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Journal articles on the topic 'Slip boundary conditions'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

López-Lemus, J., and R. M. Velasco. "Slip boundary conditions in Couette flow." Physica A: Statistical Mechanics and its Applications 274, no. 3-4 (December 1999): 454–65. http://dx.doi.org/10.1016/s0378-4371(99)00270-8.

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2

Gupta, A. K., and D. Surya. "Benard-Marangoni Convection with Free Slip Bottom and Mixed Thermal Boundary Conditions." Mathematical Journal of Interdisciplinary Sciences 2, no. 2 (March 3, 2014): 141–54. http://dx.doi.org/10.15415/mjis.2014.22011.

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3

He, Xin, Kai Zhang, and Chunpei Cai. "Stability Analysis on Nonequilibrium Supersonic Boundary Layer Flow with Velocity-Slip Boundary Conditions." Fluids 4, no. 3 (July 31, 2019): 142. http://dx.doi.org/10.3390/fluids4030142.

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This paper presents our recent work on investigating velocity slip boundary conditions’ effects on supersonic flat plate boundary layer flow stability. The velocity-slip boundary conditions are adopted and the flow properties are obtained by solving boundary layer equations. Stability analysis of two such boundary layer flows is performed by using the Linear stability theory. A global method is first utilized to obtain approximate discrete mode values. A local method is then utilized to refine these mode values. All the modes in these two scenarios have been tracked upstream-wisely towards the leading edge and also downstream-wisely. The mode values for the no-slip flows agree well with the corresponding past results in the literature. For flows with slip boundary conditions, a stable and an unstable modes are detected. Mode tracking work is performed and the results illustrate that the resonance phenomenon between the stable and unstable modes is delayed with slip boundary conditions. The enforcement of the slip boundary conditions also shortens the unstable mode region. As to the conventional second mode, flows with slip boundary conditions can be more stable streamwisely when compared with the results for corresponding nonslip flows.

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4

LE ROUX, C. "STEADY STOKES FLOWS WITH THRESHOLD SLIP BOUNDARY CONDITIONS." Mathematical Models and Methods in Applied Sciences 15, no. 08 (August 2005): 1141–68. http://dx.doi.org/10.1142/s0218202505000686.

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We prove the existence, uniqueness and continuous dependence on the data of weak solutions to boundary-value problems that model steady flows of incompressible Newtonian fluids with wall slip in bounded domains. The flows satisfy the Stokes equations and a nonlinear slip boundary condition: for slip to occur, the magnitude of the tangential traction must exceed a prescribed threshold, which is independent of the normal stress, and where slip occurs the tangential traction is equal to a prescribed, possibly nonlinear, function of the slip velocity. In addition, a Dirichlet condition is imposed on a component of the boundary if the domain is rotationally symmetric. The method of proof is based on a variational inequality formulation of the problem and fixed point arguments which utilize wellposedness results for the Stokes problem with a slip condition of the "friction type".

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5

Asmolov, Evgeny S., and Olga I. Vinogradova. "Effective slip boundary conditions for arbitrary one-dimensional surfaces." Journal of Fluid Mechanics 706 (June 7, 2012): 108–17. http://dx.doi.org/10.1017/jfm.2012.228.

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AbstractIn many applications it is advantageous to construct effective slip boundary conditions, which could fully characterize flow over patterned surfaces. Here we focus on laminar shear flows over smooth anisotropic surfaces with arbitrary scalar slip $b(y)$, varying in only one direction. We derive general expressions for eigenvalues of the effective slip-length tensor, and show that the transverse component is equal to half of the longitudinal one, with a two times larger local slip, $2b(y)$. A remarkable corollary of this relation is that the flow along any direction of the one-dimensional surface can be easily determined, once the longitudinal component of the effective slip tensor is found from the known spatially non-uniform scalar slip.

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6

Dione, Ibrahima, Cristian Tibirna, and José Urquiza. "Stokes equations with penalised slip boundary conditions." International Journal of Computational Fluid Dynamics 27, no. 6-7 (July 2013): 283–96. http://dx.doi.org/10.1080/10618562.2013.821114.

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7

Guo, Ben-yu. "Navier–Stokes equations with slip boundary conditions." Mathematical Methods in the Applied Sciences 31, no. 5 (2008): 607–26. http://dx.doi.org/10.1002/mma.932.

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8

Meijer, H. E. H., and C. P. J. M. Verbraak. "Modeling of extrusion with slip boundary conditions." Polymer Engineering and Science 28, no. 11 (June 1988): 758–72. http://dx.doi.org/10.1002/pen.760281108.

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9

Dynnikova, Galina Ya. "General expression of aerodynamic force under different boundary conditions (slip, partial slip, no-slip)." Physics of Fluids 33, no. 6 (June 2021): 063104. http://dx.doi.org/10.1063/5.0055304.

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10

Mitsuya, Y. "Stokes Roughness Effects on Hydrodynamic Lubrication. Part II—Effects Under Slip Flow Boundary Conditions." Journal of Tribology 108, no. 2 (April 1, 1986): 159–66. http://dx.doi.org/10.1115/1.3261154.

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Stokes roughness effects on hydrodynamic lubrication are studied in the slip flow regime. Slip flow boundary conditions for Navier-Stokes equations are derived, assuming that the fluid on a surface slips due to the molecular mean free path along the surface, even if the surface is rough. The perturbation method for Navier-Stokes equations, which was derived in Part I of this report, is then applied. Slip flow effects on load carrying capacity and frictional force are numerically clarified for both Stokes and Reynolds roughnesses. In the slip flow regime, second-order quantities induced by Stokes effects, such as flow rate, load carrying capacity, and frictional force are in proportion to the wavenumber squared. This phenomenon relative to the quantities being proportional is also the same as that in the continuum flow regime. As a result of velocity slippage, the load carrying capacity in Stokes roughness is found to decrease more than in Reynolds roughness for incompressible films, while the relationship is reversed for compressible films having a high compressibility number. The simulation of random roughness, which is generated by numerical means, clarifies one important result: the average slip flow effects associated with random Stokes roughness become similar to the slip flow effects in deterministic sinusoidal Stokes roughness, whose wavelength and height are statistically equivalent to those of random roughness. Although attention should be given to the fact that Stokes effects on random roughness demonstrate considerable scattering with the continuum flow, such scattering diminishes with the slip flow.

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11

Mansur, Syahira, and Anuar Ishak. "The Magnetohydrodynamic Boundary Layer Flow of a Nanofluid past a Stretching/Shrinking Sheet with Slip Boundary Conditions." Journal of Applied Mathematics 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/907152.

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The magnetohydrodynamic (MHD) boundary layer flow of a nanofluid past a stretching/shrinking sheet with velocity, thermal, and solutal slip boundary conditions is studied. Numerical solutions to the governing equations were obtained using a shooting method. The skin friction coefficient and the local Sherwood number increase as the stretching/shrinking parameter increases. However, the local Nusselt number decreases with increasing the stretching/shrinking parameter. The range of the stretching/shrinking parameter for which the solution exists increases as the velocity slip parameter and the magnetic parameter increase. For the shrinking sheet, the skin friction coefficient increases as the velocity slip parameter and the magnetic parameter increase. For the stretching sheet, it decreases when the velocity slip parameter and the magnetic parameter increase. The local Nusselt number diminishes as the thermal slip parameter increases while the local Sherwood number decreases with increasing the solutal slip parameter. The local Nusselt number is lower for higher values of Lewis number, Brownian motion parameter, and thermophoresis parameter.

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12

Bayazitoglu, Yildiz, and Gokturk Tunc. "Extended Slip Boundary Conditions for Microscale Heat Transfer." Journal of Thermophysics and Heat Transfer 16, no. 3 (July 2002): 472–75. http://dx.doi.org/10.2514/2.6704.

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13

Méolans, J. G. "Thermal slip boundary conditions in vibrational nonequilibrium flows." Mechanics Research Communications 30, no. 6 (November 2003): 629–37. http://dx.doi.org/10.1016/s0093-6413(03)00083-1.

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14

Beaume, Cédric, Hsien-Ching Kao, Edgar Knobloch, and Alain Bergeon. "Localized rotating convection with no-slip boundary conditions." Physics of Fluids 25, no. 12 (December 2013): 124105. http://dx.doi.org/10.1063/1.4843155.

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15

Palaniappan, D., and Prabir Daripa. "Interior Stokes flows with stick-slip boundary conditions." Physica A: Statistical Mechanics and its Applications 297, no. 1-2 (August 2001): 37–63. http://dx.doi.org/10.1016/s0378-4371(01)00226-6.

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16

Marques Jr., W., G. M. Kremer, and F. M. Sharipov. "Couette flow with slip and jump boundary conditions." Continuum Mechanics and Thermodynamics 12, no. 6 (December 1, 2000): 379–86. http://dx.doi.org/10.1007/s001610050143.

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17

Datta, Sunil, and Satya Deo. "Stokes flow with slip and Kuwabara boundary conditions." Proceedings Mathematical Sciences 112, no. 3 (August 2002): 463–75. http://dx.doi.org/10.1007/bf02829798.

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18

Akhtar, N., G. A. H. Chowdhury, and S. K. Sen. "Stokes flow before plane boundary with mixed stick-slip boundary conditions." Applied Mathematics and Mechanics 32, no. 6 (June 2011): 795–804. http://dx.doi.org/10.1007/s10483-011-1459-8.

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19

Sauzay, Maxime, Pierre Evrard, and Karine Bavard. "Influence of Slip Localization on Surface Relief Formation and Grain Boundary Microcrack Nucleation." Key Engineering Materials 465 (January 2011): 35–40. http://dx.doi.org/10.4028/www.scientific.net/kem.465.35.

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Slip localization is often observed in metallic polycrystals after cyclic deformation (persistent slip bands) or pre-irradiation followed by tensile deformation (channels). To evaluate its influence on surface relief formation and grain boundary microcrack nucleation, crystalline finite element (FE) computations are carried out using microstructure inputs (slip band aspect ratio/spacing). Slip bands (low critical resolved shear stress (CRSS)) are embedded in small elastic aggregates. Slip band aspect ratio and neighboring grain orientations influence strongly the surface slips. But only a weak effect of slip band CRSS, spacing and grain boundary orientation is observed. Analytical formulae are deduced which allow an easy prediction of the surface and bulk slips. The computed slips are in agreement with experimental measures (AFM/TEM measures on pre-irradiated austenitic stainless steels and nickel, copper and precipitate-strengthened alloy subjected to cyclic loading). Grain boundary normal stresses are computed for various materials and loading conditions. A square root dependence with respect to the distance to the slip band corner is found similarly to the pile-up stress field. But the equivalent stress intensity factor is considerably lower. Analytical formulae are proposed for predicting the grain boundary normal stress field depending on the microstructure lengths. Finally, an energy balance criterion is applied using the equivalent elastic energy release rate and the surface/grain boundary energies. The predicted macroscopic stresses for microcrack nucleation are compared to the experimental ones.

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20

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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21

CASADO-DÍAZ, J., M. LUNA-LAYNEZ, and F. J. SUÁREZ-GRAU. "ASYMPTOTIC BEHAVIOR OF A VISCOUS FLUID WITH SLIP BOUNDARY CONDITIONS ON A SLIGHTLY ROUGH WALL." Mathematical Models and Methods in Applied Sciences 20, no. 01 (January 2010): 121–56. http://dx.doi.org/10.1142/s0218202510004179.

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For an oscillating boundary of period and amplitude ε, it is known that the asymptotic behavior when ε tends to zero of a three-dimensional viscous fluid satisfying slip boundary conditions is the same as if we assume no-slip (adherence) boundary conditions. Here we consider the case where the period is still ε but the amplitude is δε with δε/ε converging to zero. We show that if [Formula: see text] tends to infinity, the equivalence between the slip and no-slip conditions still holds. If the limit of [Formula: see text] belongs to (0, +∞) (critical size), then we still have the slip boundary conditions in the limit but with a bigger friction coefficient. In the case where [Formula: see text] tends to zero the boundary behaves as a plane boundary. Besides the limit equation, we also obtain an approximation (corrector result) of the pressure and the velocity in the strong topology of L2 and H1 respectively.

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22

Kreml, Ondřej, Šárka Nečasová, and Tomasz Piasecki. "Local existence of strong solutions and weak–strong uniqueness for the compressible Navier–Stokes system on moving domains." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 5 (April 1, 2019): 2255–300. http://dx.doi.org/10.1017/prm.2018.165.

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AbstractWe consider the compressible Navier–Stokes system on time-dependent domains with prescribed motion of the boundary. For both the no-slip boundary conditions as well as slip boundary conditions we prove local-in-time existence of strong solutions. These results are obtained using a transformation of the problem to a fixed domain and an existence theorem for Navier–Stokes like systems with lower order terms and perturbed boundary conditions. We also show the weak–strong uniqueness principle for slip boundary conditions which remained so far open question.

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23

Jang, Jaesung, and Yong-Hwan Kim. "Gaseous slip flow of a rectangular microchannel with non-uniform slip boundary conditions." Microfluidics and Nanofluidics 9, no. 2-3 (February 3, 2010): 513–22. http://dx.doi.org/10.1007/s10404-010-0567-6.

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24

Sahraoui, M., and M. Kaviany. "Slip and no-slip velocity boundary conditions at interface of porous, plain media." International Journal of Heat and Mass Transfer 35, no. 4 (April 1992): 927–43. http://dx.doi.org/10.1016/0017-9310(92)90258-t.

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25

French, Melodie E., and Cailey B. Condit. "Slip partitioning along an idealized subduction plate boundary at deep slow slip conditions." Earth and Planetary Science Letters 528 (December 2019): 115828. http://dx.doi.org/10.1016/j.epsl.2019.115828.

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26

YI, H. H., and X. F. YANG. "THE EFFECT OF SLIP BOUNDARY ON THE PARTICLE MOTIONS IN A MICRO-CHANNEL WITH LATTICE BOLTZMANN SIMULATIONS." International Journal of Modern Physics B 24, no. 23 (September 20, 2010): 4537–46. http://dx.doi.org/10.1142/s0217979210054786.

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The effect of slip boundary on the particle motions in a micro-planar channel is studied by lattice Boltzmann method. The property of the particle in different surface slip conditions is investigated extensively by simulating the particle trajectories and analyzing the trajectory differences between slip and nonslip conditions. The simulation results show that the particle behavior is affected by the surface slip conditions, especially in the region, which is between the critical position and the channel center, for nonsymmetrical boundary slip. The factors affecting the critical position, including boundary slip velocity and flow Reynolds number, are also studied numerically. The results are expected to find extensive applications and may be helpful to understand recent observations on micro-slip flows with suspensions.

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27

Matthews, M. T., and J. M. Hill. "Micro/nano thermal boundary layer equations with slip creep jump boundary conditions." IMA Journal of Applied Mathematics 72, no. 6 (August 16, 2007): 894–911. http://dx.doi.org/10.1093/imamat/hxm051.

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28

Vipulanandan, C., and A. N. Williams. "Effect of Interface Conditions on Dynamic Ice-Structure Interaction." Journal of Offshore Mechanics and Arctic Engineering 111, no. 1 (February 1, 1989): 70–77. http://dx.doi.org/10.1115/1.3257142.

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Elastic wave theory is utilized to investigate the influence of interface boundary conditions on the dynamic characteristics of a circular cylindrical structure subjected to steady-state and impulsive horizontal excitation while surrounded by an elastic ice medium of infinite horizontal extent. The influence of modified interface boundary conditions relating the shear stresses to the relative displacement (slip) or relative velocity (rate of slip) on the stiffness and damping parameters are studied and the results are compared to the usual fixed and free boundary conditions on the cylinder surface.

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29

Kuo, L. S., and P. H. Chen. "Effects of Slip Boundary Conditions on Rayleigh-Bénard Convection." Journal of Mechanics 25, no. 2 (June 2009): 205–12. http://dx.doi.org/10.1017/s1727719100002665.

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AbstractThis work studied the Rayleigh-Bénard convection under the first-order slip boundary conditions in both hydrodynamic and thermal fields. The variation principle was applied to find the critical Rayleigh number of instability. The exteneded relations of the critical Rayleigh number (Rc) and the wavenumber (ac) under partially slip boundary conditions were derived. The numerical results showed that both Rc and ac are decreasing with increasing the Knudsen number. The dependence of Rc on the Knudsen number (K) shows that when K≤10−3, the boundary can be considered as nonslip, while K≥10, it can be considered as free boundaries. The maximum change rate occurs when the Knudsen number is around 0.1, indicating that the system would be affected significantly in that range.

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30

Liu, Chun, and Jie Shen. "On liquid crystal flows with free-slip boundary conditions." Discrete & Continuous Dynamical Systems - A 7, no. 2 (2001): 307–18. http://dx.doi.org/10.3934/dcds.2001.7.307.

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31

Andersson, Helge I., and Ole Andreas Valnes. "Slip-flow boundary conditions for non-Newtonian lubrication layers." Fluid Dynamics Research 24, no. 4 (April 1999): 211–17. http://dx.doi.org/10.1016/s0169-5983(98)00022-7.

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32

Luchini, Paolo. "Linearized no-slip boundary conditions at a rough surface." Journal of Fluid Mechanics 737 (November 25, 2013): 349–67. http://dx.doi.org/10.1017/jfm.2013.574.

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AbstractLinearized boundary conditions are a commonplace numerical tool in any flow problems where the solid wall is nominally flat but the effects of small waviness or roughness are being investigated. Typical examples are stability problems in the presence of undulated walls or interfaces, and receptivity problems in aerodynamic transition prediction or turbulent flow control. However, to pose such problems properly, solutions in two mathematical distinguished limits have to be considered: a shallow-roughness limit, where not only roughness height but also its aspect ratio becomes smaller and smaller, and a small-roughness limit, where the size of the roughness tends to zero but its aspect ratio need not. Here a connection between the two solutions is established through an analysis of their far-field behaviour. As a result, the effect of the surface in the small-roughness limit, obtained from a numerical solution of the Stokes problem, can be recast as an equivalent shallow-roughness linearized boundary condition corrected by a suitable protrusion coefficient (related to the protrusion height used years ago in the study of riblets) and a proximity coefficient, accounting for the interference between multiple protrusions in a periodic array. Numerically computed plots and interpolation formulas of such correction coefficients are provided.

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33

Chemetov, N. V., and S. N. Antontsev. "Euler equations with non-homogeneous Navier slip boundary conditions." Physica D: Nonlinear Phenomena 237, no. 1 (January 2008): 92–105. http://dx.doi.org/10.1016/j.physd.2007.08.012.

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34

Latyshev, A. V., and A. A. Yushkanov. "Moment Boundary Conditions in Rarefied Gas Slip-Flow Problems." Fluid Dynamics 39, no. 2 (March 2004): 339–53. http://dx.doi.org/10.1023/b:flui.0000030317.95193.59.

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35

Watanabe, Jiro. "On incompressible viscous fluid flows with slip boundary conditions." Journal of Computational and Applied Mathematics 159, no. 1 (October 2003): 161–72. http://dx.doi.org/10.1016/s0377-0427(03)00568-5.

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36

JESSLÉ, DIDIER, ANTONÍN NOVOTNÝ, and MILAN POKORNÝ. "STEADY NAVIER–STOKES–FOURIER SYSTEM WITH SLIP BOUNDARY CONDITIONS." Mathematical Models and Methods in Applied Sciences 24, no. 04 (January 28, 2014): 751–81. http://dx.doi.org/10.1142/s0218202513500668.

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We consider a problem modeling the steady flow of a compressible heat conducting Newtonian fluid subject to the slip boundary condition for the velocity. Assuming the pressure law of the form p(ϱ, ϑ) ~ ϱγ + ϱϑ, we show (under additional assumptions on the heat conductivity and the viscosity) that for any γ > 1 there exists a variational entropy solution to our problem (i.e. the weak formulation of the total energy balance is replaced by the entropy inequality and the global total energy balance). Moreover, if [Formula: see text] (together with further restrictions on the heat conductivity), the solution is in fact a weak one. The results are obtained without any restriction on the size of the data.

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37

Nageswara Rao, B. "Improved Slip-Flow Boundary Conditions for Thin Lubrication Layers." Journal of Applied Mechanics 53, no. 3 (September 1, 1986): 723–24. http://dx.doi.org/10.1115/1.3171838.

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38

Duong-Hong, Duc, Nhan Phan-Thien, and Xijun Fan. "An implementation of no-slip boundary conditions in DPD." Computational Mechanics 35, no. 1 (September 1, 2004): 24–29. http://dx.doi.org/10.1007/s00466-004-0595-8.

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39

Raja Sekhar, G. P., K. Tejeswara Rao, B. S. Padmavathi, and T. Amaranath. "Two dimensional Stokes flows with slip-stick boundary conditions." Mechanics Research Communications 22, no. 5 (September 1995): 491–501. http://dx.doi.org/10.1016/0093-6413(95)00053-t.

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40

Aoki, Kazuo, Céline Baranger, Masanari Hattori, Shingo Kosuge, Giorgio Martalò, Julien Mathiaud, and Luc Mieussens. "Slip Boundary Conditions for the Compressible Navier–Stokes Equations." Journal of Statistical Physics 169, no. 4 (October 7, 2017): 744–81. http://dx.doi.org/10.1007/s10955-017-1886-8.

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41

KAMRIN, KEN, MARTIN Z. BAZANT, and HOWARD A. STONE. "Effective slip boundary conditions for arbitrary periodic surfaces: the surface mobility tensor." Journal of Fluid Mechanics 658 (July 16, 2010): 409–37. http://dx.doi.org/10.1017/s0022112010001801.

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In a variety of applications, most notably microfluidics design, slip-based boundary conditions have been sought to characterize fluid flow over patterned surfaces. We focus on laminar shear flows over surfaces with periodic height fluctuations and/or fluctuating Navier scalar slip properties. We derive a general formula for the ‘effective slip’, which describes equivalent fluid motion at the mean surface as depicted by the linear velocity profile that arises far from it. We show that the slip and the applied stress are related linearly through a tensorial mobility matrix, and the method of domain perturbation is then used to derive an approximate formula for the mobility law directly in terms of surface properties. The specific accuracy of the approximation is detailed, and the mobility relation is then utilized to address several questions, such as the determination of optimal surface shapes and the effect of random surface fluctuations on fluid slip.

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42

Li, Yifan, Yunlu Pan, and Xuezeng Zhao. "Interface conditions of roughness-induced superoleophilic and superoleophobic surfaces immersed in hexadecane and ethylene glycol." Beilstein Journal of Nanotechnology 8 (November 27, 2017): 2504–14. http://dx.doi.org/10.3762/bjnano.8.250.

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Interface conditions are an important property that can affect the drag of fluid flow. For surfaces with different oleophobicity, the boundary slip at the solid–oil interface is mostly larger than that at the solid–water interface. Roughness is a key factor for the wettability of superoleophilic/superoleophobic surfaces, and it has been found to affect the effective value of slip length in measurements. Moreover, there are no studies on the effect of roughness on slip at interfaces between oil and superoleophilic/superoleophobic surfaces. A theoretical description of the real surface roughness is yet to be found. Results show that the effective slip length is negative and decreases with an increasing root mean squared (RMS) roughness of surfaces, as the increasing roughness enhances the area with discontinuous slip at the solid–liquid interface. The underlying mechanisms are analyzed. The amplitude parameters of surface roughness could significantly inhibit the degree of boundary slip on both superoleophilic surfaces in Wenzel state and superoleophobic surfaces in Cassie state immersed in oil. The oleic systems were likely to enhance boundary slip and resulted in a corresponding reduction in drag with decreasing roughness on the solid–oil interfaces.

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43

Borzenko, Evgeny, and Olga Dyakova. "Numerical Simulation of Newtonian Fluid Flow in a T-Channel with no Slip/Slip Boundary Conditions on a Solid Wall." Key Engineering Materials 743 (July 2017): 480–85. http://dx.doi.org/10.4028/www.scientific.net/kem.743.480.

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The planar flow of a Newtonian incompressible fluid in a T-shaped channel is investigated. Three fluid interaction models with solid walls are considered: no slip boundary condition, Navier slip boundary condition and slip boundary condition with slip yield stress. The fluid flow is provided by uniform pressure profiles at the boundary sections of the channel. The problem is numerically solved using a finite difference method based on the SIMPLE procedure. Characteristic flow regimes have been found for the described models of liquid interaction with solid walls. The estimation of the influence of the Reynolds number, pressure applied to the boundary sections and the parameters of these models on the flow pattern was performed. The criterial dependences describing main characteristics of the flow under conditions of the present work have been demonstrated.

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44

Sun, Qian, Yonghong Wu, Lishan Liu, and B. Wiwatanapataphee. "Solution of Time Periodic Electroosmosis Flow with Slip Boundary." Abstract and Applied Analysis 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/789147.

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Recent research confirms that slip of a fluid on the solid surface occurs at micrometer scale. Slip on solid surface may cause the change of interior material deformation which consequently leads to the change of velocity profile and stress field. This paper concerns the time periodic electroosmotic flow in a channel with slip boundary driven by an alternating electric field, which arises from the study of particle manipulation and separation such as flow pumping and mixing enhancement. Although exact solutions to various flow problems of electroosmotic flows under the no-slip condition have been obtained, exact solutions for problems under slip boundary conditions have seldom been addressed. In this paper, an exact solution is derived for the time periodic electroosmotic flow in two-dimensional straight channels under slip boundary conditions.

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45

Sahraoui, M., and M. Kaviany. "Slip and no-slip temperature boundary conditions at interface of porous, plain media: conduction." International Journal of Heat and Mass Transfer 36, no. 4 (March 1993): 1019–33. http://dx.doi.org/10.1016/s0017-9310(05)80286-8.

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Mallea-Zepeda, Exequiel, Eber Lenes, and Elvis Valero. "Boundary Control Problem for Heat Convection Equations with Slip Boundary Condition." Mathematical Problems in Engineering 2018 (2018): 1–14. http://dx.doi.org/10.1155/2018/7959761.

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We analyze an optimal boundary control problem for heat convection equations in a three-dimensional domain, with mixed boundary conditions. We prove the existence of optimal solutions, by considering boundary controls for the velocity vector and the temperature. The analyzed optimal control problem includes the minimization of a Lebesgue norm between the velocity and some desired field, as well as the temperature and some desired temperature. By using the Lagrange multipliers theorem we derive an optimality system. We also give a second-order sufficient condition.

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SHIBUTANI, Yoji, Tomoyuki HIROUCHI, and Tomohito TSURU. "OS0104 Slip Transfer Easiness of Dislocation to Grain Boundary using Boundary Interaction Conditions." Proceedings of the Materials and Mechanics Conference 2012 (2012): _OS0104–1_—_OS0104–3_. http://dx.doi.org/10.1299/jsmemm.2012._os0104-1_.

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Sahoo, Bikash, Sébastien Poncet, and Fotini Labropulu. "Suction/Injection Effects on the Swirling Flow of a Reiner-Rivlin Fluid near a Rough Surface." Journal of Fluids 2015 (January 5, 2015): 1–5. http://dx.doi.org/10.1155/2015/253504.

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The similarity equations for the Bödewadt flow of a non-Newtonian Reiner-Rivlin fluid, subject to uniform suction/injection, are solved numerically. The conventional no-slip boundary conditions are replaced by corresponding partial slip boundary conditions, owing to the roughness of the infinite stationary disk. The combined effects of surface slip (λ), suction/injection velocity (W), and cross-viscous parameter (L) on the momentum boundary layer are studied in detail. It is interesting to find that suction dominates the oscillations in the velocity profiles and decreases the boundary layer thickness significantly. On the other hand, injection has opposite effects on the velocity profiles and the boundary layer thickness.

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Fernandes, Célio, Luís Lima Ferrás, Florian Habla, Olga Sousa Carneiro, and João Miguel Nóbrega. "Implementation of partial slip boundary conditions in an open-source finite-volume-based computational library." Journal of Polymer Engineering 39, no. 4 (March 26, 2019): 377–87. http://dx.doi.org/10.1515/polyeng-2018-0343.

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Abstract This paper reports the implementation of slip boundary conditions in the open-source computational library OpenFOAM. The linear and nonlinear Navier slip laws, which are newly implemented in this paper, can be used both for Newtonian and viscoelastic constitutive models. For the former case, the Couette flow assumption near the wall is employed, and for the latter, the cell-centered extra-stress tensor components are linearly extrapolated to the wall. The validation is performed by comparing the numerical results obtained for Newtonian and simplified Phan-Thien-Tanner constitutive model fluids in Couette and Poiseuille flows, with existing analytical solutions. The results obtained using different slip factors were shown to be in agreement with the analytical solutions, even for the most extreme cases where the slip factor is high enough to induce a plug flow pattern for the velocity field. The newly implemented boundary conditions are also used to study the influence of slip in polymer processing, namely in the production of an extruded profile. The results obtained show that the developed slip boundary conditions are able to deal with complex geometrical problems, and are an important tool to support the search of a balanced flow distribution in the design of profile extrusion dies.

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Martin, Michael J., and Iain D. Boyd. "Falkner-Skan Flow over a Wedge with Slip Boundary Conditions." Journal of Thermophysics and Heat Transfer 24, no. 2 (April 2010): 263–70. http://dx.doi.org/10.2514/1.43316.

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