A thermo-mechanically consistent Burnett regime continuum flow equation without Chapman-Enskog expansion

Chapman-Enskog expansion is the orthodox approach to derive continuum flow models from Boltzmann’s kinetic equation for dilute gases. Beyond the Navier-Stokes-Fourier order, these models known as Burnett hydrodynamic-regime equations violate a number of fundamental mechanical and thermodynamic principles in their original forms. This has generated a widely investigated problem in the kinetic theory of gases. In this short article, we derive a Burnett hydrodynamic-regime continuum model that is systematically consistent with all known mechanical and thermodynamic principles without using any series’ expansion. Close comparison with the conventional Burnett hydrodynamic set of equations is considered and their linear stabilities around an equilibrium point under small perturbations are presented

Transition regime analytical solution to gas mass flow rate in a rectangular micro channel

We present an analytical model predicting the experimentally observed gas mass flow rate in rectangular micro channels over slip and transition regimes without the use of any fitting parameter. Previously, Sone [1] reported a class of pure continuum regime flows that requires terms of Burnett order in constitutive equations of shear stress to be predicted appropriately. The corrective terms to the conventional Navier-Stokes equation were named the ghost effect. We demonstrate in this paper similarity between Sone ghost effect model and newly so-called ‘volume diffusion hydrodynamic model’. A generic analytical solution to gas mass flow rate in a rectangular micro channel is then obtained. It is shown that the volume diffusion hydrodynamics allows to accurately predict the gas mass flow rate up to Knudsen number of 5. This can be achieved without necessitating the use of any adjustable parameters in boundary conditions or parametric scaling laws for constitutive relations. The present model predicts the non-linear variation of pressure profile along the axial direction and also captures the change in curvature with increase in rarefaction

Dissipative mass flux and sound wave propagations in monatomic gases

Predicting sound wave dispersion in monatomic gases is a fundamental gas flow problem in rarefied gas dynamics. The Navier-Stokes-Fourier model is known to fail where local thermodynamic equilibrium breaks down. Generally, conventional gas flow models involve equations for mass-density without a dissipative mass contribution. In this paper we observe that using a dissipative mass flux contribution as a non-local-equilibrium correction can improve agreement between the continuum equation prediction of sound wave dispersion and experimental data. Two mass dissipation models are investigated: a preliminary model that simply incorporates a diffusive density term in the set of three conservation equations, and another model derived from considering microscopic fluctuations in molecular spatial distributions

An extension to the Navier-Stokes-Fourier equations by considering molecular collisions with boundaries

In this paper we propose a model for micro gas flows consisting of the Navier-Stokes-Fourier equations (NSF) extended by a description of molecular collisions with solid boundaries and discontinuous velocity slip and temperature jump boundary conditions. By considering the molecular collisions with the solid boundaries in gas flows we capture some of the near wall effects that the conventional NSF with linear stress/strain-rate and heat-flux/ temperature-gradient relationships seem to be unable to describe. The model that we propose incorporates the molecular collisions with solid boundaries as an extension to the conventional definition of the average travelling distance of molecules before experiencing intermolecular collisions (the mean free path). By considering both of these types of collisions we obtain an effective mean free path expression, which varies with distance to surfaces. The effective mean free path is proposed to be used to obtain new definitions of effective viscosity and effective thermal conductivity, which will extend the applicability of NSF equations to higher Knudsen numbers. We show results of simple flow cases that are solved using this extended NSF model and discuss limitations to the model due to various assumptions. We also mention interesting ideas for further development of the model based on a more detailed gas description

Wall temperature jump in polyatomic gas flows

This article deals with the calculations of the temperature jump at the wall for gas flows in the slip regime. The analytical calculations are based on kinetic boundary conditions developed especially for polyatomic molecules. When compared to an expression previously obtained for unstructured molecules, the polyatomic molecule temperature jump reveals supplementary terms of bulk viscosity type due to the internal mode excitation. These terms may be important in high speed flows or in gas flows displaying significant relative density variation at the wall

The concept of mass-density in classical thermodynamics and the Boltzmann kinetic equation for dilute gases

In this paper we discuss the mass-density of gas media as represented in kinetic theory. It is argued that conventional representations of this variable in gas kinetic theory contradict a macroscopic field variable and thermodynamic property in classical thermodynamics. We show that in cases where mass-density variations exist throughout the medium, introducing the mass-density as a macroscopic field variable leads to a restructuring of the diffusive/convective fluxes and implies some modifications to the hydrodynamic equations describing gas flows and heat transfer. As an illustration, we consider the prediction of mass-density profiles in a simple heat conduction problem between parallel plates maintained at different temperatures

Mediating between AI and highly specialized users

We report part of the design experience gained in X-Media, a system for knowledge management and sharing. Consolidated techniques of interaction design (scenario-based design) had to be revisited to capture the richness and complexity of intelligent interactive systems. We show that the design of intelligent systems requires methodologies (faceted scenarios) that support the investigation of intelligent features and usability factors simultaneously. Interaction designers become mediators between intelligent technology and users, and have to facilitate reciprocal understanding

Temperature jump and slip velocity calculations from an anisotropic scattering kernel

This article deals with the problem of temperature jump and slip velocity at the wall in gas/surface interaction. A consistent modelling of an impermeable surface involving an anisotropic scattering kernel developed in previous works is used to establish boundary conditions in unstructured molecule gas flows. Thus a temperature jump relation is derived in which the gas viscous effects at the wall and the mean velocity gradients appear. Likewise, a slip velocity relation is obtained in which both the slip coeffcient and the thermal creep coeffcient depend on the wall-to-gas temperature ratio. Moreover, both the temperature jump and the slip velocity relations involve not only one accommodation coeffcient as in usual expressions, but also the gas/surface information through the various (notably normal and tangential) accommodation coeffcients of the momentum components