On the Laminar Two-Dimensional Free Jet of an Incompressible Pseudoplastic Fluid

1972 ◽  
Vol 39 (4) ◽  
pp. 1162-1164 ◽  
Author(s):  
C. Atkinson
Keyword(s):  
Flow Behavior ◽  
Closed Form Solution ◽  
Form Solution ◽  
Numerical Results ◽  
Two Dimensional ◽  
Pseudoplastic Fluid ◽  
Flow Behavior Index ◽  
Free Jet ◽  
Boundary Layer Equations ◽  
Behavior Index

A closed-form solution is obtained to boundary-layer equations given by Lemieux and Unny [1] for the free outflow of a non-Newtonian pseudoplastic fluid from a two-dimensional orifice into a mass of the same fluid. Results deduced from this solution are compared with numerical results given in [1]. The analytical solution given here contradicts some of these numerical results when the flow behavior index of the fluid is less than or equal to a half.

Solutions of Laminar Jet Flow Problems for Non-Newtonian Power-Law Fluids

1978 ◽  
Vol 100 (3) ◽  
pp. 363-366 ◽  
Author(s):  
E. M. Mitwally
Keyword(s):  
Power Law ◽  
Flow Behavior ◽  
Flow Behavior Index ◽  
Free Jets ◽  
Free Jet ◽  
Laminar Jet ◽  
Flow Problems ◽  
Power Law Fluids ◽  
Flow Configurations ◽  
Behavior Index

Solutions are presented for laminar flow of non-Newtonian power-law fluids. The flow configurations cover the two-dimensional plane and radial free jets, the axisymmetrical (circular) free jet, and the plane and radial wall jets. When the flow behavior index is unity, the present results agree well with those already published for the case of Newtonian fluids.

The Laminar Two-Dimensional Free Jet of an Incompressible Pseudoplastic Fluid

1968 ◽  
Vol 35 (4) ◽  
pp. 810-812 ◽  
Author(s):  
P. F. Lemieux ◽  
T. E. Unny
Keyword(s):  
Boundary Layer ◽  
Exact Solution ◽  
Similarity Solutions ◽  
Turbulent Jet ◽  
Two Dimensional ◽  
Pseudoplastic Fluid ◽  
Free Jet ◽  
Boundary Layer Equations ◽  
Turbulent Jet Flow ◽  
Special Case

Boundary-layer equations have been used to obtain an exact solution for the free outflow of a non-Newtonian pseudoplastic fluid from a two-dimensional orifice into a mass of the same fluid. Existence of similarity solutions has been proved. The results obtained by Schlichting for the Newtonian fluid flow is shown to be the special case of the more general analysis given here. Though further effort is necessary to investigate the turbulent jet flow, the analysis presented here should make a definite contribution in this definition.

Effects of Greek Pomegranate Extracts in the Antioxidant Properties and Storage Stability of Kefir

2019 ◽  
Vol 15 (4) ◽  
pp. 437-441 ◽  
Author(s):  
Vasiliki Lagouri ◽  
Georgia Dimitreli ◽  
Aikatarini Kouvatsi
Keyword(s):  
Antioxidant Activity ◽  
Dairy Products ◽  
Storage Time ◽  
Storage Stability ◽  
Flow Behavior ◽  
Antioxidant Properties ◽  
Flow Behavior Index ◽  
Ph Values ◽  
Dpph Activity ◽  
Behavior Index

Background: Oxidation reactions are known to shorten the shelf life and cause damage to foods rich in fat, such as dairy products. One way to limit oxidation and increase the shelf life of fermented dairy products is to use natural antioxidants. The aim of this study was to examine the effect of adding pomegranate extracts in the antioxidant properties, rheological characteristics and the storage stability of the fermented product of kefir. Methods: The Pomegranate Juice (PGJ) and Peel Extracts (PGPE) (5%, 10% w/v) were added to kefir and the antioxidant properties were evaluated by using the methods of radical scavenging activity (DPPH) and Ferric Reducing Antioxidant Power Activity (FRAP). Spectrophotometric and instrumental methods were used to determine the Total Phenols (TPs), pH values, viscosity and flow behavioral index values of enriched with pomegranate kefir samples. The same properties were tested when kefir samples stored at 4°C for 7, 14, 21 and 28 days. Results: The addition of PGJ and PGPE results in an increase in the antioxidant activity (DPPH, FRAP) and total phenol content (TPs) of kefir samples. Increasing the concentration of the added PGJ and PGPE, results in an increase in the TP content and the DPPH activity of kefir. As far as the storage time is concerned, the results showed an increase in the amount of TP at 7th day and a reduction in the DPPH activity in the 14th day of storage. In contrary to the DPPH method, the increase in storage time has resulted in a reduction in antioxidant activity by the FRAP method. The addition of PGJ and PGPE in kefir results in a decrease in pH values while the pH of kefir samples increased during storage at 4°C for 28 days. The addition of PGJ and PGPE to kefir samples results to a decrease in viscosity and an increase in the flow behavior index. Increasing storage time results in increased flow behavior index of kefir samples. Conclusion: The addition of PGJ and PGPE increased the antioxidant activity and total phenols of the kefir product and preserved its properties during the total storage time of 28 days at 4°C.

Electroosmotic Flow of Power-Law Fluids in a Slit Microchannel

2009 ◽  
Author(s):  
Cunlu Zhao ◽  
Chun Yang
Keyword(s):  
Shear Stress ◽  
Double Layer ◽  
Power Law ◽  
Dynamic Viscosity ◽  
Electroosmotic Flow ◽  
Flow Behavior ◽  
Flow Behavior Index ◽  
Power Law Fluids ◽  
Hyperbolic Cosine ◽  
Behavior Index

Electroosmotic flow of power-law fluids in a slit channel is analyzed. The governing equations including the linearized Poisson–Boltzmann equation, the Cauchy momentum equation and the continuity equation are solved to seek analytical expressions for the shear stress, dynamic viscosity and velocity distributions. Specifically, exact solutions of the velocity distributions are explicitly found for several special values of the flow behavior index. Furthermore, with the implementation of an approximate scheme for the hyperbolic cosine function, approximate solutions of the velocity distributions are obtained. In addition, a mathematical expression for the average electroosmotic velocity is derived for large values of the dimensionless electrokinetic parameter, κH, in a fashion similar to the Smoluchowski equation. Hence, a generalized Smoluchowski velocity is introduced by taking into account contributions due to the finite thickness of the electric double layer and the flow behavior index of power-law fluids. Finally, calculations are performed to examine the effects of κH, flow behavior index, double layer thickness, and applied electric field on the shear stress, dynamic viscosity, velocity distribution, and average velocity/flow rate of the electroosmotic flow of power-law fluids.

On Wall Effects in Cavity Flows

1984 ◽  
Vol 28 (01) ◽  
pp. 70-75
Author(s):  
C. C. Hsu
Keyword(s):  
Numerical Results ◽  
Cavity Flows ◽  
Two Dimensional ◽  
Wall Effects ◽  
Free Jet ◽  
Theoretical Predictions ◽  
Experimental Findings ◽  
Good Agreement

Simple wall correction rules for two-dimensional and nearly two-dimensional cavity flows in closed or free jet water tunnels, based on existing linearized analyses, are made. Numerical results calculated from these expressions are compared with existing experimental findings. The present theoretical predictions are, in general, in good agreement with data.

scholarly journals Analytic Solution for Systems of Two-Dimensional Time Conformable Fractional PDEs by Using CFRDTM

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Abir Chaouk ◽  
Maher Jneid
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Analytic Solution ◽  
Closed Form Solution ◽  
Form Solution ◽  
Two Dimensional ◽  
Fractional Pdes ◽  
Differential Transform ◽  
Computational Work ◽  
Similar Solutions

In this study we use the conformable fractional reduced differential transform (CFRDTM) method to compute solutions for systems of nonlinear conformable fractional PDEs. The proposed method yields a numerical approximate solution in the form of an infinite series that converges to a closed form solution, which is in many cases the exact solution. We inspect its efficiency in solving systems of CFPDEs by working on four different nonlinear systems. The results show that CFRDTM gave similar solutions to exact solutions, confirming its proficiency as a competent technique for solving CFPDEs systems. It required very little computational work and hence consumed much less time compared to other numerical methods.

Compressibility of Two-Dimensional Cavities of Various Shapes

1986 ◽  
Vol 53 (3) ◽  
pp. 500-504 ◽  
Author(s):  
R. W. Zimmerman
Keyword(s):  
Closed Form Solution ◽  
Mapping Function ◽  
Complex Stress ◽  
Form Solution ◽  
Hydrostatic Compression ◽  
Biaxial Compression ◽  
Cavity Surface ◽  
Uniform Pressure ◽  
Two Dimensional ◽  
Stress Functions

Muskhelishvili-Kolosov complex stress functions are used to find the stresses and displacements around two-dimensional cavities under plane strain or plane stress. The boundary conditions considered are either uniform pressure at the cavity surface with vanishing stresses at infinity, or a traction-free cavity surface with uniform biaxial compression at infinity. A closed-form solution is obtained for the case where the mapping function from the interior of the unit circle to the region outside of the cavity has a finite number of terms. The area change of the cavity due to hydrostatic compression at infinity is examined for a variety of shapes, and is found to correlate closely with the square of the perimeter of the hole.

Shear Rate Corrections for Herschel-Bulkley Fluids in Couette Geometry

2008 ◽  
Vol 18 (3) ◽  
pp. 34482-1-34482-11 ◽  
Author(s):  
Vassilios C. Kelessidis ◽  
Roberto Maglione
Keyword(s):  
Flow Behavior ◽  
Flow Equation ◽  
Oil Field ◽  
Rheological Parameters ◽  
Concentric Cylinder ◽  
Flow Behavior Index ◽  
Shear Rates ◽  
Power Law Fluids ◽  
Good Agreement ◽  
Behavior Index

AbstractA methodology is presented to invert the flow equation of a Herschel-Bulkley fluid in Couette concentric cylinder geometry, thus enabling simultaneous computation of the true shear rates, γ̇HB, and of the three Herschel-Bulkley rheological parameters. The errors made when these rheological parameters are computed using Newtonian shear rates, γ̇N, as it is normal practice by research and industry personnel, can then be estimated. Quantification of these errors has been performed using narrow gap viscometer data from literature, with most of them taken with oil-field rheometers. The results indicate that significant differences exist between the yield stress and the flow behavior index computed using γ̇HB versus the parameters obtained using γ̇N and this is an outcome of the higher γ̇HB values. Predicted true shear rates and rheological parameters are in very good agreement with results reported by other investigators, who have followed different approaches to invert the flow equation, both for yield-pseudoplastic and power-law fluids.

scholarly journals Performance of New Austrian Tunneling Method (NATM) in Weak Rock Case Study

2018 ◽  
Vol 7 (4.20) ◽  
pp. 40
Author(s):  
Heba Kamal ◽  
. .
Keyword(s):  
Finite Element ◽  
Closed Form Solution ◽  
Side Wall ◽  
Form Solution ◽  
Two Dimensional ◽  
Phase 2 ◽  
Actual Case ◽  
Tunneling Method ◽  
New Austrian Tunneling Method

The decline in the over ground utilizable space and increment in development of metro structures, cut and cover structures are winding up fairly difficult to conceptualize and build. In this examination, a nonlinear two dimensional limited component investigation was completed to show the New Austrian Tunneling Method (NATM) burrow developed in frail shake utilizing the business limited component with joint programming PHASE 2.The validity of the numerical modeling procedure performed by the author was checked by making back-analysis for an actual case study of Strengen Tunnel which is one of the biggest expressways in western Austria.  A comprehensive parametric study was performed on a hypothetical circle tunnel. Two dimensional numerical simulations with the finite element with joint software PHASE 2 have been performed to ground behaviour with   the results of the numerical analysis are presented and   discussed for recommendations for future work. In general the tangential stress at side wall and crown  obtained from  finite element with joints are  nearly equal or higher than the closed form solution and equivalent continuum.                                                                                   

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