Values Of Power Law Exponent Research Articles

Boundary layer flow on a moving surface in otherwise quiescent pseudo-plastic non-Newtonian fluids

A theoretical analysis for the boundary layer flow over a continuous moving surface in an otherwise quiescent pseudo-plastic non-Newtonian fluid medium was presented. The types of potential flows necessary for similar solutions to the boundary layer equations were determined and the solutions were numerically presented for different values of power law exponent.

The Shielding Effectiveness of Composite Media - a Parametric Analysis Supporting an Engineering Perspective

This paper is presented as an example of a parametric approach that may be applied to engineering the radio and microwave properties of composite materials in the context of providing electromagnetic shielding capability. In this case, the composites are formed by a conductive filler component embedded within an insulating material. The effective electromagnetic (permittivity) properties of the composite are modeled under the quasistatic approximation using the McLachlan general effective medium model, which enables the impact of the percolation (insulator-conductor) transition to be explored. Composites within the transition region exhibit a power-law nature to their effective material properties. The power-law exponents may take a range of values above a limiting value set by the dimensionality of the filler particle network within the composite and with the assumption of a perfectly random distribution of filler particles. In practice, the values of the power-law exponents depend on the chemical interactions between the constituents, the processing conditions and the nature of the inter-particle charge transport. The paper demonstrates the implications of different values of power-law exponent in the context of the trade-off between shielding effectiveness and composite thickness.

Mathematical modelling of blood flow in curved arteries

We study the mixed convection boundary layer heat transfer of power law fluid over a moving conveyor along an inclined plate. The effects of shear flow and power law viscosity on the temperature field are taken into account according to a modified Fourier law. Approximate analytical solutions are obtained by the homotopy analysis method (HAM). Results indicate that heat transfer is strongly dependent on the values of power law exponent, inclination angle, boundary velocity ratio and Prandtl number. Three distinct characteristics are found for power law exponents 0 < n < 1, n = 1 and n > 1, especially the nonlinear behavior due to skin friction and local Nusselt number shown in Figs. 4 and 17, which has never been reported before. The decrease of inclination angle causes the loss of velocity boundary layer but the gain of temperature boundary layer. Heat transfer efficiency is enhanced but skin friction is diminished with the increase in velocity ratio (the ratio of conveyor velocity/mean velocity of flow field). Critical ratio (with skin friction zero) is obtained which strongly depends on the power law exponent. The effects of involved parameters on the velocity and temperature fields are analyzed.

Similarity solutions of energy and momentum boundary layer equations for a power-law shear driven flow over a semi-infinite flat plate

The problem of a steady forced convection thermal boundary-layer driven by a power-law shear is investigated. The search for similarity solutions reduces the problem to a couple of ordinary differential equations containing three parameters: the exponent of the decaying exterior velocity profile, the exponent of the power-law prescribing the thermal condition on the wall and Prandtl number. The effects of these parameters on the existence and form of similarity solution are investigated and the functional dependence of the local Nusselt number on these parameters is reported and discussed. An analysis of the assumptions usually accepted to derive similarity solutions is also reported in order to show the range of values of the exterior velocity power-law exponent for which such solutions may exist.

Power law fluid model incorporated into elastohydrodynamic lubrication theory of line contact

An algorithm is developed for the study of the infinitely long slider bearing in general form, considering the lubricant to be an incompressible power law fluid in isothermal conditions. The earlier works on this topic were considered by taking cavitation boundary conditions when a cylinder moves over a plane lubricated with a power law fluid and in EHL solution in a particular case, viz. pure rolling of a cylinder over an identical cylinder. We have considered a general solution including elastohydrodynamic lubrication (EHL) for different values of power law exponent. Deviation of values of central film thickness for different values of power law exponent from those for Newtonian lubricants are presented. The effects of the power law exponent on the central film thickness, minimum film thickness and load capacity are analysed. The effects of rolling and sliding velocities of contact surfaces are also analysed in terms of an equivalent radius of a cylinder moving over a moving plane. Film shapes and pressure distributions are also calculated numerically and presented graphically for various values of central film thickness considered in this paper. A number of observations obtained here with pseudoplastic nature of lubricants are in good agreement with the experimental results. The theoretical observations suggest the behaviour of common lubricants as pseudoplastic fluids in the cases of slowly moving surfaces and motion under heavy load.

Characterization of the cellular microstructure of ocular lens using 2D power law analysis.

Power law analysis provides a quantitative method for characterization of spatial fluctuations in the cellular microstructure of the ocular lens. In the power law analysis, Fourier components of the spatial fluctuations are computed, and the relationship between the amplitude, A, and spatial frequency, f, of the components is defined by a power law function: [formula, see text]. The exponent of the function, beta, defines the scaling of the amplitude of the Fourier components as a function of spatial frequency. We performed two-dimensional power law analysis on electron micrographs of lens cells ranging from transparent to opaque. We identified two values of power law exponent, beta, for the spatial fluctuations of all lens cells, one for low- and a second for high-spatial frequencies. In the low-spatial frequency region, the value of beta was in the range of 0.53 to 1.33, for transparent and opaque cells. In the high-spatial frequency region, the value of beta increased from 2.78 for transparent lens cells to 3.60 for opaque lens cells. The power law analysis provides a new method for quantitative characterization of the spatial fluctuations in the microstructure of transparent and opaque lens cells.

ON RUPTURE OF A THINNING FILM OF NON-NEWTONIAN POWER LAW LIQUID†

Abstract A linear stability analysis of a thinning film of non-Newtonian power law liquid has been employed to predict the critical thickness of rupture of films with immobile interfaces experiencing only van der Waals interactions. The assumption of immobile interfaces makes the above analysis equally applicable to the stability of foam as well as emulsion thin films. Psuedoplastic liquid thin films are found to be significantly less stable than Newtonian films. Power law liquid thin films are more stable for liquids with larger values of power law exponents and larger values of consistency indices. The critical thickness of film rupture is very sensitive to the power law exponent. As expected, the critical thickness of film rupture increases for stronger van der Walls interactions as well as for smaller surface tensions, these effects being more pronounced for psuedoplastic liquid films than their Newtonian counterparts.

Solution properties of gum exudates from Sterculia urens (Karaya gum)

Dilute solution properties of Karaya gum from Sterculia urens were studied using size-exclusion chromatography, static and dynamic light scattering and viscosity experiments in 0·1 m aq. NaCl. Solubility in water was found to be strongly dependent on the degree of acetylation. The native acetylated Karaya gum assumes a rather compact and branched conformation in aqueous solution, as evidenced by the low values of power-law exponents. In contrast, the fully deacetylated Karaya gum assumes a more expanded conformation and behaves as a random coil.

Corner Flow of Power Law Fluids

A local analysis of the flow of power law fluids near corners is performed. The equation for the stream function is shown to allow separated solutions in plane polar coordinates. The radial behavior is shown to be algebraic and results are given for the exponent for different values of corner angle and power law exponent. In addition, the critical angle for the onset of an eddy structure is found as function of the power law exponent.

An analysis of the Hui-Riedel equation

We consider several of the features exhibited by the equation derived by Hui and Riedel for the angular variation of the stress function near the tip of a crack propagating under steady-state, quasi-static, antiplane strain conditions in an elastic/power-law creeping material. We show that the regularity condition imposed in front of the crack tip by Hui and Riedel as an extra boundary condition is in fact implicit in the physically derived boundary conditions, and does not therefore constitute an independent boundary condition. On the other hand, these physical boundary conditions do not imply that the solution is regular on the crack flank. Despite an apparent shortage of boundary conditions, uniqueness of positive solutions can be explained as behavior typical of certain kinds of nonlinear eigenvalue problems. We further examine the asymptotic behavior of the solution for large values of the power-law exponent. Here it is shown that the solution is not the elastic-perfectly plastic solution, as might be supposed, but rather a solution which is in good agreement with the numerical results of Hui and Riedel.