Journal articles: 'Weissenberg number'

1

Hao, Jian, and Tsorng-Whay Pan. "Simulation for high Weissenberg number." Applied Mathematics Letters 20, no. 9 (September 2007): 988–93. http://dx.doi.org/10.1016/j.aml.2006.12.003.

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2

Keunings, Roland. "On the high Weissenberg number problem." Journal of Non-Newtonian Fluid Mechanics 20 (January 1986): 209–26. http://dx.doi.org/10.1016/0377-0257(86)80022-2.

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Evans, J. D. "Re-entrant corner flows of upper convected Maxwell fluids: the small and high Weissenberg number limits." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2076 (July 21, 2006): 3749–74. http://dx.doi.org/10.1098/rspa.2006.1737.

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We discuss here the steady planar flow of the upper convected Maxwell fluid at re-entrant corners in the singular limits of small and large Weissenberg number. The Weissenberg number is a parameter representing the dimensionless relaxation time and hence the elasticity of the fluid. Its value determines the strength of the fluid memory and thus the influence of elastic effects over viscosity. The small Weissenberg limit is that in which the elastic effects are small and the fluid's memory is weak. It is an extremely singular limit in which the behaviour of a Newtonian fluid is obtained in a main core region away from the corner and walls. Elastic effects are confined to boundary layers at the walls and core regions nearer to the corner. The actual asymptotic structure comprises a complicated four-region structure. The other limit of interest is the large Weissenberg limit (or high Weissenberg number problem) in which the elastic effects now dominate in the main regions of the flow. We explain how the transition in solution from Weissenberg order 1 flows to high Weissenberg flows is achieved, with the singularity in the stress field at the corner remaining the same but its effects now extending over larger length-scales. Implicit in this analysis is the absence of a lip vortex. We also show (for the main core region) that there is a small reduction in the velocity field at the corner and walls where it becomes smoother. This high Weissenberg number limit has a six-region local asymptotic structure and comment is made on its relevance to the case in which a lip vortex is present.

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Lin, Che-Yu, and Chao-An Lin. "Direct Numerical Simulations of Turbulent Channel Flow With Polymer Additives." Journal of Mechanics 36, no. 5 (August 6, 2020): 691–98. http://dx.doi.org/10.1017/jmech.2020.34.

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ABSTRACTDirect numerical simulations have been applied to simulate flows with polymer additives. FENE-P (finite-extensible-nonlinear-elastic-Peterlin) dumbbell model solving for the conformation tensor is adopted to investigate the influence of the polymer on the flowfield. Boundary treatments of the conformation tensor on the flowfield are examined first, where boundary condition based on the linear extrapolation scheme provides more accurate results with second-order accurate error norms. Further simulations of the turbulent channel flow at different Weissenberg numbers are also conducted to investigate the influence on drag reduction. Drag reduction increases in tandem with the increase of Weissenberg number and the increase saturates at Weτ~200, where the drag reduction is close to the maximum drag reduction (MDR) limit. At the regime of y+ > 5, the viscous layer thickens with the increase of the Weissenberg number showing a departure from the traditional log-law profile, and the velocity profiles approach the MDR line at high Weissenberg number. The Reynolds stress decreases in tandem with the increase of Weτ, whereas the levels of laminar stress and polymer stress act adversely. However, as the Weissenberg number increases, the proportion of the laminar stress in the total stress increases, and this contributes to the drag reduction of the polymer flow.

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Yu, Zhaosheng, Peng Wang, Jianzhong Lin, and Howard H. Hu. "Equilibrium positions of the elasto-inertial particle migration in rectangular channel flow of Oldroyd-B viscoelastic fluids." Journal of Fluid Mechanics 868 (April 11, 2019): 316–40. http://dx.doi.org/10.1017/jfm.2019.188.

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In this paper, the lateral migration of a neutrally buoyant spherical particle in the pressure-driven rectangular channel flow of an Oldroyd-B fluid is numerically investigated with a fictitious domain method. The aspect ratio of the channel cross-section considered is 1 and 2, respectively. The particle lateral motion trajectories are shown for the bulk Reynolds number ranging from 1 to 100, the ratio of the solvent viscosity to the total viscosity being 0.5, and a Weissenberg number up to 1.5. Our results indicate that the lateral equilibrium positions located on the cross-section midline, diagonal line, corner and channel centreline occur successively as the fluid elasticity is increased, for particle migration in square channel flow with finite fluid inertia. The transition of the equilibrium position depends strongly on the elasticity number (the ratio of the Weissenberg number to the Reynolds number) and weakly on the Reynolds number. The diagonal-line equilibrium position occurs at an elasticity number ranging from roughly 0.001 to 0.02, and can coexist with the midline and corner equilibrium positions. When the fluid inertia is negligibly small, particles migrate towards the channel centreline, or the closest corner, depending on their initial positions and the Weissenberg number, and the corner attractive area first increases and then decreases as the Weissenberg number increases. For particle migration in a rectangular channel with an aspect ratio of 2, the transition of the equilibrium position from the midline, ‘diagonal line’ (the line where two lateral shear rates are equal to each other), off-centre long midline and channel centreline takes place as the Weissenberg number increases at moderate Reynolds numbers. An off-centre equilibrium position on the long midline is observed for a large blockage ratio of 0.3 (i.e. the ratio of the particle diameter to the channel height is 0.3) at a low Reynolds number. This off-centre migration is driven by shear forces, unlike the elasticity-induced rapid inward migration, which is driven by the normal force (pressure or first normal stress difference).

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Miller, Joel C., and J. M. Rallison. "Instability of coextruded elastic liquids at high Weissenberg number." Journal of Non-Newtonian Fluid Mechanics 143, no. 2-3 (May 2007): 88–106. http://dx.doi.org/10.1016/j.jnnfm.2007.01.008.

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Lee, Daewoong, and Kyung Hyun Ahn. "Time–Weissenberg number superposition in planar contraction microchannel flows." Journal of Non-Newtonian Fluid Mechanics 210 (August 2014): 41–46. http://dx.doi.org/10.1016/j.jnnfm.2014.05.004.

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8

GOTO, Ikuhisa, Hikaru WAKI, Shuichi IWATA, Hideki MORI, and Tsutomu ARAGAKI. "Numerical analysis of viscoelastic flow at high Weissenberg number." Proceedings of the Fluids engineering conference 2000 (2000): 155. http://dx.doi.org/10.1299/jsmefed.2000.155.

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9

Huo, Xiaokai, and Wen-An Yong. "Global existence for viscoelastic fluids with infinite Weissenberg number." Communications in Mathematical Sciences 15, no. 4 (2017): 1129–40. http://dx.doi.org/10.4310/cms.2017.v15.n4.a10.

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10

Trebotich, David. "Toward a solution to the high Weissenberg number problem." PAMM 7, no. 1 (December 2007): 2100073–74. http://dx.doi.org/10.1002/pamm.200700989.

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11

Evans, J. D. "High Weissenberg number boundary layer structures for UCM fluids." Applied Mathematics and Computation 387 (December 2020): 124952. http://dx.doi.org/10.1016/j.amc.2019.124952.

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12

Ijaz Khan, M., and Faris Alzahrani. "Activation energy and binary chemical reaction effect in nonlinear thermal radiative stagnation point flow of Walter-B nanofluid: Numerical computations." International Journal of Modern Physics B 34, no. 13 (May 20, 2020): 2050132. http://dx.doi.org/10.1142/s0217979220501325.

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This paper examines nonlinear thermal radiative stagnation point flow of Walter-B nanofluid. The characteristics of nanofluid are explored using Brownian motion and thermophoresis effects. In the presence of uniform magnetic field, fluid is conducting electrically. Furthermore, phenomena of mass and heat transfer are studied by implementing the effects of chemical reaction, Joule heating and activation energy. Outcomes of distinct variables such as induced magnetic parameter, Eckert number, thermal radiation parameter, Weissenberg number, ratio of rate constant, heat capacity ratio, thermal Biot number, solutal Biot number, Prandtl number, heat generation parameter, Schmidt number on concentration, temperature and velocity distributions are explored. The numerical method is implemented to solve the governing flow expression. Further, Sherwood number, Nusselt number and skin friction coefficient are analyzed and discussed in tables. Weissenberg number have opposite behavior on velocity field while it increases for larger values of mixed convection parameter. Temperature of the fluid rises for higher values of thermal Biot number, thermophoresis diffusion coefficient, heat generation parameter and Eckert number Activation energy parameter and Weissenberg number have direct relation with concentration field.

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Zhang, Wu, Zihuang Wang, Meng Zhang, Jiahan Lin, Weiqian Chen, Yuhong Hu, and Shuzhou Li. "Flow Direction-Dependent Elastic Instability in a Symmetry-Breaking Microchannel." Micromachines 12, no. 10 (September 23, 2021): 1139. http://dx.doi.org/10.3390/mi12101139.

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This paper reports flow direction-dependent elastic instability in a symmetry-breaking microchannel. The microchannel consisted of a square chamber and a nozzle structure. A viscoelastic polyacrylamide solution was used for the instability demonstration. The instability was realized as the viscoelastic flow became asymmetric and unsteady in the microchannel when the flow exceeded a critical Weissenberg number. The critical Weissenberg number was found to be different for the forward-directed flow and the backward-directed flow in the microchannel.

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STOKES, JASON R., LACHLAN J. W. GRAHAM, NICK J. LAWSON, and DAVID V. BOGER. "Swirling flow of viscoelastic fluids. Part 2. Elastic effects." Journal of Fluid Mechanics 429 (February 25, 2001): 117–53. http://dx.doi.org/10.1017/s0022112000002901.

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A torsionally driven cavity has been used to examine the influence of elasticity on the swirling flow of constant-viscosity elastic liquids (Boger fluids). A wealth of phenomena is observed as the degree of inertia, elasticity and viscous forces are varied by using a range of low- to high-viscosity flexible polyacrylamide Boger fluids and a semi-rigid xanthan gum Boger fluid. As the inertia is decreased and elasticity increased by using polyacrylamide Boger fluids, the circulation rates for a ‘Newtonian-like’ secondary flow decreases until flow reversal occurs owing to the increasing magnitude of the primary normal stress difference. For each polyacrylamide fluid, the flow becomes highly unstable at a critical combination of Reynolds number and Weissenberg number resulting in a new time-dependent elastic instability. Each fluid is characterized by a dimensionless elasticity number and a correlation with Reynolds number is found for the occurrence of the instability. In the elasticity dominated flow of the polyacrylamide Boger fluids, the instability disrupts the flow dramatically and causes an increase in the peak axial velocity along the central axis by as much as 400%. In this case, the core vortex spirals with the primary motion of fluid and is observed in some cases at Reynolds numbers much less than unity. Elastic ‘reverse’ flow is observed for the xanthan gum Boger fluid at high Weissenberg number. As the Weissenberg number decreases, and Reynolds number increases, counter-rotating vortices flowing in the inertial direction form on the rotating lid. The peak axial velocity decreases for the xanthan gum Boger fluid with decreasing Weissenberg number. In addition, several constitutive models are used to describe accurately the rheological properties of the fluids used in this work in shear and extensional flow. This experimental investigation of a complex three-dimensional flow using well-characterized fluids provides the information necessary for the validation of non-Newtonian constitutive models through numerical analysis of the torsionally driven cavity flow.

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Nagendra, N., CH Amanulla, M. Sudhakar Reddy, and V. Ramachandra Prasad. "Hydromagnetic Flow of Heat and Mass Transfer in a Nano Williamson Fluid Past a Vertical Plate With Thermal and Momentum Slip Effects: Numerical Study." Nonlinear Engineering 8, no. 1 (January 28, 2019): 127–44. http://dx.doi.org/10.1515/nleng-2017-0057.

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Abstract In this article, the study of heat, momentum and mass (species) transfer in an electro-conductive polymer on the external surface of a vertical plate. The effects of Brownian motion and thermophoresis are incorporated in the model in the presence of both heat and nanoparticle mass transfer convective conditions. The Williamson viscoelastic model is employed which is representative of certain industrial polymers. The non-dimensional, transformed boundary layer equations for momentum and energy are solved with the second order accurate implicit Keller box finite difference method under appropriate boundary conditions. The influence of Weissenberg number, magnetic body force parameter, thermal slip parameter, hydrodynamic slip parameter, stream wise variable and Prandtl number on thermo fluid characteristics are presented graphically and discussed. A weak elevation in temperature accompanies increasing Weissenberg number whereas a significant acceleration in the flow is computed near the plate surface. Rate of heat transfer is reduced with increases the Weissenberg number. The study is relevant to enrobing processes for electric-conductive nano-materials, of potential use in aerospace, smart coating transport phenomena and other industries.

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16

Mohamadali, Meysam, and Nariman Ashrafi. "Similarity Solution for High Weissenberg Number Flow of Upper-Convected Maxwell Fluid on a Linearly Stretching Sheet." Journal of Engineering 2016 (2016): 1–10. http://dx.doi.org/10.1155/2016/9718786.

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High Weissenberg boundary layer flow of viscoelastic fluids on a stretching surface has been studied. The flow is considered to be steady, low inertial, and two-dimensional. Upon proper scaling and by means of an exact similarity transformation, the nonlinear momentum and constitutive equations of each layer transform into the respective system of highly nonlinear and coupled ordinary differential equations. Numerical solutions to the resulting boundary value problem are obtained using an efficient shooting technique in conjunction with a variable stepping method for different values of pressure gradients. It is observed that, unlike the Newtonian flows, in order to maintain a potential flow, normal stresses must inevitably develop. The velocity field and stresses distributions over plate are presented for difference values of pressure gradient and Weissenberg numbers.

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17

Sobh, Ayman Mahmoud. "Slip flow in peristaltic transport of a Carreau fluid in an asymmetric channel." Canadian Journal of Physics 87, no. 8 (August 2009): 957–65. http://dx.doi.org/10.1139/p09-027.

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In this paper, peristaltic transport of a Carreau fluid in an asymmetric channel is studied theoretically under zero Reynolds number and long-wavelength approximation for both slip and no-slip flow (Kn = 0). The problem is analyzed using a perturbation expansion in terms of the Weissenberg number as a parameter. Analytic forms for the axial velocity component and the pressure gradient are obtained to second order. The pressure rise is computed numerically and explained graphically. Moreover, the effects of the slip parameter, Weissenberg number, power-law index, and phase difference on the pressure gradient, the axial velocity, and the trapping phenomena have been discussed.

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18

Renardy, Michael. "High weissenberg number boundary layers for the upper convected Maxwell fluid." Journal of Non-Newtonian Fluid Mechanics 68, no. 1 (January 1997): 125–32. http://dx.doi.org/10.1016/s0377-0257(96)01491-7.

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19

Ervin, Vincent J., and Hyesuk Lee. "Defect correction method for viscoelastic fluid flows at high Weissenberg number." Numerical Methods for Partial Differential Equations 22, no. 1 (2005): 145–64. http://dx.doi.org/10.1002/num.20090.

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20

Tsai, Tai-Ping, and David S. Malkus. "Numerical breakdown at high Weissenberg number in non-Newtonian contraction flows." Rheologica Acta 39, no. 1 (January 14, 2000): 62–70. http://dx.doi.org/10.1007/s003970050007.

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21

Di Iorio, Elena, Pierangelo Marcati, and Stefano Spirito. "Splash Singularities for a General Oldroyd Model with Finite Weissenberg Number." Archive for Rational Mechanics and Analysis 235, no. 3 (October 22, 2019): 1589–660. http://dx.doi.org/10.1007/s00205-019-01451-z.

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22

Hussain, Azad, Aysha Rehman, Sohail Nadeem, M. Y. Malik, Alibek Issakhov, Lubna Sarwar, and Shafiq Hussain. "A Combined Convection Carreau–Yasuda Nanofluid Model over a Convective Heated Surface near a Stagnation Point: A Numerical Study." Mathematical Problems in Engineering 2021 (April 3, 2021): 1–14. http://dx.doi.org/10.1155/2021/6665743.

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The focus of this manuscript is on two-dimensional mixed convection non-Newtonian nanofluid flow near stagnation point over a stretched surface with convectively heated boundary conditions. The modeled equation representing nonlinear flow is transformed into a system of ordinary differential equations by implementing appropriate similarity transformations. The generated structure is numerically solved by applying the bvp4c method. Consequences of various involved parameters, e.g., stretching parameter, mixed convection parameter, thermophoresis parameter, Brownian movement parameter, Lewis number, Weissenberg number, Prandtl number, Biot number, buoyancy ratio parameter, mass and heat transport rates on temperature and velocity, the stretched surface, and nanoparticle concentration patterns are analyzed. Outcomes are shown graphically and displayed in tables. Velocity fluctuations are responded to by growing parameters of mixed convection and Weissenberg number. Concentration and thermal fields are also discovered for the Prandtl number. There are also flow line diagrams to analyze the behavior.

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23

Bielça Silva, Luciene Aparecida, and Messias Meneguette. "Log-Conformation Representation of Hiperbolic Conservation Laws with Source Term." TEMA (São Carlos) 15, no. 3 (January 27, 2014): 293. http://dx.doi.org/10.5540/tema.2014.015.03.0293.

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<pre>The objective of this work is to study, through a simpler equation, the statement that the numerical instability associated to the high number of Weissenberg in equations with source term can be resolved by the use of the so called logarithmic representation conformation. We will focus on hyperbolic conservation laws, but more specifically on the advection equation with source term. The source term imposes a necessity of an elastic balance, as well as the CFL convective balance for stability. We will see that the representation of such equation by log-conformation removes the restriction of stability inherent to the elastic balance pointed out by [3] as the cause of high Weissenberg number problem (HWNP).</pre>

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Henry, Christopher K., Giuseppe R. Palmese, and Nicolas J. Alvarez. "The evolution of crystalline structures during gel spinning of ultra-high molecular weight polyethylene fibers." Soft Matter 14, no. 44 (2018): 8974–85. http://dx.doi.org/10.1039/c8sm01597j.

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The Weissenberg number during gel spinning controls the crystalline morphology of the as spun UHMWPE fiber. The final drawn crystalline morphology strongly depends on the starting as-spun crystalline structure.

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Khan, Mohd Bilal, and C. Sasmal. "Effect of chain scission on flow characteristics of wormlike micellar solutions past a confined microfluidic cylinder: a numerical analysis." Soft Matter 16, no. 22 (2020): 5261–72. http://dx.doi.org/10.1039/d0sm00407c.

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26

Renardy, Michael. "On the high Weissenberg number limit of the upper convected Maxwell fluid." Journal of Non-Newtonian Fluid Mechanics 165, no. 1-2 (January 2010): 70–74. http://dx.doi.org/10.1016/j.jnnfm.2009.10.001.

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27

Phan-Thien, N. "Squeezing of an Oldroyd-B fluid from a tube: Limiting Weissenberg number." Rheologica Acta 24, no. 1 (January 1985): 15–21. http://dx.doi.org/10.1007/bf01329258.

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28

Elshehawey, Elsayed F., and Ayman M. F. Sobh. "Peristaltic viscoelastic fluid motion in a tube." International Journal of Mathematics and Mathematical Sciences 26, no. 1 (2001): 21–34. http://dx.doi.org/10.1155/s0161171201003556.

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Peristaltic motion of viscoelastic incompressible fluid in an axisymmetric tube with a sinusoidal wave is studied theoretically in the case that the radius of the tube is small relative to the wavelength. Oldroyd flow has been considered in this study and the problem is formulated and analyzed using a perturbation expansion in terms of the variation of the wave number. This analysis can model the chyme movement in the small intestine by considering the chyme as an Oldroyd fluid. We found out that the pumping rate of Oldroyd fluid is less than that for a Newtonian fluid. Further, the effects of Reynolds number, Weissenberg number, amplitude ratio and wave number on the pressure rise and friction force have been discussed. It is found that the pressure rise does not depend on Weissenberg number at a certain value of flow rate. The results are studied for various values of the physical parameters of interest.

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Hayat, T., Y. Wang, A. M. Siddiqui, and K. Hutter. "Peristaltic motion of a Johnson-Segalman fluid in a planar channel." Mathematical Problems in Engineering 2003, no. 1 (2003): 1–23. http://dx.doi.org/10.1155/s1024123x03308014.

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This paper is devoted to the study of the two-dimensional flow of a Johnson-Segalman fluid in a planar channel having walls that are transversely displaced by an infinite, harmonic travelling wave of large wavelength. Both analytical and numerical solutions are presented. The analysis for the analytical solution is carried out for small Weissenberg numbers. (A Weissenberg number is the ratio of the relaxation time of the fluid to a characteristic time associated with the flow.) Analytical solutions have been obtained for the stream function from which the relations of the velocity and the longitudinal pressure gradient have been derived. The expression of the pressure rise over a wavelength has also been determined. Numerical computations are performed and compared to the perturbation analysis. Several limiting situations with their implications can be examined from the presented analysis.

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Khan, Masood, Mehwish Manzur, and Masood Rahman. "Boundary-layer flow and heat transfer of cross fluid over a stretching sheet." Thermal Science 23, no. 1 (2019): 307–18. http://dx.doi.org/10.2298/tsci160919111k.

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The current study is a pioneering work in presenting the boundary-layer equations for the 2-D flow and heat transfer of the Cross fluid over a linearly stretching sheet. The system of PDE is turned down into highly non-linear ODE by applying suitable similarity transformations. The stretching sheet solutions are presented via. a numerical technique namely the shooting method and graphs are constructed. The impact of the emerging parameters namely the power-law index, n, the local Weissenberg number, We, and the Prandtl number on the velocity and temperature fields are investigated through graphs. The numerical values of the local skin friction coefficient and the local Nusselt number are also presented in tabular form. Additionally, the graphs are sketched for the local skin friction coefficient and the local Nusselt number. It is observed that with growing values of the local Weissenberg number the velocity profiles exhibited a decreasing trend while opposite behavior is seen for the temperature field. Further, comparisons are made with previously available literature for some limiting cases and an excellent agreement is achieved.

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31

Hayat, T., Naheed Batool, H. Yasmin, A. Alsaedi, and M. Ayub. "Peristaltic flow of Williamson fluid in a convected walls channel with Soret and Dufour effects." International Journal of Biomathematics 09, no. 01 (November 2, 2015): 1650012. http://dx.doi.org/10.1142/s1793524516500121.

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Peristaltic flow of magnetohydrodynamic (MHD) Williamson fluid in a symmetric channel is addressed. Modeling is given with Soret and Dufour effects. Channel walls have compliant properties. Analysis has been carried out through long wavelength and low Reynolds number approach. The obtained series solutions for small Weissenberg number are developed. Impact of variables reflecting the salient features of wall properties, Biot numbers and Soret and Dufour on the velocity, temperature and concentration has been point out. Trapping phenomenon is also analyzed.

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Zaman, Akbar, M. Sajid, and Nabeela Kousar. "Biomedical study of effects nanoparticles on unsteady blood (non-Newtonian) flow through a catheterized stenotic vessel." Canadian Journal of Physics 97, no. 5 (May 2019): 487–97. http://dx.doi.org/10.1139/cjp-2018-0376.

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The purpose of this article is to theoretically discuss the unsteady hemo-dynamics of blood through a catheterized overlapping stenotic vessel with nanoparticles. The nature of the blood is characterized by the constitutive Cross model equation. This study is conducted under the assumption of mild stenotic conditions and the equations of momentum and temperature are simplified after making this assumption. Explicit finite difference method is employed to obtain the numerical results of the governing equations. Results for different values of emerging parameters, such as Weissenberg number, Lewis number, thermophoresis parameter, and Brownian motion parameter are shown at different locations of an arterial cross section. These results demonstrate a pictorial way to comprehend the theoretical biomedical problem. These results reveal that Lewis number (Le) and visco-elastic parameter Weissenberg number (We) both are decreasing functions of velocity profiles at each arterial cross section. Furthermore, it is also noted that the thermophoresis parameter (Nt) quantitatively decreases the flow of blood inside the vessel while the Brownian motion parameter (Nb) shows the opposite effects on blood flow; it increases the magnitude of velocity.

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Renardy, Michael. "The high Weissenberg number limit of the UCM model and the Euler equations." Journal of Non-Newtonian Fluid Mechanics 69, no. 2-3 (April 1997): 293–301. http://dx.doi.org/10.1016/s0377-0257(96)01544-3.

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34

Zheng, R., N. Phan-Thien, and R. I. Tanner. "On the flow past a sphere in a cylindrical tube: Limiting Weissenberg number." Journal of Non-Newtonian Fluid Mechanics 36 (December 1990): 27–49. http://dx.doi.org/10.1016/0377-0257(90)85002-g.

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35

Belan, S., A. Chernykh, and V. Lebedev. "Boundary layer of elastic turbulence." Journal of Fluid Mechanics 855 (September 21, 2018): 910–21. http://dx.doi.org/10.1017/jfm.2018.662.

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We investigate theoretically the near-wall region in elastic turbulence of a dilute polymer solution in the limit of large Weissenberg number. As has been established experimentally, elastic turbulence possesses a boundary layer where the fluid velocity field can be approximated by a steady shear flow with relatively small fluctuations on the top of it. Assuming that at the bottom of the boundary layer the dissolved polymers can be considered as passive objects, we examine analytically and numerically the statistics of the polymer conformation, which is highly non-uniform in the wall-normal direction. Next, imposing the condition that the passive regime terminates at the border of the boundary layer, we obtain an estimate for the ratio of the mean flow to the magnitude of the flow fluctuations. This ratio is determined by the polymer concentration, the radius of gyration of polymers and their length in the fully extended state. The results of our asymptotic analysis reproduce the qualitative features of elastic turbulence at finite Weissenberg numbers.

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GRAHAM, M. D. "Effect of axial flow on viscoelastic Taylor–Couette instability." Journal of Fluid Mechanics 360 (April 10, 1998): 341–74. http://dx.doi.org/10.1017/s0022112098008611.

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Viscoelastic flow instabilities can arise from gradients in elastic stresses in flows with curved streamlines. Circular Couette flow displays the prototypical instability of this type, when the azimuthal Weissenberg number Weθ is O(ε−1/2), where ε measures the streamline curvature. We consider here the effect of superimposed steady axial Couette or Poiseuille flow on this instability. For inertialess flow of an upper-convected Maxwell or Oldroyd-B fluid in the narrow gap limit (ε[Lt ]1), the analysis predicts that the addition of a relatively weak steady axial Couette flow (axial Weissenberg number Wez=O(1)) can delay the onset of instability until Weθ is significantly higher than without axial flow. Weakly nonlinear analysis shows that these bifurcations are subcritical. The numerical results are consistent with a scaling analysis for Wez[Gt ]1, which shows that the critical azimuthal Weissenberg number for instability increases linearly with Wez. Non-axisymmetric disturbances are very strongly suppressed, becoming unstable only when ε1/2Weθ= O(We2z). A similar, but smaller, stabilizing effect occurs if steady axial Poiseuille flow is added. In this case, however, the bifurcations are converted from subcritical to supercritical as Wez increases. The observed stabilization is due to the axial stresses introduced by the axial flow, which overshadow the destabilizing hoop stress. If only a weak (Wez[les ]1) steady axial flow is added, the flow is actually slightly destabilized. The analysis also elucidates new aspects of the stability problems for plane shear flows, including the exact structure of the modes in the continuous spectrum, and illustrates the connection between these problems and the viscoelastic circular Couette flow.

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Sankar, D. S. "Perturbation analysis for pulsatile flow of Carreau fluid through tapered stenotic arteries." International Journal of Biomathematics 09, no. 04 (April 22, 2016): 1650063. http://dx.doi.org/10.1142/s1793524516500637.

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The pulsatile flow of blood in a tapered narrow artery with overlapping time-dependent stenosis is mathematically analyzed, modeling blood as Carreau fluid. Perturbation method is employed for solving the resulting nonlinear system of equations along with the appropriate boundary conditions. The analytic solutions to the pressure gradient, velocity distribution, flow rate, wall shear stress and longitudinal impedance to flow are obtained in the asymptotic form. The variation of the aforesaid flow quantities with respect to various physical parameters such as maximum depth of the stenosis, angle of tapering of the artery, power law index, Reynolds number, pulsatile amplitude of the flow and Weissenberg number is investigated. It is found that the wall shear stress and longitudinal impedance to flow increase with the increase of the angle of tapering of the artery, the maximum depth of the stenosis and pulsatile Reynolds number and these decrease with the increase of the amplitude of the flow, power law index and Weissenberg number. The mean velocity of blood decreases significantly with the increase of the artery radius, maximum depth of the stenosis, angle of tapering of the artery.

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38

Ali, Hashim, and Masood Khan. "Impact of heat transfer analysis on Carreau fluid-flow past a static/moving wedge." Thermal Science 22, no. 2 (2018): 809–20. http://dx.doi.org/10.2298/tsci160115169a.

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The foremost aspiration of the present endeavor is to investigate the boundary-layer flow of a generalized Newtonian Carreau fluid model past a static/moving wedge. In addition, the effects of heat transfer on the flow field are also taken into account. The governing equations of the problem based on the boundary-layer approximation are changed into a non-dimensional structure by introducing the local similarity transformations. The subsequent system of ODE has been numerically integrated with fifth-order Runge-Kutta method. Influence of the velocity ratio parameter, the wedge angle parameter, the Weissenberg number, the power law index, and the Prandtl number on the skin friction and Nusselt number are analyzed. The variation of the skin friction as well as other flow characteristics has been presented graphically to capture the influence of these parameters. The results indicate that the increasing value of the wedge angle substantially accelerates the fluid velocity while an opposite behavior is noticed in the temperature field. Moreover, the skin friction coefficient for the growing Weissenberg number significantly enhances for the shear thickening fluid and show the opposite behavior of shear thinning fluid. However, the local Nusselt number has greater values in the case of moving wedge. An excellent comparison with previously published works in various special cases has been made.

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39

Kim, Ju Min, Changkwon Chung, Kyung Hyun Ahn, and Seung Jong Lee. "Time-Weissenberg Number Superposition in 4:1 Planar Contraction Flow of a Viscoelastic Fluid." Nihon Reoroji Gakkaishi 33, no. 4 (2005): 191–97. http://dx.doi.org/10.1678/rheology.33.191.

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King, J. R. C., and S. J. Lind. "High Weissenberg number simulations with incompressible Smoothed Particle Hydrodynamics and the log-conformation formulation." Journal of Non-Newtonian Fluid Mechanics 293 (July 2021): 104556. http://dx.doi.org/10.1016/j.jnnfm.2021.104556.

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Rusak, Zvi, Nguyen Ly, John A. Tichy, and Shixiao Wang. "Near-critical swirling flow of a viscoelastic fluid in a circular pipe." Journal of Fluid Mechanics 814 (February 6, 2017): 325–60. http://dx.doi.org/10.1017/jfm.2017.16.

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The interaction between flow inertia and elasticity in high-Reynolds-number, axisymmetric and near-critical swirling flows of an incompressible and viscoelastic fluid in an open finite-length straight circular pipe is studied at the limit of low elasticity. The stresses of the viscoelastic fluid are described by the generalized Giesekus constitutive model. This model helps to focus the analysis on low fluid elastic effects with shear thinning of the viscosity. The application of the Giesekus model to columnar streamwise vortices is first investigated. Then, a nonlinear small-disturbance analysis is developed from the governing equations of motion. It reveals the complicated interactions between flow inertia, swirl and fluid rheology. An effective Reynolds number that links between steady states of swirling flows of a viscoelastic fluid and those of a Newtonian fluid is revealed. The effects of the fluid viscosity, relaxation time, retardation time and mobility parameter on the flow development in the pipe and on the critical swirl for the appearance of vortex breakdown are explored. It is found that in vortex flows with either an axial jet or an axial wake profile, increasing the shear thinning by decreasing the ratio of the viscoelastic characteristic times from one (with fixed values of the Weissenberg number and the mobility parameter) increases the critical swirl ratio for breakdown. Increasing the fluid elasticity by increasing the Weissenberg number from zero (with a fixed ratio of the viscoelastic characteristic times and a fixed value of the mobility parameter) or increasing the fluid mobility parameter from zero (with fixed values of the Weissenberg number and the ratio of viscoelastic times) causes a similar effect. The results may explain the trend of changes in the appearance of breakdown zones as a function of swirl level that were observed in the experiments by Stokes et al. (J. Fluid Mech., vol. 429, 2001, pp. 67–115), where Boger fluids were used. This work extends for the first time the theory of vortex breakdown to include effects of non-Newtonian fluids.

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Ahmad, Riaz, Asma Farooqi, Rashada Farooqi, Nawaf N. Hamadneh, Md Fayz-Al-Asad, Ilyas Khan, Muhammad Sajid, Ghulam Bary, and Muhammad Farooq Saleem Khan. "An Analytical Approach to Study the Blood Flow over a Nonlinear Tapering Stenosed Artery in Flow of Carreau Fluid Model." Complexity 2021 (July 29, 2021): 1–11. http://dx.doi.org/10.1155/2021/9921642.

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The current study provides an analytical approach to analyze the blood flow through a stenosed artery by using the Carreau fluid model. The flow governing equations are derived under the consideration of mild stenosis. Mathematical analysis has been carried out by considering the blood as non-Newtonian nature. Then, the analytical solution has been investigated by using the regular perturbation technique. The solutions obtained by this perturbation are up to the second-order in dimensionless Weissenberg number We . The performed computations of various parameter values such as velocity, wall shear stress, shear stress, and resistance impedance at the stenotic throat are discussed in detail for different values of Weissenberg number We . The obtained results demonstrate that for shear-thinning fluid, the fluid velocity increases with the increasing parameter m while opposite behavior is observed with the increase in We . Hence, the presented numerical analysis reveals many aspects of the flow by considering the blood as a non-Newtonian Carreau fluid model, and the presented model can be equally applicable to other bio-mathematical studies.

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Hina, Sadia, Tasawar Hayat, and Saleem Asghar. "Peristaltic transport of Johnson–Segalman fluid in a curved channel with compliant walls." Nonlinear Analysis: Modelling and Control 17, no. 3 (July 25, 2012): 297–311. http://dx.doi.org/10.15388/na.17.3.14057.

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The present investigation deals with the peristaltic flow of an incompressible Johnson–Segalman fluid in a curved channel. Effects of the channel wall properties are taken into account. The associated equations for peristaltic flow in a curved channel are modeled. Mathematical analysis is simplified under long wavelength and low Reynolds number assumptions. The solution expressions are established for small Weissenberg number. Effects of several embedded parameters on the flow quantities are discussed.

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Khan, Shahid, Mahmoud M. Selim, Aziz Khan, Asad Ullah, Thabet Abdeljawad, Ikramullah, Muhammad Ayaz, and Wali Khan Mashwani. "On the Analysis of the Non-Newtonian Fluid Flow Past a Stretching/Shrinking Permeable Surface with Heat and Mass Transfer." Coatings 11, no. 5 (May 12, 2021): 566. http://dx.doi.org/10.3390/coatings11050566.

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The 3D Carreau fluid flow through a porous and stretching (shrinking) sheet is examined analytically by taking into account the effects of mass transfer, thermal radiation, and Hall current. The model equations, which consist of coupled partial differential equations (PDEs), are simplified to ordinary differential equations (ODEs) through appropriate similarity relations. The analytical procedure of HAM (homotopy analysis method) is employed to solve the coupled set of ODEs. The functional dependence of the hydromagnetic 3D Carreau fluid flow on the pertinent parameters are displayed through various plots. It is found that the x-component of velocity gradient (f′(η)) enhances with the higher values of the Hall and shrinking parameters (m,ϱ), while it reduces with magnetic parameter and Weissenberg number (M,We). The y-component of fluid velocity (g(η)) rises with the augmenting values of m and M, while it drops with the augmenting viscous nature of the Carreau fluid associated with the varying Weissenberg number. The fluid temperature θ(η) enhances with the increasing values of radiation parameter (Rd) and Dufour number (Du), while it drops with the rising Prandtl number (Pr). The concentration field (ϕ(η)) augments with the rising Soret number (Sr) while drops with the augmenting Schmidt number (Sc). The variation of the skin friction coefficients (Cfx and Cfz), Nusselt number (Nux) and Sherwood number (Shx) with changing values of these governing parameters are described through different tables. The present and previous published results agreement validates the applied analytical procedure.

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Hartnett, J. P. "1990 Max Jakob Memorial Award Lecture: Viscoelastic Fluids: A New Challenge in Heat Transfer." Journal of Heat Transfer 114, no. 2 (May 1, 1992): 296–303. http://dx.doi.org/10.1115/1.2911275.

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A review of the current knowledge on the fluid mechanics and heat transfer behavior of viscoelastic aqueous polymer solutions in channel flow is presented. Both turbulent and laminar flow conditions are considered. Although the major emphasis is on fully established circular pipe flow, some results are also reported for flow in a 2:1 rectangular channel. For fully established turbulent channel flow, it was found that the friction factor, f, and the dimensionless heat transfer factor, jH, were functions of the Reynolds number and a dimensionless elasticity value, the Weissenberg number. For Weissenberg values greater than approximately 10 (the critical value) the friction factor was found to be a function only of the Reynolds number; for values less than 10 the friction factor was a function of both Re and Ws. For the dimensionless heat transfer coefficient jH the corresponding critical Weissenberg value was found to be about 100. The heat transfer reduction is always greater than the friction factor reduction; consequently, the heat transfer per unit pumping power decreases with increasing elasticity. For fully established laminar pipe flow of aqueous polymer solutions, the measured values of the friction factor and dimensionless heat transfer coefficient were in excellent agreement with the values predicted for a power law fluid. For laminar flow in a 2:1 rectangular channel the fully developed friction factor measurements were also in agreement with the power law prediction. In contrast, the measured local heat transfer coefficients for aqueous polymer solutions in laminar flow through the 2:1 rectangular duct were two to three times the values predicted for a purely viscous power law fluid. It is hypothesized that these high heat transfer coefficients are due to secondary motions, which come about as a result of the unequal normal stresses occurring in viscoelastic fluids. The anomalous behavior of one particular aqueous polymer solution—namely, polyacrylic acid (Carbopol)—is described in some detail, raising some interesting questions as to how viscoelastic fluids should be classified. In closing, a number of challenging research opportunities in the study of viscoelastic fluids are presented.

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Labropulu, F. "Unsteady Stagnation-Point Flow of a Viscoelastic Fluid in the Presence of a Magnetic Field." International Journal of Mathematics and Mathematical Sciences 2008 (2008): 1–15. http://dx.doi.org/10.1155/2008/573425.

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The unsteady two-dimensional stagnation point flow of the Walters B' fluid impinging on an infinite plate in the presence of a transverse magnetic field is examined and solutions are obtained. It is assumed that the infinite plate aty=0is making harmonic oscillations in its own plane. A finite difference technique is employed and solutions for small and large frequencies of the oscillations are obtained for various values of the Hartmann's number and the Weissenberg number.

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Mahdy, A., and Ali J. Chamkha. "Unsteady MHD boundary layer flow of tangent hyperbolic two-phase nanofluid of moving stretched porous wedge." International Journal of Numerical Methods for Heat & Fluid Flow 28, no. 11 (November 5, 2018): 2567–80. http://dx.doi.org/10.1108/hff-12-2017-0499.

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Purpose The purpose of this paper is to address the thermo-physical impacts of unsteady magneto-hydrodynamic (MHD) boundary layer flow of non-Newtonian tangent hyperbolic nanofluid past a moving stretching wedge. To delineate the nanofluid, the boundary conditions for normal fluxes of the nanoparticle volume fraction are chosen to be vanish. Design/methodology/approach The local similarity transformation is implemented to reformulate the governing PDEs into coupled non-linear ODEs of higher order. Then, numerical solution is obtained for the simplified governing equations with the aid of finite difference technique. Findings Numerical calculations point out that pressure gradient parameter leads to improve all skin friction coefficient, rate of heat transfer and absolute value of rate of nanoparticle concentration. As well as, lager values of Weissenberg number tend to upgrade the skin friction coefficient, while power law index and velocity ratio parameter reduce the skin friction coefficient. Again, the horizontal velocity component enhances with upgrading power law index, unsteadiness parameter, velocity ratio parameter and Darcy number and it reduces with rising values of Weissenberg number. Originality/value A numerical treatment of unsteady MHD boundary layer flow of tangent hyperbolic nanofluid past a moving stretched wedge is obtained. The problem is original.

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TANOUE, Shuichi, Jiro KOGA, Toshihisa KAJIWARA, Yoshiyuki IEMOTO, and Kazumori FUNATSU. "High Weissenberg Number Problem and Numerical Simulation of an Annular Extrudate Swell of Viscoelastic Fluids." Seikei-Kakou 9, no. 10 (1997): 817–24. http://dx.doi.org/10.4325/seikeikakou.9.817.

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Renardy, Michael. "Asymptotic structure of the stress field in flow past a cylinder at high Weissenberg number." Journal of Non-Newtonian Fluid Mechanics 90, no. 1 (April 2000): 13–23. http://dx.doi.org/10.1016/s0377-0257(99)00050-6.

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Fattal, Raanan, and Raz Kupferman. "Time-dependent simulation of viscoelastic flows at high Weissenberg number using the log-conformation representation." Journal of Non-Newtonian Fluid Mechanics 126, no. 1 (February 2005): 23–37. http://dx.doi.org/10.1016/j.jnnfm.2004.12.003.

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Journal articles on the topic 'Weissenberg number'

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