Recovery of Transport Coefficients in Navier-Stokes Equations from Modeled Boltzmann Equation

AIAA Journal ◽  
2007 ◽  
Vol 45 (4) ◽  
pp. 737-739 ◽  
Author(s):  
R. C. K. Leung ◽  
E. W. S. Kam ◽  
R. M. C. So
Keyword(s):  
Boltzmann Equation ◽  
Stokes Equations ◽  
Transport Coefficients ◽  
Navier Stokes ◽  
Navier Stokes Equations

scholarly journals On the Navier-Stokes equations with temperature-dependent transport coefficients

2006 ◽  
Vol 2006 ◽  
pp. 1-14 ◽  
Author(s):  
Eduard Feireisl ◽  
Josef Málek
Keyword(s):  
Stokes Equations ◽  
Transport Coefficients ◽  
Three Dimensional ◽  
Periodic Problem ◽  
Large Data ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Long Time ◽  
Spatially Periodic ◽  
Dependent Transport

We establish long-time and large-data existence of a weak solution to the problem describing three-dimensional unsteady flows of an incompressible fluid, where the viscosity and heat-conductivity coefficients vary with the temperature. The approach reposes on considering the equation for the total energy rather than the equation for the temperature. We consider the spatially periodic problem.

scholarly journals From Boltzmann to incompressible Navier–Stokes in Sobolev spaces with polynomial weight

2018 ◽  
Vol 17 (01) ◽  
pp. 85-116 ◽  
Author(s):  
Marc Briant ◽  
Sara Merino-Aceituno ◽  
Clément Mouhot
Keyword(s):  
Boltzmann Equation ◽  
Knudsen Number ◽  
Exponential Decay ◽  
Sobolev Spaces ◽  
Stokes Equations ◽  
Linear Part ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
The Cauchy Problem ◽  
Global Equilibrium

We study the Boltzmann equation on the [Formula: see text]-dimensional torus in a perturbative setting around a global equilibrium under the Navier–Stokes linearization. We use a recent functional analysis breakthrough to prove that the linear part of the equation generates a [Formula: see text]-semigroup with exponential decay in Lebesgue and Sobolev spaces with polynomial weight, independently of the Knudsen number. Finally, we prove well-posedness of the Cauchy problem for the nonlinear Boltzmann equation in perturbative setting and an exponential decay for the perturbed Boltzmann equation, uniformly in the Knudsen number, in Sobolev spaces with polynomial weight. The polynomial weight is almost optimal. Furthermore, this result only requires derivatives in the space variable and allows to connect solutions to the incompressible Navier–Stokes equations in these spaces.

CHAPMAN-ENSKOG EXPANSION FOR A DISCRETE VELOCITY MODEL OF A GAS MIXTURE WITH BI-MOLECULAR CHEMICAL REACTIONS

1994 ◽  
Vol 04 (03) ◽  
pp. 355-372 ◽  
Author(s):  
R. MONACO ◽  
M. PANDOLFI BIANCHI ◽  
A. ROSSANI
Keyword(s):  
Chemical Reactions ◽  
Stokes Equations ◽  
Transport Coefficients ◽  
Kinetic Equations ◽  
Velocity Model ◽  
Navier Stokes ◽  
Thermodynamical Equilibrium ◽  
Navier Stokes Equations ◽  
Discrete Velocity ◽  
Discrete Velocity Model

We propose a new discrete velocity model of the Boltzmann equation for a mixture of four gases admitting particle elastic collisions and bi-molecular chemical reactions. We first prove an H-theorem and determine the thermodynamical equilibrium state. A Chapman-Enskog expansion on the kinetic equations is then performed, deriving both the Euler and the Navier-Stokes equations of the model. Finally the transport coefficients of diffusivity and viscosity are provided as well.

scholarly journals Transport coefficients for low and high-rate mass transfer along a biological horizontal cylinder

2006 ◽  
Vol 10 (2) ◽  
pp. 441-447
Author(s):  
Alberto A. Barreto ◽  
Mauri Fortes ◽  
Wanyr R. Ferreira ◽  
Luiz C. A. Crespo
Keyword(s):  
Mass Transfer ◽  
Stokes Equations ◽  
Transport Coefficients ◽  
Horizontal Cylinder ◽  
Transport Processes ◽  
High Rate ◽  
Navier Stokes ◽  
Transfer Coefficients ◽  
Navier Stokes Equations ◽  
Drying Conditions

Knowledge of heat and mass transfer coefficients is essential for drying simulation studies or design of food and grain thermal processes, including drying. This work presents the full development of a segregated finite element method to solve convection-diffusion problems. The developed scheme allows solving the incompressible, steady-state Navier-Stokes equations and convective-diffusive problems with temperature and moisture dependent properties. The problem of simultaneous energy, momentum and species transfer along an infinite, horizontal cylinder under drying conditions in forced convection is presented, considering conditions normally found in biological material thermal treatment or drying. Numerical results for Nusselt and Sherwood numbers were compared against available empirical expressions; the results agreed within the associated experimental errors. For high rate mass transport processes, the proposed methodology allows to simulate drying conditions involving wall convective mass flux by a simple inclusion of the appropriated boundary conditions.

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