the separan solution, two separation zones were also observed, as in those of Newtonian fluid. However, the sizes of the separation zones of the viscoelastic fluid are smaller than those of Newtonian fluid. Also, swelling of the streamline to the main conduit or to the lateral conduit was observed, which was not observed for Newtonian fluid. The loss coefficients of the viscoelastic fluid are larger than those of Newtonian fluid. The loss coefficients for the lateral conduit increase as the cross-sectional area of the lateral conduit is reduced, but the loss coefficients for the main conduit do not change grately.

Laminar mixed convection heat transfer to viscoelastic fluids in a 5:1 rectangular channel

The fully established friction factors and heat transfer coefficients of the laminar flow of viscoelastic fluids in a 5:1 rectangular duct were measured experimentally. The bottom wall, one of the longer sides of the duct was heated by passing direct electric current through it, yielding constant peripheral wall temperature and constant heat input per unit length along the bottom wall. The other surfaces were adiabatic. The test section is 150 hydraulic diameters long. Aqueous solutions of two different polymers (polyacrylamide and hydroxyethylcellulose) were used as viscoelastic fluids. The measured laminar friction factors agree well with the Newtonian correlation when plotted as a function of Kozicki generalized Reynolds number (i.e., f=16/ Re ∗ ). The established laminar Nusselt values for aqueous solutions of hydroxyethylcellulose, a weakly elastic fluid, are not significantly different from the values for water when compared at about the same values of Prandtl number and Rayleigh number. The Nusselt numbers for polyacrylamide solutions are about 25% higher than those for water at comparable values of Prandtl number and Rayleigh number.

Steady laminar flow of viscoelastic fluid in a curved pipe of circular cross-section with varying curvature

The steady laminar flow of viscoelastic fluid through pipes of circular cross-section, whose center-line curvature varies locally, is analyzed theoretically. The flows in three kinds of pipes whose center-lines are specified by ▪ as the examples of once, twice, and periodically curved pipes, respectively, are discussed in comparison with purely viscous flow. The analysis is valid for any other two-dimensionally curved pipes, when the center-line curvature is small. In addition, the reason why the secondary flow of a viscoelastic fluid in a curved pipe of circular cross-section is stronger than that of a purely viscous fluid is explained. In the present paper, the White—Metzner model is employed as the constitutive equation.

Anomalous heat transfer and drag in laminar flow of viscoelastic fluids

A boundary-layer approach is used to derive an expression for the heat transfer coefficient when a viscoelastic fluid flows past a cylinder. The heat-transfer coefficient becomes independent of velocity at large values of the latter, thus explaining the experimental results of James and Acosta. The agreement with the observations of these authors is, however, only qualitative, since their experiments were carried out at relatively low Reynolds numbers. By changing the exponent of the Reynolds number from the boundary-layer approximation value to one which is valid in the range used by James and Acosta, a correlation is suggested which is in satisfactory agreement with their data. Similar considerations are used to explain the additional experimental observation of James and Acosta, i.e. that the drag coefficient for the flow past a cylinder also becomes independent of velocity at large values of the latter quantity.

Stress‐induced diffusion and chemical reaction in nonhomogeneous velocity gradient fields

AbstractThe theoretical analysis of dispersion with or without stress‐induced diffusion and stress‐induced chemical reaction during laminar flow of viscoelastic fluids in capillaries is given. The results are applied to diffusion and degradation in polymers under nonhomogeneous velocity gradient fields. It is shown that the concentration profiles during dispersion are strongly dependent on axial and radial positions in the presence of stress‐induced diffusion. Stress‐induced degradation rate of macromolecules during capillary flow decreases if the macromolecules are subject to stress‐induced diffusion.

Heat transfer with laminar flow of viscoelastic fluids in pipes

Heat transfer with laminar flow of viscoelastic fluids in pipes

A pitot tube method for measuring the first normal stress difference and its influence on laminar velocity profile determinations

AbstractA scheme is outlined which enables the calculation of the normal stress difference P11‐P22 in fluids undergoing steady Poiseuille flow from measurements with a pitot tube of local velocity distributions. This new technique should enable measurements in a region of shear rate comparable to that encountered in the torsional and circular flow methods. A particularly interesting consequence of the method is it leads one to the inescapable conclusion that the presence of finite normal stresses should produce significant aberrations on the measurement of the velocity profile in the laminar flow of viscoelastic fluids. The presence of a P11‐P22 induced aberration on the velocity profile measurement suggests that caution be exercised in the practice of deducing estimates of the thickness of a boundary layer in the nonlaminar flow of these fluids.