-
Previous Article
Heisenberg picture of quantum kinetic evolution in mean-field limit
- KRM Home
- This Issue
-
Next Article
Coordinates in the relativistic Boltzmann theory
Non-Newtonian Couette-Poiseuille flow of a dilute gas
1. | Département de Physique, Université Moulay Ismaïl, Meknès, Morocco |
2. | Departamento de Física, Universidad de Extremadura, E-06071 Badajoz, Spain |
References:
[1] |
M. Alam and V. K. Chikkadi, Velocity distribution function and correlations in a granular Poiseuille flow,, J. Fluid Mech., 653 (2010), 175.
doi: 10.1017/S0022112010000200. |
[2] |
M. Alaoui and A. Santos, Poiseuille flow driven by an external force,, Phys. Fluids A, 4 (1992), 1273.
doi: 10.1063/1.858245. |
[3] |
K. Aoki, S. Takata and T. Nakanishi, A Poiseuille-type flow of a rarefied gas between two parallel plates driven by a uniform external force,, Phys. Rev. E, 65 (2002).
doi: 10.1103/PhysRevE.65.026315. |
[4] |
E. Asmolov, N. K. Makashev and V. I. Nosik, Heat transfer between parallel plates in a gas of Maxwellian molecules,, Sov. Phys. Dokl., 24 (1979), 892. Google Scholar |
[5] |
P. L. Bhatnagar, E. P. Gross and M. Krook, A model collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems,, Phy. Rev., 94 (1954), 511.
doi: 10.1103/PhysRev.94.511. |
[6] |
J. J. Brey, A. Santos and J. W. Dufty, Heat and momentum transport far from equilibrium,, Phys. Rev. A, 36 (1987), 2842.
doi: 10.1103/PhysRevA.36.2842. |
[7] |
C. Cercignani, "The Boltzmann Equation and Its Applications,'', Springer-Verlag, (1988). Google Scholar |
[8] |
C. Cercignani, "Mathematical Methods in Kinetic Theory,'', Plenum Press, (1990). Google Scholar |
[9] |
C. Cercignani, M. Lampis and S. Lorenzani, Plane Poiseuille-Couette problem in micro-electro-mechanical systems applications with gas-rarefaction effects,, Phy. Fluids, 18 (2006).
doi: 10.1063/1.2335847. |
[10] |
C. Cercignani and F. Sernagiotto, Cylindrical Poiseuille flow of a rarefied gas,, Phys. Fluids, 9 (1966), 40.
doi: 10.1063/1.1761530. |
[11] |
S. Chapman and T. G. Cowling, "The Mathematical Theory of Nonuniform Gases,'', Cambridge University Press, (1970). Google Scholar |
[12] |
V. Chikkadi and M. Alam, Slip velocity and stresses in granular Poiseuille flow via event-driven simulation,, Phys. Rev. E, 80 (2009).
doi: 10.1103/PhysRevE.80.021303. |
[13] |
J. R. Dorfman and H. van Beijeren, The kinetic theory of gases,, in, (1977), 65. Google Scholar |
[14] |
A. I. Erofeev and O. G. Friedlander, Macroscopic models for non-equilibrium flows of monatomic gas and normal solutions,, in, (2007), 117. Google Scholar |
[15] |
R. Esposito, J. L. Lebowitz and R. Marra, A hydrodynamic limit of the stationary Boltzmann equation in a slab,, Commun. Math. Phys., 160 (1994), 49.
doi: 10.1007/BF02099789. |
[16] |
M. A. Gallis, J. R. Torczynski, D. J. Rader, M. Tij and A. Santos, Normal solutions of the Boltzmann equation for highly nonequilibrium Fourier flow and Couette flow,, Phys. Fluids, 18 (2006). Google Scholar |
[17] |
M. A. Gallis, J. R. Torczynski, D. J. Rader, M. Tij and A. Santos, Analytical and numerical normal solutions of the Boltzmann equation for highly nonequilibrium Fourier and Couette flows,, in, (2007), 251. Google Scholar |
[18] |
L. S. García-Colín, R. M. Velasco and F. J. Uribe, Beyond the Navier-Stokes equations: Burnett hydrodynamics,, Phys. Rep., 465 (2008), 149.
doi: 10.1016/j.physrep.2008.04.010. |
[19] |
V. Garzó and M. López de Haro, Nonlinear transport for a dilute gas in steady Couette flow,, Phys. Fluids, 9 (1997), 776.
doi: 10.1063/1.869232. |
[20] |
V. Garzó and A. Santos, "Kinetic Theory of Gases in Shear Flows. Nonlinear Transport,'', Kluwer Academic Publishers, (2003). Google Scholar |
[21] |
S. Hess and M. Malek Mansour, Temperature profile of a dilute gas undergoing a plane Poiseuille flow,, Physica A, 272 (1999), 481.
doi: 10.1016/S0378-4371(99)00254-X. |
[22] |
L. P. Kadanoff, G. R. McNamara and G. Zanetti, A Poiseuille viscometer for lattice gas automata,, Complex Syst., 1 (1987), 791. Google Scholar |
[23] |
L. P. Kadanoff, G. R. McNamara and G. Zanetti, From automata to fluid flow: Comparisons of simulation and theory,, Phys. Rev. A, 40 (1989), 4527.
doi: 10.1103/PhysRevA.40.4527. |
[24] |
C. S. Kim, J. W. Dufty, A. Santos and J. J. Brey, Hilbert-class or "normal'' solutions for stationary heat flow,, Phys. Rev. A, 39 (1989), 328.
doi: 10.1103/PhysRevA.39.328. |
[25] |
C. S. Kim, J. W. Dufty, A. Santos and J. J. Brey, Analysis of nonlinear transport in Couette flow,, Phys. Rev A, 40 (1989), 7165.
doi: 10.1103/PhysRevA.40.7165. |
[26] |
G. M. Kremer, "An Introduction to the Boltzmann Equation and Transport Processes in Gases,'', Springer, (2010).
doi: 10.1007/978-3-642-11696-4. |
[27] |
M. Malek Mansour, F. Baras and A. L. Garcia, On the validity of hydrodynamics in plane Poiseuille flows,, Physica A, 240 (1997), 255.
doi: 10.1016/S0378-4371(97)00149-0. |
[28] |
N. K. Makashev and V. I. Nosik, Steady Couette flow (with heat transfer) of a gas of Maxwellian molecules,, Sov. Phys. Dokl., 25 (1981), 589. Google Scholar |
[29] |
J. M. Montanero, M. Alaoui, A. Santos and V. Garzó, Monte Carlo simulation of the Boltzmann equation for steady Fourier flow,, Phys. Rev. E, 49 (1994), 367.
doi: 10.1103/PhysRevE.49.367. |
[30] |
J. M. Montanero and V. Garzó, Nonlinear Couette flow in a dilute gas: Comparison between theory and molecular dynamics simulation,, Phys. Rev. E, 58 (1998), 1836.
doi: 10.1103/PhysRevE.58.1836. |
[31] |
J. M. Montanero, A. Santos and V. Garzó, Monte Carlo simulation of nonlinear Couette flow in a dilute gas,, Phys. Fluids, 12 (2000), 3060.
doi: 10.1063/1.1313563. |
[32] |
R. S. Myong, Coupled nonlinear constitutive models for rarefied and microscale gas flows: subtle interplay of kinematics and dissipation effects,, Cont. Mech. Thermodyn., 21 (2009), 389.
doi: 10.1007/s00161-009-0112-6. |
[33] |
V. I. Nosik, Heat transfer between parallel plates in a mixture of gases of Maxwellian molecules,, Sov. Phys. Dokl., 25 (1981), 495. Google Scholar |
[34] |
V. I. Nosik, Degeneration of the Chapman-Enskog expansion in one-dimensional motions of Maxwellian molecule gases,, in, 13 (1983), 237. Google Scholar |
[35] |
T. Ohwada, Y. Sone and K. Aoki, Numerical analysis of the Poiseuille and thermal transpiration flows between two parallel plates on the basis of the Boltzmann equation for hard-sphere molecules,, Phys. Fluids A, 1 (1989), 2042.
doi: 10.1063/1.857478. |
[36] |
M. C. Potter, Stability of plane Couette-Poiseuille flow,, J. Fluid Mech., 24 (1966), 609.
doi: 10.1017/S0022112066000855. |
[37] |
D. Risso and P. Cordero, Dilute gas Couette flow: Theory and molecular dynamics simulation,, Phys. Rev. E, 56 (1997), 489.
doi: 10.1103/PhysRevE.56.489. |
[38] |
D. Risso and P. Cordero, Generalized hydrodynamics for a Poiseuille flow: theory and simulations,, Phys. Rev. E, 58 (1998), 546.
doi: 10.1103/PhysRevE.58.546. |
[39] |
M. Sabbane, M. Tij and A. Santos, Maxwellian gas undergoing a stationary Poiseuille flow in a pipe,, Physica A, 327 (2003), 264.
doi: 10.1016/S0378-4371(03)00513-2. |
[40] |
A. Santos, Solutions of the moment hierarchy in the kinetic theory of Maxwell models,, Cont. Mech. Thermodyn., 21 (2009), 361.
doi: 10.1007/s00161-009-0113-5. |
[41] |
A. Santos, J. J. Brey and V. Garzó, Kinetic model for steady heat flow,, Phys. Rev. A, 34 (1986), 5047.
doi: 10.1103/PhysRevA.34.5047. |
[42] |
A. Santos, J. J. Brey, C. S. Kim and J. W. Dufty, Velocity distribution for a gas with steady heat flow,, Phys. Rev. A, 39 (1989), 320.
doi: 10.1103/PhysRevA.39.320. |
[43] |
A. Santos, V. Garzó and J. J. Brey, Comparison between the homogeneous-shear and the sliding-boundary methods to produce shear flow,, Phys. Rev. A, 46 (1992), 8018.
doi: 10.1103/PhysRevA.46.8018. |
[44] |
A. Santos and M. Tij, Gravity-driven Poiseuille flow in dilute gases. Elastic and inelastic collisions,, in, (2006), 53. Google Scholar |
[45] |
Y. Sone, Asymptotic theory of a steady flow of a rarefied gas past bodies for small Knudsen numbers,, in, (1991), 19. Google Scholar |
[46] |
Y. Sone, Flows induced by temperature fields in a rarefied gas and their ghost effect on the behavior of a gas in the continuum limit,, Annu. Rev. Fluid Mech., 32 (2000), 779.
doi: 10.1146/annurev.fluid.32.1.779. |
[47] |
Y. Sone, "Kinetic Theory and Fluid Dynamics,'', Birkhäuser, (2002). Google Scholar |
[48] |
H. Struchtrup, "Macroscopic Transport Equations for Rarefied Gas Flows. Approximation Methods in Kinetic Theory,'', Springer, (2005). Google Scholar |
[49] |
H. Struchtrup and M Torrilhon, Higher-order effects in rarefied channel flows,, Phys. Rev. E, 78 (2008).
doi: 10.1103/PhysRevE.78.046301. |
[50] |
S. A. Suslov and T. D. Tran, Revisiting plane Couette-Poiseuille flows of a piezo-viscous fluid,, J. Non-Newton. Fluid Mech., 154 (2006), 170. Google Scholar |
[51] |
P. Taheri, M. Torrilhon and H. Struchtrup, Couette and Poiseuille microflows: analytical solutions for regularized 13-moment equations,, Phys. Fluids, 21 (2009).
doi: 10.1063/1.3064123. |
[52] |
R. Tehver, F. Toigo, J. Koplik and J. R. Banavar, Thermal walls in computer simulations,, Phys. Rev. E, 57 (1998).
doi: 10.1103/PhysRevE.57.R17. |
[53] |
E. M. Thurlow and J. C. Klewicki, Experimental study of turbulent Poiseuille-Couette flow,, Phys. Fluids, 12 (2000), 865.
doi: 10.1063/1.870341. |
[54] |
M. Tij, V. Garzó and A. Santos, Influence of gravity on nonlinear transport in the planar Couette flow,, Phys. Fluids, 11 (1999), 893.
doi: 10.1063/1.869960. |
[55] |
M. Tij, M. Sabbane and A. Santos, Nonlinear Poiseuille flow in a gas,, Phys. Fluids, 10 (1998), 1021.
doi: 10.1063/1.869621. |
[56] |
M. Tij and A. Santos, Perturbation analysis of a stationary nonequilibrium flow generated by an external force,, J. Stat. Phys., 76 (1994), 1399.
doi: 10.1007/BF02187068. |
[57] |
M. Tij and A. Santos, Combined heat and momentum transport in a dilute gas,, Phys. Fluids, 7 (1995), 2858.
doi: 10.1063/1.868662. |
[58] |
M. Tij and A. Santos, Non-Newtonian Poiseuille flow of a gas in a pipe,, Physica A, 289 (2001), 336.
doi: 10.1016/S0378-4371(00)00405-2. |
[59] |
M. Tij and A. Santos, Poiseuille flow in a heated granular gas,, J. Stat. Phys., 117 (2004), 901.
doi: 10.1007/s10955-004-5710-x. |
[60] |
M. Tij, E. E. Tahiri, J. M. Montanero, V. Garzó, A. Santos and J. W. Dufty, Nonlinear Couette flow in a low density granular gas,, J. Stat. Phys., 103 (2001), 1035.
doi: 10.1023/A:1010317207358. |
[61] |
B. D. Todd and D. J. Evans, Temperature profile for Poiseuille flow,, Phys. Rev. E, 55 (1997), 2800.
doi: 10.1103/PhysRevE.55.2800. |
[62] |
K. P. Travis, B. D. Todd and D. J. Evans, Poiseuille flow of molecular fluids,, Physica A, 240 (1997), 315.
doi: 10.1016/S0378-4371(97)00155-6. |
[63] |
C. Truesdell and R. G. Muncaster, "Fundamentals of Maxwell’s Kinetic Theory of a Simple Monatomic Gas,'', Academic Press, (1980). Google Scholar |
[64] |
F. J. Uribe and A. L. Garcia, Burnett description for plane Poiseuille flow,, Phys. Rev. E, 60 (1999), 4063.
doi: 10.1103/PhysRevE.60.4063. |
[65] |
F. Vega Reyes, A. Santos and V. Garzó, Non-Newtonian granular hydrodynamics. What do the inelastic simple shear flow and the elastic Fourier flow have in common?,, Phys. Rev. Lett., 104 (2010).
doi: 10.1103/PhysRevLett.104.028001. |
[66] |
P. Welander, On the temperature jump in a rarefied gas,, Akiv för Fysik, 7 (1954), 507. Google Scholar |
[67] |
K. Xu, Super-Burnett solutions for Poiseuille flow,, Phys. Fluids, 15 (2003), 2077.
doi: 10.1063/1.1577564. |
[68] |
Y. Zheng, A. L. Garcia and B. J. Alder, Comparison of kinetic theory and hydrodynamics for Poiseuille flow,, J. Stat. Phys., 109 (2002), 495.
doi: 10.1023/A:1020498111819. |
show all references
References:
[1] |
M. Alam and V. K. Chikkadi, Velocity distribution function and correlations in a granular Poiseuille flow,, J. Fluid Mech., 653 (2010), 175.
doi: 10.1017/S0022112010000200. |
[2] |
M. Alaoui and A. Santos, Poiseuille flow driven by an external force,, Phys. Fluids A, 4 (1992), 1273.
doi: 10.1063/1.858245. |
[3] |
K. Aoki, S. Takata and T. Nakanishi, A Poiseuille-type flow of a rarefied gas between two parallel plates driven by a uniform external force,, Phys. Rev. E, 65 (2002).
doi: 10.1103/PhysRevE.65.026315. |
[4] |
E. Asmolov, N. K. Makashev and V. I. Nosik, Heat transfer between parallel plates in a gas of Maxwellian molecules,, Sov. Phys. Dokl., 24 (1979), 892. Google Scholar |
[5] |
P. L. Bhatnagar, E. P. Gross and M. Krook, A model collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems,, Phy. Rev., 94 (1954), 511.
doi: 10.1103/PhysRev.94.511. |
[6] |
J. J. Brey, A. Santos and J. W. Dufty, Heat and momentum transport far from equilibrium,, Phys. Rev. A, 36 (1987), 2842.
doi: 10.1103/PhysRevA.36.2842. |
[7] |
C. Cercignani, "The Boltzmann Equation and Its Applications,'', Springer-Verlag, (1988). Google Scholar |
[8] |
C. Cercignani, "Mathematical Methods in Kinetic Theory,'', Plenum Press, (1990). Google Scholar |
[9] |
C. Cercignani, M. Lampis and S. Lorenzani, Plane Poiseuille-Couette problem in micro-electro-mechanical systems applications with gas-rarefaction effects,, Phy. Fluids, 18 (2006).
doi: 10.1063/1.2335847. |
[10] |
C. Cercignani and F. Sernagiotto, Cylindrical Poiseuille flow of a rarefied gas,, Phys. Fluids, 9 (1966), 40.
doi: 10.1063/1.1761530. |
[11] |
S. Chapman and T. G. Cowling, "The Mathematical Theory of Nonuniform Gases,'', Cambridge University Press, (1970). Google Scholar |
[12] |
V. Chikkadi and M. Alam, Slip velocity and stresses in granular Poiseuille flow via event-driven simulation,, Phys. Rev. E, 80 (2009).
doi: 10.1103/PhysRevE.80.021303. |
[13] |
J. R. Dorfman and H. van Beijeren, The kinetic theory of gases,, in, (1977), 65. Google Scholar |
[14] |
A. I. Erofeev and O. G. Friedlander, Macroscopic models for non-equilibrium flows of monatomic gas and normal solutions,, in, (2007), 117. Google Scholar |
[15] |
R. Esposito, J. L. Lebowitz and R. Marra, A hydrodynamic limit of the stationary Boltzmann equation in a slab,, Commun. Math. Phys., 160 (1994), 49.
doi: 10.1007/BF02099789. |
[16] |
M. A. Gallis, J. R. Torczynski, D. J. Rader, M. Tij and A. Santos, Normal solutions of the Boltzmann equation for highly nonequilibrium Fourier flow and Couette flow,, Phys. Fluids, 18 (2006). Google Scholar |
[17] |
M. A. Gallis, J. R. Torczynski, D. J. Rader, M. Tij and A. Santos, Analytical and numerical normal solutions of the Boltzmann equation for highly nonequilibrium Fourier and Couette flows,, in, (2007), 251. Google Scholar |
[18] |
L. S. García-Colín, R. M. Velasco and F. J. Uribe, Beyond the Navier-Stokes equations: Burnett hydrodynamics,, Phys. Rep., 465 (2008), 149.
doi: 10.1016/j.physrep.2008.04.010. |
[19] |
V. Garzó and M. López de Haro, Nonlinear transport for a dilute gas in steady Couette flow,, Phys. Fluids, 9 (1997), 776.
doi: 10.1063/1.869232. |
[20] |
V. Garzó and A. Santos, "Kinetic Theory of Gases in Shear Flows. Nonlinear Transport,'', Kluwer Academic Publishers, (2003). Google Scholar |
[21] |
S. Hess and M. Malek Mansour, Temperature profile of a dilute gas undergoing a plane Poiseuille flow,, Physica A, 272 (1999), 481.
doi: 10.1016/S0378-4371(99)00254-X. |
[22] |
L. P. Kadanoff, G. R. McNamara and G. Zanetti, A Poiseuille viscometer for lattice gas automata,, Complex Syst., 1 (1987), 791. Google Scholar |
[23] |
L. P. Kadanoff, G. R. McNamara and G. Zanetti, From automata to fluid flow: Comparisons of simulation and theory,, Phys. Rev. A, 40 (1989), 4527.
doi: 10.1103/PhysRevA.40.4527. |
[24] |
C. S. Kim, J. W. Dufty, A. Santos and J. J. Brey, Hilbert-class or "normal'' solutions for stationary heat flow,, Phys. Rev. A, 39 (1989), 328.
doi: 10.1103/PhysRevA.39.328. |
[25] |
C. S. Kim, J. W. Dufty, A. Santos and J. J. Brey, Analysis of nonlinear transport in Couette flow,, Phys. Rev A, 40 (1989), 7165.
doi: 10.1103/PhysRevA.40.7165. |
[26] |
G. M. Kremer, "An Introduction to the Boltzmann Equation and Transport Processes in Gases,'', Springer, (2010).
doi: 10.1007/978-3-642-11696-4. |
[27] |
M. Malek Mansour, F. Baras and A. L. Garcia, On the validity of hydrodynamics in plane Poiseuille flows,, Physica A, 240 (1997), 255.
doi: 10.1016/S0378-4371(97)00149-0. |
[28] |
N. K. Makashev and V. I. Nosik, Steady Couette flow (with heat transfer) of a gas of Maxwellian molecules,, Sov. Phys. Dokl., 25 (1981), 589. Google Scholar |
[29] |
J. M. Montanero, M. Alaoui, A. Santos and V. Garzó, Monte Carlo simulation of the Boltzmann equation for steady Fourier flow,, Phys. Rev. E, 49 (1994), 367.
doi: 10.1103/PhysRevE.49.367. |
[30] |
J. M. Montanero and V. Garzó, Nonlinear Couette flow in a dilute gas: Comparison between theory and molecular dynamics simulation,, Phys. Rev. E, 58 (1998), 1836.
doi: 10.1103/PhysRevE.58.1836. |
[31] |
J. M. Montanero, A. Santos and V. Garzó, Monte Carlo simulation of nonlinear Couette flow in a dilute gas,, Phys. Fluids, 12 (2000), 3060.
doi: 10.1063/1.1313563. |
[32] |
R. S. Myong, Coupled nonlinear constitutive models for rarefied and microscale gas flows: subtle interplay of kinematics and dissipation effects,, Cont. Mech. Thermodyn., 21 (2009), 389.
doi: 10.1007/s00161-009-0112-6. |
[33] |
V. I. Nosik, Heat transfer between parallel plates in a mixture of gases of Maxwellian molecules,, Sov. Phys. Dokl., 25 (1981), 495. Google Scholar |
[34] |
V. I. Nosik, Degeneration of the Chapman-Enskog expansion in one-dimensional motions of Maxwellian molecule gases,, in, 13 (1983), 237. Google Scholar |
[35] |
T. Ohwada, Y. Sone and K. Aoki, Numerical analysis of the Poiseuille and thermal transpiration flows between two parallel plates on the basis of the Boltzmann equation for hard-sphere molecules,, Phys. Fluids A, 1 (1989), 2042.
doi: 10.1063/1.857478. |
[36] |
M. C. Potter, Stability of plane Couette-Poiseuille flow,, J. Fluid Mech., 24 (1966), 609.
doi: 10.1017/S0022112066000855. |
[37] |
D. Risso and P. Cordero, Dilute gas Couette flow: Theory and molecular dynamics simulation,, Phys. Rev. E, 56 (1997), 489.
doi: 10.1103/PhysRevE.56.489. |
[38] |
D. Risso and P. Cordero, Generalized hydrodynamics for a Poiseuille flow: theory and simulations,, Phys. Rev. E, 58 (1998), 546.
doi: 10.1103/PhysRevE.58.546. |
[39] |
M. Sabbane, M. Tij and A. Santos, Maxwellian gas undergoing a stationary Poiseuille flow in a pipe,, Physica A, 327 (2003), 264.
doi: 10.1016/S0378-4371(03)00513-2. |
[40] |
A. Santos, Solutions of the moment hierarchy in the kinetic theory of Maxwell models,, Cont. Mech. Thermodyn., 21 (2009), 361.
doi: 10.1007/s00161-009-0113-5. |
[41] |
A. Santos, J. J. Brey and V. Garzó, Kinetic model for steady heat flow,, Phys. Rev. A, 34 (1986), 5047.
doi: 10.1103/PhysRevA.34.5047. |
[42] |
A. Santos, J. J. Brey, C. S. Kim and J. W. Dufty, Velocity distribution for a gas with steady heat flow,, Phys. Rev. A, 39 (1989), 320.
doi: 10.1103/PhysRevA.39.320. |
[43] |
A. Santos, V. Garzó and J. J. Brey, Comparison between the homogeneous-shear and the sliding-boundary methods to produce shear flow,, Phys. Rev. A, 46 (1992), 8018.
doi: 10.1103/PhysRevA.46.8018. |
[44] |
A. Santos and M. Tij, Gravity-driven Poiseuille flow in dilute gases. Elastic and inelastic collisions,, in, (2006), 53. Google Scholar |
[45] |
Y. Sone, Asymptotic theory of a steady flow of a rarefied gas past bodies for small Knudsen numbers,, in, (1991), 19. Google Scholar |
[46] |
Y. Sone, Flows induced by temperature fields in a rarefied gas and their ghost effect on the behavior of a gas in the continuum limit,, Annu. Rev. Fluid Mech., 32 (2000), 779.
doi: 10.1146/annurev.fluid.32.1.779. |
[47] |
Y. Sone, "Kinetic Theory and Fluid Dynamics,'', Birkhäuser, (2002). Google Scholar |
[48] |
H. Struchtrup, "Macroscopic Transport Equations for Rarefied Gas Flows. Approximation Methods in Kinetic Theory,'', Springer, (2005). Google Scholar |
[49] |
H. Struchtrup and M Torrilhon, Higher-order effects in rarefied channel flows,, Phys. Rev. E, 78 (2008).
doi: 10.1103/PhysRevE.78.046301. |
[50] |
S. A. Suslov and T. D. Tran, Revisiting plane Couette-Poiseuille flows of a piezo-viscous fluid,, J. Non-Newton. Fluid Mech., 154 (2006), 170. Google Scholar |
[51] |
P. Taheri, M. Torrilhon and H. Struchtrup, Couette and Poiseuille microflows: analytical solutions for regularized 13-moment equations,, Phys. Fluids, 21 (2009).
doi: 10.1063/1.3064123. |
[52] |
R. Tehver, F. Toigo, J. Koplik and J. R. Banavar, Thermal walls in computer simulations,, Phys. Rev. E, 57 (1998).
doi: 10.1103/PhysRevE.57.R17. |
[53] |
E. M. Thurlow and J. C. Klewicki, Experimental study of turbulent Poiseuille-Couette flow,, Phys. Fluids, 12 (2000), 865.
doi: 10.1063/1.870341. |
[54] |
M. Tij, V. Garzó and A. Santos, Influence of gravity on nonlinear transport in the planar Couette flow,, Phys. Fluids, 11 (1999), 893.
doi: 10.1063/1.869960. |
[55] |
M. Tij, M. Sabbane and A. Santos, Nonlinear Poiseuille flow in a gas,, Phys. Fluids, 10 (1998), 1021.
doi: 10.1063/1.869621. |
[56] |
M. Tij and A. Santos, Perturbation analysis of a stationary nonequilibrium flow generated by an external force,, J. Stat. Phys., 76 (1994), 1399.
doi: 10.1007/BF02187068. |
[57] |
M. Tij and A. Santos, Combined heat and momentum transport in a dilute gas,, Phys. Fluids, 7 (1995), 2858.
doi: 10.1063/1.868662. |
[58] |
M. Tij and A. Santos, Non-Newtonian Poiseuille flow of a gas in a pipe,, Physica A, 289 (2001), 336.
doi: 10.1016/S0378-4371(00)00405-2. |
[59] |
M. Tij and A. Santos, Poiseuille flow in a heated granular gas,, J. Stat. Phys., 117 (2004), 901.
doi: 10.1007/s10955-004-5710-x. |
[60] |
M. Tij, E. E. Tahiri, J. M. Montanero, V. Garzó, A. Santos and J. W. Dufty, Nonlinear Couette flow in a low density granular gas,, J. Stat. Phys., 103 (2001), 1035.
doi: 10.1023/A:1010317207358. |
[61] |
B. D. Todd and D. J. Evans, Temperature profile for Poiseuille flow,, Phys. Rev. E, 55 (1997), 2800.
doi: 10.1103/PhysRevE.55.2800. |
[62] |
K. P. Travis, B. D. Todd and D. J. Evans, Poiseuille flow of molecular fluids,, Physica A, 240 (1997), 315.
doi: 10.1016/S0378-4371(97)00155-6. |
[63] |
C. Truesdell and R. G. Muncaster, "Fundamentals of Maxwell’s Kinetic Theory of a Simple Monatomic Gas,'', Academic Press, (1980). Google Scholar |
[64] |
F. J. Uribe and A. L. Garcia, Burnett description for plane Poiseuille flow,, Phys. Rev. E, 60 (1999), 4063.
doi: 10.1103/PhysRevE.60.4063. |
[65] |
F. Vega Reyes, A. Santos and V. Garzó, Non-Newtonian granular hydrodynamics. What do the inelastic simple shear flow and the elastic Fourier flow have in common?,, Phys. Rev. Lett., 104 (2010).
doi: 10.1103/PhysRevLett.104.028001. |
[66] |
P. Welander, On the temperature jump in a rarefied gas,, Akiv för Fysik, 7 (1954), 507. Google Scholar |
[67] |
K. Xu, Super-Burnett solutions for Poiseuille flow,, Phys. Fluids, 15 (2003), 2077.
doi: 10.1063/1.1577564. |
[68] |
Y. Zheng, A. L. Garcia and B. J. Alder, Comparison of kinetic theory and hydrodynamics for Poiseuille flow,, J. Stat. Phys., 109 (2002), 495.
doi: 10.1023/A:1020498111819. |
[1] |
Changli Yuan, Mojdeh Delshad, Mary F. Wheeler. Modeling multiphase non-Newtonian polymer flow in IPARS parallel framework. Networks & Heterogeneous Media, 2010, 5 (3) : 583-602. doi: 10.3934/nhm.2010.5.583 |
[2] |
M. Bulíček, F. Ettwein, P. Kaplický, Dalibor Pražák. The dimension of the attractor for the 3D flow of a non-Newtonian fluid. Communications on Pure & Applied Analysis, 2009, 8 (5) : 1503-1520. doi: 10.3934/cpaa.2009.8.1503 |
[3] |
Muhammad Mansha Ghalib, Azhar Ali Zafar, Zakia Hammouch, Muhammad Bilal Riaz, Khurram Shabbir. Analytical results on the unsteady rotational flow of fractional-order non-Newtonian fluids with shear stress on the boundary. Discrete & Continuous Dynamical Systems - S, 2020, 13 (3) : 683-693. doi: 10.3934/dcdss.2020037 |
[4] |
Hong Zhou, M. Gregory Forest. Anchoring distortions coupled with plane Couette & Poiseuille flows of nematic polymers in viscous solvents: Morphology in molecular orientation, stress & flow. Discrete & Continuous Dynamical Systems - B, 2006, 6 (2) : 407-425. doi: 10.3934/dcdsb.2006.6.407 |
[5] |
Igor Chueshov, Tamara Fastovska. On interaction of circular cylindrical shells with a Poiseuille type flow. Evolution Equations & Control Theory, 2016, 5 (4) : 605-629. doi: 10.3934/eect.2016021 |
[6] |
Liudmila A. Pozhar. Poiseuille flow of nanofluids confined in slit nanopores. Conference Publications, 2001, 2001 (Special) : 319-326. doi: 10.3934/proc.2001.2001.319 |
[7] |
Leif Arkeryd, Raffaele Esposito, Rossana Marra, Anne Nouri. Ghost effect by curvature in planar Couette flow. Kinetic & Related Models, 2011, 4 (1) : 109-138. doi: 10.3934/krm.2011.4.109 |
[8] |
Lars Diening, Michael Růžička. An existence result for non-Newtonian fluids in non-regular domains. Discrete & Continuous Dynamical Systems - S, 2010, 3 (2) : 255-268. doi: 10.3934/dcdss.2010.3.255 |
[9] |
Oleksiy V. Kapustyan, Pavlo O. Kasyanov, José Valero, Michael Z. Zgurovsky. Strong attractors for vanishing viscosity approximations of non-Newtonian suspension flows. Discrete & Continuous Dynamical Systems - B, 2018, 23 (3) : 1155-1176. doi: 10.3934/dcdsb.2018146 |
[10] |
Jan Sokołowski, Jan Stebel. Shape optimization for non-Newtonian fluids in time-dependent domains. Evolution Equations & Control Theory, 2014, 3 (2) : 331-348. doi: 10.3934/eect.2014.3.331 |
[11] |
Aneta Wróblewska-Kamińska. Unsteady flows of non-Newtonian fluids in generalized Orlicz spaces. Discrete & Continuous Dynamical Systems - A, 2013, 33 (6) : 2565-2592. doi: 10.3934/dcds.2013.33.2565 |
[12] |
Emil Novruzov. On existence and nonexistence of the positive solutions of non-newtonian filtration equation. Communications on Pure & Applied Analysis, 2011, 10 (2) : 719-730. doi: 10.3934/cpaa.2011.10.719 |
[13] |
Linfang Liu, Tomás Caraballo, Xianlong Fu. Exponential stability of an incompressible non-Newtonian fluid with delay. Discrete & Continuous Dynamical Systems - B, 2018, 23 (10) : 4285-4303. doi: 10.3934/dcdsb.2018138 |
[14] |
Hafedh Bousbih. Global weak solutions for a coupled chemotaxis non-Newtonian fluid. Discrete & Continuous Dynamical Systems - B, 2019, 24 (2) : 907-929. doi: 10.3934/dcdsb.2018212 |
[15] |
Leif Arkeryd, Raffaele Esposito, Rossana Marra, Anne Nouri. Erratum to: Ghost effect by curvature in planar Couette flow [1]. Kinetic & Related Models, 2012, 5 (3) : 669-672. doi: 10.3934/krm.2012.5.669 |
[16] |
Bum Ja Jin, Kyungkeun Kang. Caccioppoli type inequality for non-Newtonian Stokes system and a local energy inequality of non-Newtonian Navier-Stokes equations without pressure. Discrete & Continuous Dynamical Systems - A, 2017, 37 (9) : 4815-4834. doi: 10.3934/dcds.2017207 |
[17] |
María Anguiano, Francisco Javier Suárez-Grau. Newtonian fluid flow in a thin porous medium with non-homogeneous slip boundary conditions. Networks & Heterogeneous Media, 2019, 14 (2) : 289-316. doi: 10.3934/nhm.2019012 |
[18] |
Veronika Schleper. A hybrid model for traffic flow and crowd dynamics with random individual properties. Mathematical Biosciences & Engineering, 2015, 12 (2) : 393-413. doi: 10.3934/mbe.2015.12.393 |
[19] |
Asim Aziz, Wasim Jamshed. Unsteady MHD slip flow of non Newtonian power-law nanofluid over a moving surface with temperature dependent thermal conductivity. Discrete & Continuous Dynamical Systems - S, 2018, 11 (4) : 617-630. doi: 10.3934/dcdss.2018036 |
[20] |
Jong Yeoul Park, Jae Ug Jeong. Pullback attractors for a $2D$-non-autonomous incompressible non-Newtonian fluid with variable delays. Discrete & Continuous Dynamical Systems - B, 2016, 21 (8) : 2687-2702. doi: 10.3934/dcdsb.2016068 |
2018 Impact Factor: 1.38
Tools
Metrics
Other articles
by authors
[Back to Top]