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Journal articles on the topic 'Generalized Newtonian fluids'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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1

Málek, J., and K. R. Rajagopal. "Compressible generalized Newtonian fluids." Zeitschrift für angewandte Mathematik und Physik 61, no. 6 (March 2, 2010): 1097–110. http://dx.doi.org/10.1007/s00033-010-0061-8.

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2

Gagnon, D. A., and P. E. Arratia. "The cost of swimming in generalized Newtonian fluids: experiments with C. elegans." Journal of Fluid Mechanics 800 (July 14, 2016): 753–65. http://dx.doi.org/10.1017/jfm.2016.420.

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Numerous natural processes are contingent on microorganisms’ ability to swim through fluids with non-Newtonian rheology. Here, we use the model organism Caenorhabditis elegans and tracking methods to experimentally investigate the dynamics of undulatory swimming in shear-thinning fluids. Theory and simulation have proposed that the cost of swimming, or mechanical power, should be lower in a shear-thinning fluid compared to a Newtonian fluid of the same zero-shear viscosity. We aim to provide an experimental investigation into the cost of swimming in a shear-thinning fluid from (i) an estimate of the mechanical power of the swimmer and (ii) the viscous dissipation rate of the flow field, which should yield equivalent results for a self-propelled low Reynolds number swimmer. We find the cost of swimming in shear-thinning fluids is less than or equal to the cost of swimming in Newtonian fluids of the same zero-shear viscosity; furthermore, the cost of swimming in shear-thinning fluids scales with a fluid’s effective viscosity and can be predicted using fluid rheology and simple swimming kinematics. Our results agree reasonably well with previous theoretical predictions and provide a framework for understanding the cost of swimming in generalized Newtonian fluids.

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3

Frehse, Jens, and Michael Růžička. "Non-homogeneous generalized Newtonian fluids." Mathematische Zeitschrift 260, no. 2 (November 21, 2007): 355–75. http://dx.doi.org/10.1007/s00209-007-0278-1.

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4

Jamil, Muhammad. "First Problem of Stokes for Generalized Burgers' Fluids." ISRN Mathematical Physics 2012 (March 4, 2012): 1–17. http://dx.doi.org/10.5402/2012/831063.

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The velocity field and the adequate shear stress corresponding to the first problem of Stokes for generalized Burgers’ fluids are determined in simple forms by means of integral transforms. The solutions that have been obtained, presented as a sum of steady and transient solutions, satisfy all imposed initial and boundary conditions. They can be easily reduced to the similar solutions for Burgers, Oldroyd-B, Maxwell, and second-grade and Newtonian fluids. Furthermore, as a check of our calculi, for small values of the corresponding material parameters, their diagrams are almost identical to those corresponding to the known solutions for Newtonian and Oldroyd-B fluids. Finally, the influence of the rheological parameters on the fluid motions, as well as a comparison between models, is graphically illustrated. The non-Newtonian effects disappear in time, and the required time to reach steady-state is the lowest for Newtonian fluids.

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5

Tseng, Huan-Chang. "A revisitation of generalized Newtonian fluids." Journal of Rheology 64, no. 3 (May 2020): 493–504. http://dx.doi.org/10.1122/1.5139198.

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6

Nägele, Philipp, and Michael Růžička. "Generalized Newtonian fluids in moving domains." Journal of Differential Equations 264, no. 2 (January 2018): 835–66. http://dx.doi.org/10.1016/j.jde.2017.09.022.

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7

Diening, Lars, and Michael Růžička. "Strong Solutions for Generalized Newtonian Fluids." Journal of Mathematical Fluid Mechanics 7, no. 3 (June 14, 2005): 413–50. http://dx.doi.org/10.1007/s00021-004-0124-8.

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8

Repin, S. I. "Estimates of Deviations for Generalized Newtonian Fluids." Journal of Mathematical Sciences 123, no. 6 (October 2004): 4621–36. http://dx.doi.org/10.1023/b:joth.0000041479.59584.10.

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9

Arada, Nadir. "On Generalized Newtonian Fluids in Curved Pipes." SIAM Journal on Mathematical Analysis 48, no. 2 (January 2016): 1210–49. http://dx.doi.org/10.1137/140964709.

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10

Apushkinskaya, Darya, Michael Bildhauer, and Martin Fuchs. "Steady States of Anisotropic Generalized Newtonian Fluids." Journal of Mathematical Fluid Mechanics 7, no. 2 (May 2005): 261–97. http://dx.doi.org/10.1007/s00021-004-0118-6.

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11

da Costa Mattos, Heraldo S., and Rodrigo A. C. Dias. "Hyperbolic heat transfer in generalized Newtonian fluids." International Communications in Heat and Mass Transfer 42 (March 2013): 38–42. http://dx.doi.org/10.1016/j.icheatmasstransfer.2012.12.009.

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12

Cui, Jing Wen, Zhi Shang Liu, and Yu Chen Zhang. "Study on the Generalized Darcy's Law for Bingham and Herschel-Bulkley Fluids." Applied Mechanics and Materials 433-435 (October 2013): 1933–36. http://dx.doi.org/10.4028/www.scientific.net/amm.433-435.1933.

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Extra-heavy oil, polymer solution and some drilling fluids are typical non-Newtonian Herschel-Bulkley fluids, which behave as sheer-thinning with yield stress. In this paper, the Generalized Darcy's law for Herschel-Bulkley fluids flow in porous media was formulated, by the same way formulating the Generalized Darcy's Law for Bingham fluids. Then, the applications of the two type flow models were compared; Bingham type model was still widely applied due to its conciseness and relatively satisfied accuracy. In addition, the Generalized Darcys Law was revised to describe thixotropic non-Newtonian fluids conceptually.

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13

Vieru, D., Corina Fetecau, and C. Fetecau. "Unsteady flow of a generalized Oldroyd-B fluid due to an infinite plate subject to a time-dependent shear stress." Canadian Journal of Physics 88, no. 9 (September 2010): 675–87. http://dx.doi.org/10.1139/p10-055.

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The unsteady flow of an incompressible generalized Oldroyd-B fluid induced by an infinite plate subject to a time-dependent shear-stress is studied by means of the Fourier cosine and Laplace transforms. The solutions that have been obtained, written under integral and series form in terms of the generalized Ga,b,c(·,t) functions, are presented as a sum of the Newtonian solutions and the corresponding non-Newtonian contributions. They satisfy all imposed initial and boundary conditions, and for λ and λr → 0 reduce to the Newtonian solutions. Furthermore, the similar solutions for generalized Maxwell fluids as well as those for ordinary fluids are also obtained as limiting cases of general solutions. Finally, to reveal some relevant physical aspects of the obtained results, the diagrams of the velocity field v(y, t) have been depicted against y for different values of t and of the material and fractional parameters.

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14

Doshi, Pankaj, Ronald Suryo, Ozgur E. Yildirim, Gareth H. McKinley, and Osman A. Basaran. "Scaling in pinch-off of generalized Newtonian fluids." Journal of Non-Newtonian Fluid Mechanics 113, no. 1 (July 2003): 1–27. http://dx.doi.org/10.1016/s0377-0257(03)00081-8.

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15

Sauer, Martin. "Kolmogorov equations for randomly perturbed generalized Newtonian fluids." Mathematische Nachrichten 287, no. 17-18 (April 25, 2014): 2102–15. http://dx.doi.org/10.1002/mana.201300148.

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16

Diening, Lars, Andreas Prohl, and Michael Růžička. "Semi‐implicit Euler Scheme for Generalized Newtonian Fluids." SIAM Journal on Numerical Analysis 44, no. 3 (January 2006): 1172–90. http://dx.doi.org/10.1137/050634335.

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17

Jegatheeswaran, Sinthuran, Farhad Ein-Mozaffari, and Jiangning Wu. "Laminar mixing of non-Newtonian fluids in static mixers: process intensification perspective." Reviews in Chemical Engineering 36, no. 3 (April 28, 2020): 423–36. http://dx.doi.org/10.1515/revce-2017-0104.

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AbstractStatic mixers are widely used in various industrial applications to intensify the laminar mixing of non-Newtonian fluids. Non-Newtonian fluids can be categorized into (1) time-independent, (2) time-dependent, and (3) viscoelastic fluids. Computational fluid dynamics studies on the laminar mixing of viscoelastic fluids are very limited due to the complexity in incorporating the multiple relaxation times and the associated stress tensor into the constitutive equations. This review paper provides recommendations for future research studies while summarizing the key research contributions in the field of non-Newtonian fluid mixing using static mixers. This review discusses the different experimental techniques employed such as electrical resistance tomography, magnetic resonance imaging, planar laser-induced fluorescence, and positron emission particle tracking. A comprehensive overview of the mixing fundamentals, fluid chaos, numerical characterization of fluid stretching, development of pressure drop correlations, and derivations of generalized Reynolds number is also provided in this review paper.

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18

Contreras, Verónica Orjuela. "Symbolic Computation of Flows in Porous Medium with Cylindrical Geometry Using Maple." Advanced Materials Research 268-270 (July 2011): 116–22. http://dx.doi.org/10.4028/www.scientific.net/amr.268-270.116.

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The study of the profiles of velocity and fluid flow rate in porous media with cylindrical geometries were made, using Maple, and the results were obtained in terms of the Bessel Functions. Some of them were the generalized forms of the Haugen-Poiseuille Law. The results could be applied to synthetic media such as zeolites. Only newtonian fluids were considered, but it’s possible to consider non newtonian fluids in the future investigations.

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19

Najji, B., B. Bou-Said, and D. Berthe. "New Formulation for Lubrication With Non-Newtonian Fluids." Journal of Tribology 111, no. 1 (January 1, 1989): 29–34. http://dx.doi.org/10.1115/1.3261875.

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A global method for the solution of thermohydrodynamic problems is proposed for the analysis of lubricated contacts with non-newtonian fluids. A set of algebraic equations is obtained after introducing the weak form of the energy equation and a modified generalized equation for thin fluid flows. This last equation represents a new formulation for lubrication with non-newtonian fluids. The establishment of this equation is presented below along with several tests including explicit and implicit rheological laws with some comments on the effect of the different parameters which occur in the study.

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20

Puri, Pratap. "Stability and eigenvalue bounds of the flow of a dipolar fluid between two parallel plates." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, no. 2057 (April 25, 2005): 1401–21. http://dx.doi.org/10.1098/rspa.2004.1434.

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In this article, we derive the Orr–Sommerfeld equation for the stability of parallel flows of a dipolar fluid. The classical results found by Squire, for viscous Newtonian fluids, are generalized to the case of dipolar fluids. A sufficient condition for stability is obtained for dipolar fluids and eigenvalue bounds for the Orr–Sommerfeld equation are found.

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21

Khlifi, M. El, D. Souchet, M. Hajjam, and F. Bouyahia. "Numerical Modeling of Non-Newtonian Fluids in Slider Bearings and Channel Thermohydrodynamic Flow." Journal of Tribology 129, no. 3 (January 19, 2007): 695–99. http://dx.doi.org/10.1115/1.2736732.

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A three-dimensional thermohydrodynamic model is developed to predict non-Newtonian lubricant behavior in slider bearings and channel flow. The generalized Reynolds equation is established using the concept of generalized Newtonian fluids (GNF) and the temperature field is determined with the energy equation. The chosen rheological models are the power-law, Bingham, and Hershel–Bulkley models. The last two models hold uniformly in yielded and unyielded regions using the approach proposed by Papanastasiou. The results present the evolution of the velocity, pressure, and thermal fields. The power loss, load capacity, and friction coefficient are analyzed. Comparisons are made with Newtonian lubricants and other recent non-Newtonian computational analyses.

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22

Li, Chun Rui, and Lian Cun Zheng. "Exact Solutions for the Fractional Time-Dependent Oldroyd-B Fluid Model Subject to a Constantly Accelerated Shear Stress." Applied Mechanics and Materials 518 (February 2014): 114–19. http://dx.doi.org/10.4028/www.scientific.net/amm.518.114.

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In this paper, based on the fractional model, we present an investigation on the couette flow of a generalized Oldroyd-B fluid within an infinite cylinder subject to a time-dependent shear stress which is affected by the internal constantly decelerated pressure gradient. By using the fractional derivatives Laplace and finite Hankel transforms, the obtained solutions for the velocity field and shear stress, written in terms of generalized R function, are presented the similar characteristics with Newtonian and non-Newtonian fluids. Moreover, the effects of various parameters are systematically analyzed.

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23

Keslerová, R., and K. Kozel. "Numerical solution of laminar incompressible generalized Newtonian fluids flow." Applied Mathematics and Computation 217, no. 11 (February 2011): 5125–33. http://dx.doi.org/10.1016/j.amc.2010.07.049.

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24

Bae, Hyeong-Ohk. "Regularity criterion for generalized Newtonian fluids in bounded domains." Journal of Mathematical Analysis and Applications 421, no. 1 (January 2015): 489–500. http://dx.doi.org/10.1016/j.jmaa.2014.06.072.

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25

Keslerová, Radka, Hynek Řezníček, and Tomáš Padělek. "Numerical modelling of generalized Newtonian fluids in bypass tube." Advances in Computational Mathematics 45, no. 4 (May 27, 2019): 2047–63. http://dx.doi.org/10.1007/s10444-019-09684-y.

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26

Bahmani, Alireza, and Hadi Kargarsharifabad. "Magnetohydrodynamic free convection of non-Newtonian power-law fluids over a uniformly heated horizontal plate." Thermal Science 24, no. 2 Part B (2020): 1323–34. http://dx.doi.org/10.2298/tsci190102110b.

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The MHD free convection flow of non-Newtonian power-law fluids over a horizontal plate subjected to a constant heat flux is studied. The results are presented for various values of the three influential parameters, i. e. the generalized Hart?mann number, the generalized Prandtl number, and the non-Newtonian power-law viscosity index. Increasing the Hartmann number increases the thermal boundary-layer thickness and the surface temperature and consequently decreases the wall skin friction and Nusselt number. A lower generalized Prandtl number results in a larger skin friction coefficient and higher wall temperature as well as thicker thermal boundary-layer. The viscosity index is predicted to influence the flow conditions depending on the value of generalized Hartmann number. At high generalized Prandtl number numbers, by decreasing non-Newtonian power-law index, the wall skin friction, temperature scale, and thermal boundary-layer thickness are increased and the Nusselt number is decreased, while the opposite trend is observed for low generalized Prandtl number. A general correlation for the Nusselt number is derived using the numerical results

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27

Geissert, Matthias, Karoline Götze, and Matthias Hieber. "$L^{p}$-theory for strong solutions to fluid-rigid body interaction in Newtonian and generalized Newtonian fluids." Transactions of the American Mathematical Society 365, no. 3 (August 3, 2012): 1393–439. http://dx.doi.org/10.1090/s0002-9947-2012-05652-2.

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28

Jamil, Muhammad, Najeeb Alam Khan, and Abdul Rauf. "Oscillating Flows of Fractionalized Second Grade Fluid." ISRN Mathematical Physics 2012 (April 4, 2012): 1–23. http://dx.doi.org/10.5402/2012/908386.

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New exact solutions for the motion of a fractionalized (this word is suitable when fractional derivative is used in constitutive or governing equations) second grade fluid due to longitudinal and torsional oscillations of an infinite circular cylinder are determined by means of Laplace and finite Hankel transforms. These solutions are presented in series form in term of generalized Ga,b,c(⋅,t) functions and satisfy all imposed initial and boundary conditions. In special cases, solutions for ordinary second grade and Newtonian fluids are obtained. Furthermore, other equivalent forms of solutions for ordinary second grade and Newtonian fluids are presented and written as sum of steady-state and transient solutions. The solutions for Newtonian fluid coincide with the well-known classical solutions. Finally, by means of graphical illustrations, the influence of pertinent parameters on fluid motion as well as comparison among different models is discussed.

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29

Wang, Xiaoping, Haitao Qi, and Huanying Xu. "Transient electro-osmotic flow of generalized second-grade fluids under slip boundary conditions." Canadian Journal of Physics 95, no. 12 (December 2017): 1313–20. http://dx.doi.org/10.1139/cjp-2017-0179.

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This work investigates the transient slip flow of viscoelastic fluids in a slit micro-channel under the combined influences of electro-osmotic and pressure gradient forcings. We adopt the generalized second-grade fluid model with fractional derivative as the constitutive equation and the Navier linear slip model as the boundary conditions. The analytical solution for velocity distribution of the electro-osmotic flow is determined by employing the Debye–Hückel approximation and the integral transform methods. The corresponding expressions of classical Newtonian and second-grade fluids are obtained as the limiting cases of our general results. These solutions are presented as a sum of steady-state and transient parts. The combined effects of slip boundary conditions, fluid rheology, electro-osmotic, and pressure gradient forcings on the fluid velocity distribution are also discussed graphically in terms of the pertinent dimensionless parameters. By comparison with the two cases corresponding to the Newtonian fluid and the classical second-grade fluid, it is found that the fractional derivative parameter β has a significant effect on the fluid velocity distribution and the time when the fluid flow reaches the steady state. Additionally, the slip velocity at the wall increases in a noticeable manner the flow rate in an electro-osmotic flow.

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30

MÁLEK, J., M. RŮŽIČKA, and V. V. SHELUKHIN. "HERSCHEL–BULKLEY FLUIDS: EXISTENCE AND REGULARITY OF STEADY FLOWS." Mathematical Models and Methods in Applied Sciences 15, no. 12 (December 2005): 1845–61. http://dx.doi.org/10.1142/s0218202505000996.

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The equations for steady flows of Herschel–Bulkley fluids are considered and the existence of a weak solution is proved for the Dirichlet boundary-value problem. The rheology of such a fluid is defined by a yield stress τ* and a discontinuous constitutive relation between the Cauchy stress and the symmetric part of the velocity gradient. Such a fluid stiffens if its local stresses do not exceed τ*, and it behaves like a non-Newtonian fluid otherwise. We address here a class of nonlinear fluids which includes shear-thinning p-law fluids with 9/5 < p ≤ 2. The flow equations are formulated in the stress-velocity setting (cf. Ref. 25). Our approach is different from that of Duvaut–Lions (cf. Ref. 10) developed for classical Bingham visco-plastic materials. We do not apply the variational inequality but make use of an approximation of the Herschel–Bulkley fluid with a generalized Newtonian fluid with a continuous constitutive law.

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31

BREIT, D., L. DIENING, and S. SCHWARZACHER. "SOLENOIDAL LIPSCHITZ TRUNCATION FOR PARABOLIC PDEs." Mathematical Models and Methods in Applied Sciences 23, no. 14 (October 10, 2013): 2671–700. http://dx.doi.org/10.1142/s0218202513500437.

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We consider functions u ∈ L∞(L2)∩Lp(W1, p) with 1 < p < ∞ on a time–space domain. Solutions to nonlinear evolutionary PDEs typically belong to these spaces. Many applications require a Lipschitz approximation uλ of u which coincides with u on a large set. For problems arising in fluid mechanics one needs to work with solenoidal (divergence-free) functions. Thus, we construct a Lipschitz approximation, which is also solenoidal. As an application we revise the existence proof for non-stationary generalized Newtonian fluids of Diening, Ruzicka and Wolf, Existence of weak solutions for unsteady motions of generalized Newtonian fluids, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 9 (2010) 1–46. Since div uλ = 0, we are able to work in the pressure free formulation, which heavily simplifies the proof. We also provide a simplified approach to the stationary solenoidal Lipschitz truncation of Breit, Diening and Fuchs, Solenoidal Lipschitz truncation and applications in fluid mechanics, J. Differential Equations253 (2012) 1910–1942.

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32

Xue, Changfeng, and Junxiang Nie. "Exact Solutions of Rayleigh-Stokes Problem for Heated Generalized Maxwell Fluid in a Porous Half-Space." Mathematical Problems in Engineering 2008 (2008): 1–10. http://dx.doi.org/10.1155/2008/641431.

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The Rayleigh-Stokes problem for a generalized Maxwell fluid in a porous half-space with a heated flat plate is investigated. For the description of such a viscoelastic fluid, a fractional calculus approach in the constitutive relationship model is used. By using the Fourier sine transform and the fractional Laplace transform, exact solutions of the velocity and the temperature are obtained. Some classical results can be regarded as particular cases of our results, such as the classical solutions of the first problem of Stokes for Newtonian viscous fluids, Maxwell fluids, and Maxwell fluids in a porous half-space.

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33

Rushd, Sayeed, Noor Hafsa, Majdi Al-Faiad, and Md Arifuzzaman. "Modeling the Settling Velocity of a Sphere in Newtonian and Non-Newtonian Fluids with Machine-Learning Algorithms." Symmetry 13, no. 1 (January 2, 2021): 71. http://dx.doi.org/10.3390/sym13010071.

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The traditional procedure of predicting the settling velocity of a spherical particle is inconvenient as it involves iterations, complex correlations, and an unpredictable degree of uncertainty. The limitations can be addressed efficiently with artificial intelligence-based machine-learning algorithms (MLAs). The limited number of isolated studies conducted to date were constricted to specific fluid rheology, a particular MLA, and insufficient data. In the current study, the generalized application of ML was comprehensively investigated for Newtonian and three varieties of non-Newtonian fluids such as Power-law, Bingham, and Herschel Bulkley. A diverse set of nine MLAs were trained and tested using a large dataset of 967 samples. The ranges of generalized particle Reynolds number (ReG) and drag coefficient (CD) for the dataset were 10−3 < ReG (-) < 104 and 10−1 < CD (-) < 105, respectively. The performances of the models were statistically evaluated using an evaluation metric of the coefficient-of-determination (R2), root-mean-square-error (RMSE), mean-squared-error (MSE), and mean-absolute-error (MAE). The support vector regression with polynomial kernel demonstrated the optimum performance with R2 = 0.92, RMSE = 0.066, MSE = 0.0044, and MAE = 0.044. Its generalization capability was validated using the ten-fold-cross-validation technique, leave-one-feature-out experiment, and leave-one-data-set-out validation. The outcome of the current investigation was a generalized approach to modeling the settling velocity.

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34

Wróblewska-Kamińska, Aneta. "Unsteady flows of non-Newtonian fluids in generalized Orlicz spaces." Discrete & Continuous Dynamical Systems - A 33, no. 6 (2013): 2565–92. http://dx.doi.org/10.3934/dcds.2013.33.2565.

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35

Lawal, Adeniyi, and Dilhan M. Kalyon. "NOIMISOTHERMAL MODEL OF SINGLE SCREW EXTRUSION OF GENERALIZED NEWTONIAN FLUIDS." Numerical Heat Transfer, Part A: Applications 26, no. 1 (July 1994): 103–21. http://dx.doi.org/10.1080/10407789408955983.

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36

Keslerová, Radka, Hynek Řezníček, and Tomáš Padělek. "Numerical solution of flow in bypass for generalized Newtonian fluids." Journal of Physics: Conference Series 1391 (November 2019): 012101. http://dx.doi.org/10.1088/1742-6596/1391/1/012101.

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37

MALASPINAS, ORESTIS, GUY COURBEBAISSE, and MICHEL DEVILLE. "SIMULATION OF GENERALIZED NEWTONIAN FLUIDS WITH THE LATTICE BOLTZMANN METHOD." International Journal of Modern Physics C 18, no. 12 (December 2007): 1939–49. http://dx.doi.org/10.1142/s0129183107011832.

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This paper proposes a study of the computational efficiency of a lattice Boltzmann model (LBM) solver to simulate the behavior of a generalized Newtonian fluid. We present recent progress concerning a 4-1 planar contraction considering a power-law and a Carreau-law model. First we compare the power-law model for a Poiseuille flow with the analytical solution, and show that our model is second-order accurate in space. Then we compare the results obtained with LBM for both laws to those obtained using a commercial finite element solver for the 4-1 plane sharp corner contraction.

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38

Seregin, G. A. "Attractors for equations describing the flow of generalized Newtonian fluids." Journal of Mathematical Sciences 101, no. 5 (October 2000): 3539–62. http://dx.doi.org/10.1007/bf02680151.

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39

Shanthini, W., and K. Nandakumar. "Bifurcation phenomena of generalized newtonian fluids in curved rectangular ducts." Journal of Non-Newtonian Fluid Mechanics 22, no. 1 (January 1986): 35–60. http://dx.doi.org/10.1016/0377-0257(86)80003-9.

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40

Guo, Xiaoyi. "Decay of Potential Vortex and Diffusion of Temperature in a Generalized Oldroyd-B Fluid through a Porous Medium." Mathematical Problems in Engineering 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/719464.

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Based on a modified Darcy law, the decay of potential vortex and diffusion of temperature in a generalized Oldroyd-B fluid with fractional derivatives through a porous medium is studied. Exact solutions of the velocity and temperature fields are obtained in terms of the generalized Mittag-Leffler function by using the Hankel transform and discrete Laplace transform of the sequential fractional derivatives. One of the solutions is the sum of the Newtonian solutions and the non-Newtonian contributions. As limiting cases of the present solutions, the corresponding solutions of the fractional Maxwell fluid and classical Maxwell fluids are given. The influences of the fractional parameters, material parameters, and the porous space on the decay of the vortex are interpreted by graphical results.

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41

Jamil, Muhammad, and Najeeb Alam Khan. "Slip Effects on Fractional Viscoelastic Fluids." International Journal of Differential Equations 2011 (2011): 1–19. http://dx.doi.org/10.1155/2011/193813.

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Unsteady flow of an incompressible Maxwell fluid with fractional derivative induced by a sudden moved plate has been studied, where the no-slip assumption between the wall and the fluid is no longer valid. The solutions obtained for the velocity field and shear stress, written in terms of Wright generalized hypergeometric functions , by using discrete Laplace transform of the sequential fractional derivatives, satisfy all imposed initial and boundary conditions. The no-slip contributions, that appeared in the general solutions, as expected, tend to zero when slip parameter is . Furthermore, the solutions for ordinary Maxwell and Newtonian fluids, performing the same motion, are obtained as special cases of general solutions. The solutions for fractional and ordinary Maxwell fluid for no-slip condition also obtained as limiting cases, and they are equivalent to the previously known results. Finally, the influence of the material, slip, and the fractional parameters on the fluid motion as well as a comparison among fractional Maxwell, ordinary Maxwell, and Newtonian fluids is also discussed by graphical illustrations.

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42

Bakhtiyarov, Sayavur I., Jimmie C. Oxley, James L. Smith, and Philipp M. Baldovi. "Rheological studies of functional polyurethane composite." Journal of Elastomers & Plastics 50, no. 3 (June 30, 2017): 222–40. http://dx.doi.org/10.1177/0095244317715787.

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The rheological dynamic characteristics of the functional Polyurethane composite as well as its compounds ( triethanolamine (TEOA) and toluene-2,4-diisocyanate (TDI)) with and without solid additives (aluminum flakes) were experimentally measured using a computer-controlled mechanical spectrometer (rheometer) ARES-G2. Rheological studies showed that both components behave as viscous Newtonian fluids. TEOA exhibits a strong temperature-thickening behavior. TEOA with aluminum flake additives behaves as a viscous Newtonian fluid. The effective viscosity of the two-phase mixture increases with the concentration of the aluminum additive and decreases with the temperature rise. The rheometric tests showed that the effective viscosity of the TDI/Al mixture increases with the aluminum content. The mixture exhibits thermal-thickening and shear-thinning behaviors with the yield stress. The system can be described with the Bingham plastic model. It is determined that TEOA/TDI composite exhibits a strong time-thickening and shear-thinning behaviors. The rheological behavior of this composite can be described with the power-law generalized non-Newtonian fluid model. The effective viscosity of TEOA/TDI/Al composite increases with both the testing time (exponentially) and the aluminum content (polynomial) in the mixture. However, these shear-thinning composites obey the power-law generalized non-Newtonian fluid model, and their flow curves can be described by the logarithmic law.

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43

Nagy-György, Péter, and Csaba Hős. "A Graphical Technique for Solving the Couette-Poiseuille Problem for Generalized Newtonian Fluids." Periodica Polytechnica Chemical Engineering 63, no. 1 (May 15, 2018): 200–209. http://dx.doi.org/10.3311/ppch.11817.

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This paper addresses the mixed Couette-Poiseuille problem, that is the flow between two parallel plates, in the presence of simultaneous pressure gradient and wall motion. Instead of the wall-normal coordinate y, we use the local shear stress as our primary variable and rewrite the corresponding formulae for the velocity profile, flow rate, etc. This gives rise to a graphical technique for solving the problem in the case of arbitrary (possibly measured) generalized Newtonian fluid rheology. We demonstrate the use of the proposed technique on two problems: (a) Bingham fluid and (b) a non-Newtonian fluid with general, nonmonotonous viscosity function.

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Mishra, P., N. Nirmalkar, and R. P. Chhabra. "Free Convection from a Heated Vertical Cone in Generalized Newtonian Fluids." Journal of Thermophysics and Heat Transfer 33, no. 4 (October 2019): 932–45. http://dx.doi.org/10.2514/1.t5614.

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45

Lawal, A., and D. M. Kalyon. "Compressive Squeeze Flow of Generalized Newtonian Fluids with Apparent Wall Slip." International Polymer Processing 15, no. 1 (March 2000): 63–71. http://dx.doi.org/10.3139/217.1561.

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Bildhauer, Michael, and Martin Fuchs. "Regularization of convex variational problems with applications to generalized Newtonian fluids." Archiv der Mathematik 84, no. 2 (February 2005): 155–70. http://dx.doi.org/10.1007/s00013-004-1221-x.

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47

Sin, Cholmin. "Local higher integrability for unsteady motion equations of generalized Newtonian fluids." Nonlinear Analysis 200 (November 2020): 112029. http://dx.doi.org/10.1016/j.na.2020.112029.

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48

Keslerová, Radka, David Trdlička, and Hynek Řezníček. "Numerical simulation of steady and unsteady flow for generalized Newtonian fluids." Journal of Physics: Conference Series 738 (August 2016): 012112. http://dx.doi.org/10.1088/1742-6596/738/1/012112.

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49

Bruschke, M. V., and S. G. Advani. "Flow of generalized Newtonian fluids across a periodic array of cylinders." Journal of Rheology 37, no. 3 (May 1993): 479–98. http://dx.doi.org/10.1122/1.550455.

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WILCZYNSKI, KRZYSZTOF, BOGDAN LACZYNSKI, and ADAM CZAPLARSKI. "Modeling of generalized flow of newtonian fluids by the POLYFLOW system." Polimery 43, no. 02 (February 1998): 115–20. http://dx.doi.org/10.14314/polimery.1998.115.

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