The linearized Boltzmann equation: a concise and accurate solution of the temperature-jump problem

2003 ◽  
Vol 77 (4) ◽  
pp. 417-432 ◽  
Author(s):  
C.E. Siewert
Keyword(s):  
Boltzmann Equation ◽  
Temperature Jump ◽  
Accurate Solution ◽  
Jump Problem ◽  
Linearized Boltzmann Equation

The Slip Problems for a Simple Gas

1971 ◽  
Vol 26 (6) ◽  
pp. 964-972 ◽  
Author(s):  
S.K. Loyalka
Keyword(s):  
Boltzmann Equation ◽  
Temperature Jump ◽  
Velocity Slip ◽  
Polyatomic Gas ◽  
Extra Effort ◽  
Linearized Boltzmann Equation ◽  
Multicomponent Gas ◽  
Interaction Law ◽  
Temperature Jump Coefficient ◽  
Polyatomic Gas Mixtures

Abstract Simple and accurate expressions for the velocity slip coefficient, the slip in the thermal creep, and the temperature jump coefficient are obtained by applying a variational technique to the linearized Boltzmann equation for a simple gas. Completely general forms of the boundary conditions are used, and the final results are presented in a form such that the results for any particular intermolecular force law or the gas-surface interaction law can easily be calculated. Further, it is shown that, with little extra effort, the present results can be easily extended to include the case of a polyatomic gas. It is felt that the present work, together with a recent paper in which the author has considered the solutions of the linearized Boltzmann equation for a monatomic multicomponent gas mixture, provide the desired basis for the consideration of the various slip problems associated with the polyatomic gas mixtures.

Theory of Boundary Conditions for the Boltzmann Equation

1977 ◽  
Vol 32 (6) ◽  
pp. 521-531 ◽  
Author(s):  
L. Waldmann
Keyword(s):  
Boltzmann Equation ◽  
Boundary Conditions ◽  
Temperature Jump ◽  
Functional Relation ◽  
Linearized Boltzmann Equation ◽  
Kinetic Boundary ◽  
The Difference ◽  
Molecular Distribution Function ◽  
Transport Relaxation ◽  
Slip Coefficients

Abstract In preceding papers, Refs. 1,2, boundary conditions were developed for transport-relaxation equations by aid of a general reciprocity postulate for the interface. The same method is now used for the linearized Boltzmann equation. A new scheme emerges: the kinetic boundary conditions consist in a linear functional relation between interfacial "forces and fluxes" - in the sense of non-equilibrium thermodynamics - which are, broadly speaking, given by the sum and the difference of the molecular distribution function and its time-reversed, at the wall. The general properties of the kernels occurring in this atomistic boundary law are studied. The phenomenological surface coefficients of (generalized) linear thermo-hydrodynamics, as e. g. temperature jump, slip coefficients etc., can in a simple way be expressed by the kernel of the atomistic boundary law. This kernel is explicitly worked out for completely thermalizing wall collisions.

THE SEMICONTINUOUS BOLTZMANN EQUATION: TOWARDS A MODEL FOR FLUID DYNAMIC APPLICATIONS

1993 ◽  
Vol 03 (01) ◽  
pp. 65-93 ◽  
Author(s):  
E. LONGO ◽  
L. PREZIOSI ◽  
N. BELLOMO
Keyword(s):  
Boltzmann Equation ◽  
Differential Equations ◽  
Thermodynamic Equilibrium ◽  
Temperature Jump ◽  
Fluid Dynamic ◽  
Angular Variable ◽  
Jump Problem ◽  
The Boltzmann Equation ◽  
Continuous Models

This paper proposes a semicontinuous model of the Boltzmann equation for gas particles moving in the plane in all possible directions, but with a finite, large, number of velocity moduli. The model, called the n-semicontinuous Boltzmann equation, consists in a system of integro-differential equations with one-fold integrals over a suitable angular variable. Thermodynamic equilibrium is studied in details. The model is then applied to the analysis of a temperature jump problem. The results are compared with the ones obtained by continuous models of the Boltzmann equation.

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