Drag characteristics of power law fluids on an upstream moving surface

The specific problem to be considered here concerns the boundary layer problem of a non-Newtonian fluid on a flat plate in length, whose surface has a constant velocity opposite in the direction to that of the mainstream with Uw 〉〉 U∞, or alternatively when the plate surface velocity is kept fixed but the stream speed is reduced to zero. A theoretical analysis for a boundary layer flow is made and the self-similar equation is determined. Solutions are presented numerically for special power index and the associated transfer behavior is discussed.

Approximate analytical solutions and approximate value of skin friction coeffcient for boundary layer of power law fluids

This paper presents a theoretical analysis for laminar boundary layer flow in a power law non-Newtonian fluids. The Adomian analytical decomposition technique is presented and an approximate analytical solution is obtained. The approximate analytical solution can be expressed in terms of a rapid convergent power series with easily computable terms. Reliability and efficiency of the approximate solution are verified by comparing with numerical solutions in the literature. Moreover, the approximate solution can be successfully applied to provide values for the skin friction coefficient of the laminar boundary layer flow in power law non-Newtonian fluids.

Calculation Method of Power Law Fluid Equivalent Permeability Considering Capillary Shape

While studying the flow of oil and gas in the reservoir, it is not realistic that capillary with circular section is only used to express the pores. It is more representative to simulate porous media pore with kinds of capillary with triangle or rectangle section etc. In the condition of the same diameter, when polymer for oil displacement flows in the porous medium, there only exists shear flow which can be expressed with power law model. Based on fluid flow-pressure drop equation in single capillary, this paper gives a calculation method of equivalent permeability of power law fluid of single capillary and capillary bundles with different sections.

Exact Solutions of a Power Law Fluid Model in Posttreatment Analysis of Wire Coating with Linearly Varying Boundary Temperature

In this paper, analysis of post-treatment of wire coating is presented. Coating material satisfies power law fluid model. Exact solutions for the velocity field, volume flow rate and average velocity are obtained. Moreover, the heat transfer results are presented for different cases of linearly varying on the boundaries. The variations of velocity, volume flow rate, radius of coated wire, shear rate and the force on the total wire are presented graphically and discussed.

The Tangential Force Distribution on Inner Cylinder of Power Law Fluid Flowing in Eccentric Annuli with the Inner Cylinder Reciprocating Axially

Based on the governing equations of the inner cyinder of the unsteady flow of the power law fluid in eccentric annuli with the inner cylinder reciprocating axially in bipolar coordinate system, the calculation formulae of tangential force were established, and the relevant numerical calculation method was given. Taking the aqueous solution of partially hydrolyzed polyacrylamides (HPAM) for examples, the tangential forces were calculated by using the formulae and numerical calculation method mentioned above;the curves of the tangential force on the wall of the inner cylinder of HPAM aqueous solution were plotted;and the effects on the tangential force of the flow behavior index of the power law fluid, the stroke and the stroke frequency of the inner cylinder were analyzed.

Numerical Study of Thermal Boundary Layer on a Continuous Moving Surface in Power Law Fluids

This paper investigates flow and heat transfer of power law fluids on a continuous moving surface. The temperature distribution is obtained numerically by considering the effect of the power law viscosity on thermal diffusivity and the characteristics of the flow and heat transfer are analyzed. The results show that the distribution of the thermal boundary layer depends not only on the velocity ratio parameter of the plate, but also on the power law index and Prandtl number of fluids.

An Analysis of the Characteristics of the Thermal Boundary Layer in Power Law Fluid

This paper presents a theoretical analysis of the heat transfer for the boundary layer flow on a continuous moving surface in power law fluid. The expressions of the thermal boundary layer thickness with the different heat conductivity coefficients are obtained according to the theory of the dimensional analysis of fluid dynamics and heat transfer. And the numerical results of CFD agree well with the proposed expressions. The estimate formulas can be successfully applied to giving the thermal boundary layer thickness.

Shear Force Distribution and Heat Transfer in Laminar Boundary Layer Flows for Power Law Fluid

Analytical and numerical solutions are presented for the momentum and energy laminar boundary layer equations in power law fluids utilizing a similarity transformation and the shooting technique. The results indicated that for power law exponents 0< n ≤1, the skin friction σ decreases with increasing n , and the dimensionless shear force decreases with increasing dimensionless velocity t . When Pr =1, the velocity distribution in the viscous boundary layer is the same as the temperature distribution in the thermal boundary layer and δ=δ T. For Pr >1, the increase of the viscous diffusion exceeds that of thermal diffusion with increasing Pr , i.e. , δ T (t)<δ(t) . The thermal diffusion ratio increases with increasing n(0<n≤1) .

Experimental Investigation of Dimensionless Velocity and Shearing Stress in Boundary Layer Flow on Continuous Moving Surface in Power Law Fluids

An analysis is carried out to study the steady flow characteristics from a continuous flat surface moving in a parallel free stream of non-Newtonian power law fluid. The constitutive equations of the fluid are transformed into dimensionless ones. The velocity field is measured by Particle Image Velocimetry. Experimental results are obtained for the distribution of velocity. The influence of wall velocity ratio parameter on boundary layer flow field is observed in the experiment. Dimensionless velocity distribution and shearing stress distribution are obtained by post-processing experimental results. The effects of various physical parameters like velocity ratio parameter and similarity variable on various momentum transfer characteristics are discussed in detail and shown graphically. It is indicated that dimensionless velocity increases with velocity ratio parameter and similarity variable, and that dimensionless shearing stress decreases with velocity ratio parameter and similarity variable.

A SECOND-ORDER MOMENT TURBULENCE MODEL FOR POWER LAW FLUID WITH PARTICLES

The USM-θ model of power law fluid for dense two-phase turbulent flow was developed, which combines the unified second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collision. This model was used to simulate the turbulent flow of power law fluid single-phase in pipe. It is shown that the USM- θ model has better prediction result than the κf -κf - κ- εp -θ model. The USM-O model was then used to simulate the dense two-phase turbulent up flow of power law fluid with particles. With the increase of the flow exponent, the velocities of power law fluid and particles increase near the pipe centre. Comparison between the two-phase flow of power law fluid-particle and of liquid-particle indicates that the axial fluctuation velocity of fluid phase and particle phase in liquid-particle two-phase flow is smaller than that in the power law fluid two-phase flow, but the two-phase velocities of power law fluid-particle and liquid-particle are close to each other.

SOLUTION OF THE RAYLEIGH PROBLEM FOR A POWER-LAW NON-NEWTONIAN CONDUCTING FLUID VIA GROUP METHOD

An investigation is made of the magnetic Rayleigh problem where a semi_infinite plate is given an impulsive motion and thereafter moves with constant velocity in a non_Newtonian power law fluid of infinite extent. The solution of this highly non_linear problem is obtained by means of the transformation group theoretic approach. The one_parameter group transformation reduces the number of independent variables by one and the governing partial differential equation with the boundary conditions reduce to an ordinary differential equation with the appropriate boundary conditions. Effect of the some parameters on the velocity u(y,t) has been studied and the results are plotted.

Similarity solutions for non-Newtonian power-law fluid flow

The problem of the boundary layer flow of power law non-Newtonian fluids with a novel boundary condition is studied. The existence and uniqueness of the solutions are examined, which are found to depend on the curvature of the solutions for different values of the power law index n. It is established with the aid of the Picard-Lindelof theorem that the nonlinear boundary value problem has a unique solution in the global domain for all values of the power law index n but with certain conditions on the curva- ture of the solutions. This is done after a suitable transformation of the dependent and independent variables. For 0 〈 n ≤ 1, the solution has a positive curvature, while for n 〉 1, the solution has a negative or zero curvature on some part of the global domain. Some solutions are presented graphically to illustrate the results and the behaviors of the solutions.

OBTAINING THE CRITICAL DRAW RATIO OF DRAW RESONANCE IN MELT SPINNING FOR POWER LAW POLYMER FLUIDS

A direct difference method has been developed for Non-Newtonian power law fluids to solve the simultaneous non-linear partial differential equations of melt spinning, and to determine the critical draw ratio for draw resonance. The results show that for shear thin fluids, the logarithm of the critical draw ratio has a well defined linear relationship with the power index for isothermal and uniform tension melt spinning. When the power index approaches zero, the critical draw ratio points at unity, indicating no melt spinning can be processed stably for such fluids. For shear thick fluids, the critical draw ratio increases in a more rapid way with increasing the power index.

Suitable Heat Transfer Model for Self-Similar Laminar Boundary Layer in Power Law Fluids

The classical power law non-Newtonian fluids energy boundary layer equation is proved improper to describe the self-similar heat transfer. A theoretical analysis for momentum and energy boundary layer transfer behavior is made and the full similarity heat boundary layer equation is developed, which may be characterized by a power law relationship between shear stress and velocity gradient with the Falkner-Skan equation as a special case. Both analytical and numerical solutions are presented for momentum and energy boundary layer equations by using the similarity transformation and shooting technique and the associated transfer characteristics are discussed.

Effects of nonlinear velocity slip and temperature jump onpseudo-plastic power-law fluid over moving permeable surface in presence of magnetic field

Flow and heat transfer of a pseudo-plastic power-law fluid over a stretching permeable surface with the magnetic effect is investigated. In the boundary conditions,the nonlinear temperature jump and the velocity slip are considered. Semi-similarity equations are obtained and solved by bvp4c with MATLAB. The problem can be considered as an extension of the previous work done by Mahmoud(Mahmoud, M. A. A. Slip velocity effect on a non-Newtonian power-law fluid over a moving permeable surface with heat generation. Mathematical and Computer Modelling, 54, 1228–1237(2011)). Efforts are made to discuss the effects of the power-law number, slip velocity, and temperature jump on the dimensionless velocity and temperature distribution.

Characteristics of Convection Heat Transfer in Power⁃Law Fluid Saturated Porous Media Channel

Considering Brinkman⁃Forchheimer extended Darcy flow and local thermal non⁃equilibrium effect,a general model of forced convection with viscous dissipation in power⁃law fluid saturated porous media channel was established.The dimensionless temperature profiles and Nusselt number were numerically solved using the classical fourth⁃order Runge Kutta method under a constant heat flux boundary condition.The conclusion showed that the fluid⁃solid temperature distributions were significantly affected by dimensionless Bi,k,Da,Br,and F,and the effects of power⁃law indexes on convection heat transfer characteristics were also non⁃negligible.

Symmetries of boundary layer equations of power-law fluids of second grade

A modified power-law fluid of second grade is considered. The model is a combination of power-law and second grade fluid in which the fluid may exhibit normal stresses, shear thinning or shear thickening behaviors. The equations of motion are derived for two dimensional incompressible flows, and from which the boundary layer equations are derived. Symmetries of the boundary layer equations are found by using Lie group theory, and then group classification with respect to power-law index is performed. By using one of the symmetries, namely the scaling symmetry, the partial differential system is transformed into an ordinary differential system, which is numerically integrated under the classical boundary layer conditions. Effects of power-law index and second grade coefficient on the boundary layers are shown and solutions are contrasted with the usual second grade fluid solutions.

The axisymmetric long-wave interfacial stability of core-annular flow of power-law fluid with surfactant

The long wave stability of core-annular flow of power-law fluids with an axial pressure gradient is investigated at low Reynolds number. The interface between the two fluids is populated with an insoluble surfactant. The analytic solution for the growth rate of perturbation is obtained with long wave approximation. We are mainly concerned with the effects of shear-thinning/thickening property and interfacial surfactant on the flow stability. The results show that the influence of shear-thinning/thickening property accounts to the change of the capillary number. For a clean interface, the shear-thinning property enhances the capillary instability when the interface is close to the pipe wall. The converse is true when the interface is close to the pipe centerline. For shear-thickening fluids, the situation is reversed. When the interface is close to the pipe centerline, the capillary instability can be restrained due to the influence of surfactant. A parameter set can be found under which the flow is linearly stable.

On energy boundary layer equations in power law non-Newtonian fluids

The hear transfer mechanism and the constitutive models for energy boundary layer in power law fluids were investigated.Two energy transfer constitutive equations models were proposed based on the assumption of similarity of velocity field momentum diffusion and temperature field heat transfer.The governing systems of partial different equations were transformed into ordinary differential equations respectively by using the similarity transformation group.One model was assumed that Prandtl number is a constant,and the other model was assumed that viscosity diffusion is analogous to thermal diffusion.The solutions were presented analytically and numerically by using the Runge-Kutta formulas and shooting technique and the associated transfer characteristics were discussed.

Mixture flow of particles and power-law fluid in round peristaltic tube

The erythrocyte and blood flowing in the blood vessel can be treated as the two-phase flow of the mixture of particles and a power-law fluid in a peristaltic tube.In the present work, the peristaltic transport of a power-law fluid and the suspension of particles in a tube is investigated by a perturbation method using the long wavelength approximation. The influence of different parameters on the velocity profile and streamlines is explored. Results show that there is a deflection of the flow field when the power-law index n = 0.5 or 1.5 compared with the Newtonian fluid where the trapping zone is symmetric to a certain cross section. The flux rate and reflux of the material are identified,and the conditions under which the reflux appears are determined. Moreover, a reflux phenomenon occurs near the wall. The trapping zone is related to not only the tube geometry and the flow flux but also the fluid properties. Both the length and width of the trapping zone increase with an increase in θ or φ. The trapping zone is more difficult to produce in the shear-thinning fluid than the shear-thickening fluid.