Some Couette flows of a Maxwell fluid with wall slip condition

2013 ◽  
Vol 7 (1) ◽  
pp. 209-219 ◽  
Author(s):  
Dumitru Vieru ◽  
Azhar Zafar
Keyword(s):  
Wall Slip ◽  
Maxwell Fluid ◽  
Slip Condition

Stokes flows of a Maxwell fluid with wall slip condition

2011 ◽  
Vol 89 (10) ◽  
pp. 1061-1071 ◽  
Author(s):  
Dumitru Vieru ◽  
Abdul Rauf
Keyword(s):  
Relative Velocity ◽  
Wall Slip ◽  
Maxwell Fluid ◽  
Approximate Solutions ◽  
Vortex Sheet ◽  
Exact Expression ◽  
Small Time ◽  
Newtonian Fluids ◽  
Slip Condition ◽  
Stokes Flows

Stokes flows of a Maxwell fluid produced by the motion of a wall are analyzed under the slip condition at the boundary. The wall is assumed to be translated in its plane with a given velocity. The relative velocity between the fluid at the wall and the wall is assumed to be proportional to the shear rate at the wall. The exact expressions for the velocity and shear stress are determined by means of a Laplace transform. The velocity fields corresponding to both slip and nonslip conditions for Maxwell and viscous Newtonian fluids are obtained. Two particular cases, namely sinusoidal oscillations and translation with a constant velocity of the wall, are studied. In the case of flows of a Maxwell fluid with a nonslip boundary condition, the velocity is discontinuous across a vortex sheet; this situation does not appear for flows with slip conditions. In this case, the velocity is always continuous. Because the exact expression for the velocity is rather complicated, two small-time and large-time expressions of the velocity are derived. Results for Maxwell fluids are compared with those of viscous Newtonian fluids in both cases of the flow with slip and nonslip conditions. Also, the exact and approximate solutions are compared and good agreement is found. In addition, the influence of the slip coefficient on the velocity and on the relative velocity is studied.

scholarly journals Twice Order Slip on the Flows of Fractionalized MHD Viscoelastic Fluid

2019 ◽  
Vol 12 (3) ◽  
pp. 1018-1051 ◽  
Author(s):  
Muhammad Jamil ◽  
Israr Ahmed
Keyword(s):  
Shear Stress ◽  
Velocity Field ◽  
Magnetic Force ◽  
Mhd Flow ◽  
Maxwell Fluid ◽  
Slip Condition ◽  
Bottom Plate ◽  
Oscillatory Movement ◽  
The Impact ◽  
Slip Coefficients

The objective of this article is to investigate the effect of twice order slip on the MHD flow of fractionalized Maxwell fluid through a permeable medium produced by oscillatory movement of an infinite bottom plate. The governing equations are developed by fractional calculus approach. The exact analytical results for velocity field and related shear stress are calculated using Laplace transforms and presented in terms of generalized M-function satisfying all imposed initial and boundary conditions. The flow results for fractionalized Maxwell, traditional Maxwell and Newtonian fluid with and without slips, in the presence and absence of magnetic and porous effects are derived as the limiting cases. The impact of fractional parameter, slip coefficients, magnetic force and porosity parameter over the velocity field and shear stress are discussed and analyzed through graphical illustrations. The outcomes demonstrate that the speed comparing to streams with slip condition is lower than that for stream with non-slip conditions, and the speed with second-slip condition is lower than that with first-order slip condition.

Rheology and Hydraulics of Polymer (HEC) Based Drilling Foams at Ambient Temperature Conditions

SPE Journal ◽  
2007 ◽  
Vol 12 (01) ◽  
pp. 100-107 ◽  
Author(s):  
Zhu Chen ◽  
Ramadan Mohammed Ahmed ◽  
Stefan Z. Miska ◽  
Nicholas E. Takach ◽  
Mengjiao Yu ◽  
...  
Keyword(s):  
Large Scale ◽  
Wall Slip ◽  
Slip Condition ◽  
Rheological Parameters ◽  
Rheological Characterization ◽  
Pressure Losses ◽  
Aqueous Foams ◽  
Model Predictions ◽  
Foam Drilling ◽  
Foam Rheology

Summary An experimental investigation on polymer-based drilling foams was carried out. Rheology tests were performed with foams that have different concentrations of hydroxylethylcellulose (HEC) and 1% commercial surfactant. Experiments were conducted in a large-scale flow loop that permits foam flow through 2-, 3-, and 4-in. pipe sections, and a 6×3.5-in. annular section. During the experiments, frictional pressure losses across the pipe and annular sections were measured for different gas/liquid flow rates, polymer concentrations (0, 0.25, and 0.5%), and foam qualities (70, 80, and 90%). Significant rheological variations were observed between aqueous foams containing no polymers and polymer-thickened foams. Experimental data show three distinct flow curves for the 2-, 3-, and 4-in. pipe sections, which indicates the presence of wall slip. The Oldroyd-Jastrzebski approach was used to calculate the wall slip velocity and determine the true shear rate. It has been found that wall slip decreases as the foam quality or polymer concentration increases. Two foam hydraulic models, which use slip-corrected and slip-uncorrected rheological parameters, have been proposed. These models are applicable for predicting pressure loss in pipes and annuli. Model predictions for the annular test section are compared with the measured data. A satisfactory agreement between the model predictions and measured data is obtained. This paper will help to better design foam drilling and cleanup operations. Introduction The use of drilling foams is increasing because foams exhibit properties that are desirable in many drilling operations. In practice, aqueous and polymer-based foams have been used with commercial success. However, drilling-foam rheology and hydraulics are still not sufficiently understood to minimize the risk and costs associated with foam drilling. It is generally accepted that the addition of polymers to the liquid phase affects the viscosity and stability of foams. However, the degree to which the bulk properties of drilling foams are enhanced by polymers has not been well understood and is difficult to predict. For safe and economical foam drilling, accurate knowledge of bottomhole pressure is essential. However, foam rheology and pressure drop predictions are not accurate enough to provide adequate hydraulic design information such as equivalent circulation density. This problem is more pronounced when polymers are added, because the apparent foam viscosity of polymer-thickened foams can be significantly higher than aqueous foams. It becomes apparent that there is a need for polymer foam rheological characterization in order to improve the knowledge of foam rheology and hydraulics. Foam rheological characterization was carried out using large-scale, single-pass pipe viscometers (composed of 2-, 3-, and 4-in. pipe sections). Foam qualities were varied from 70 to 90%. Test pressure and temperature were 100 psig and 80°F. Two foam hydraulic models were considered, assuming both no-slip condition at the wall and slip condition at the wall. The first model assumes no-slip boundary conditions in both pipes and annulus. By assuming no slip condition at the wall, slip-uncorrected foam rheological parameters were obtained from the pipe viscometer measurements. It has been found that if we plot friction factors vs. Reynolds numbers for all test data, regardless of pipe diameters, foam qualities, and flow rates, a single curve is obtained. This curve is similar to that obtained for incompressible fluid flow. Pressure drop in the annulus is calculated with the proposed model, and satisfactory predictions are obtained. The second model is based on the assumption that there is wall slip in both pipes and annulus. Rheological parameters and wall-slip coefficient corrections were first obtained using Oldroyd-Jastrzebski approach. The annular pressure losses are predicted based on slip-corrected rheological parameters and wall-slip coefficient correlations.

New approach to mimic rheological actual shear rate under wall slip condition

2018 ◽  
Vol 35 (4) ◽  
pp. 1409-1418 ◽  
Author(s):  
Ren Jie Chin ◽  
Sai Hin Lai ◽  
Shaliza Ibrahim ◽  
Wan Zurina Wan Jaafar ◽  
Ahmed Hussein Kamel Ahmed Elshafie
Keyword(s):  
Shear Rate ◽  
Wall Slip ◽  
Slip Condition ◽  
New Approach

scholarly journals Thermal radiation effects on stagnation point flow past a stretching/shrinking sheet in a Maxwell fluid with slip condition

2017 ◽  
Vol 890 ◽  
pp. 012021 ◽  
Author(s):  
Nazila Ishak ◽  
Hasmawani Hashim ◽  
Muhammad Khairul Anuar Mohamed ◽  
Norhafizah Md Sarif ◽  
Norhayati Rosli ◽  
...  
Keyword(s):  
Thermal Radiation ◽  
Stagnation Point ◽  
Radiation Effects ◽  
Maxwell Fluid ◽  
Slip Condition ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Flow Past

scholarly journals Influence of slip condition on peristaltic transport of a viscoelastic fluid with fractional Burger’s model

2011 ◽  
Vol 15 (2) ◽  
pp. 501-515 ◽  
Author(s):  
Dharmendra Tripathi ◽  
Praveen Gupta ◽  
Subir Das
Keyword(s):  
Viscoelastic Fluid ◽  
Approximate Analytical Solution ◽  
Volume Flow Rate ◽  
Wall Slip ◽  
Volume Flow ◽  
Slip Condition ◽  
Slip Parameter ◽  
Analysis Method ◽  
Long Wavelength ◽  
Homotopy Analysis

The investigation is to explore the transportation of a viscoelastic fluid with fractional Burgers? model by peristalsis through a channel under the influence of wall slip condition. This analysis has been carried out under the assumption of long wavelength and low Reynolds number. An approximate analytical solution of the problem is obtained by using Homotopy Analysis method (HAM). It is assumed that the cross-section of the channel varies sinusoidally along the length of channel. The expressions for axial velocity, volume flow rate and pressure gradient are obtained. The effects of fractional parameters ? and ?, material constants ?1,?2,?3, slip parameter k and amplitude ? on the pressure difference and friction force across one wavelength are discussed numerically and with the help of illustrations.

Numerical Simulation of Effect of Slip Conditions on PVC Co-Rotating Twin-Screw Extrusion

2011 ◽  
Vol 189-193 ◽  
pp. 1946-1954 ◽  
Author(s):  
Ying Han Cao ◽  
Jin Nan Chen
Keyword(s):  
Flow Rate ◽  
Volumetric Flow Rate ◽  
Wall Slip ◽  
Slip Condition ◽  
Twin Screw Extruder ◽  
Slip Coefficient ◽  
Twin Screw Extrusion ◽  
Screw Extruder ◽  
Slip Conditions ◽  
Twin Screw

The effect of wall conditions on the co-rotating parallel twin-screw extrusion of rigid polyvinyl chloride (RPVC) is studied. The relationship between the shear stress at the screw wall and the slip velocity of the flowing melt obeys Navier’s linear law. At zero pressure difference between the entrance and exit of the melting section of twin-screw extruder, the volumetric flow rate and 3D isothermal flow fields of RPVC are calculated under different wall slip conditions in the metering section of the twin-screw extruder by using the evolution technique in POLYFLOW. The results show that when the slip coefficient is smaller than 104Pa*s/m , the volumetric flow rate of the melt is constant, corresponding to the full slip condition. When the slip coefficient is larger than 104Pa*s/m , with the slip coefficient decreasing, the volumetric flow rate and viscosity increase, but the gradients of velocity, pressure, and shear rate decrease. The residual stress of the product is thus reduced. Therefore, increasing wall slip is good for the stability of polymer extrusion and the product quality. The dispersive and the distributive mixing of the twin-screw extruder under full slip and no slip conditions are also studied. Results show that the mixing performance under no-slip condition is better than under full-slip condition, but slip at the wall is good for the extrusion of heat-sensitive materials.

scholarly journals Influence of Slip Condition on Unsteady Free Convection Flow of Viscous Fluid with Ramped Wall Temperature

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Sami Ul Haq ◽  
Ilyas Khan ◽  
Farhad Ali ◽  
Arshad Khan ◽  
Tarek Nabil Ahmed Abdelhameed
Keyword(s):  
Heat Transfer ◽  
Free Convection ◽  
Viscous Fluid ◽  
Wall Temperature ◽  
Wall Slip ◽  
Slip Condition ◽  
Convection Flow ◽  
Slip Parameter ◽  
Free Convection Flow ◽  
Laplace Transform Technique

The objective of this study is to explore the influence of wall slip condition on a free convection flow of an incompressible viscous fluid with heat transfer and ramped wall temperature. Exact solution of the problem is obtained by using Laplace transform technique. Graphical results to see the effects of Prandtl number Pr, timet, and slip parameterηon velocity and skin friction for the case of ramped and constant temperature of the plate are provided and discussed.

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