Normal solutions of the Boltzmann equation for highly nonequilibrium Fourier flow and Couette flow

The state of a single-species monatomic gas from near-equilibrium to highly nonequilibrium conditions is investigated using analytical and numerical methods. Normal solutions of the Boltzmann equation for Fourier flow (uniform heat flux) and Couette flow (uniform shear stress) are found in terms of the heat-flux and shear-stress Knudsen numbers. Analytical solutions are found for inverse-power-law molecules from hard-sphere through Maxwell at small Knudsen numbers using Chapman-Enskog (CE) theory and for Maxwell molecules at finite Knudsen numbers using a moment-hierarchy (MH) method. Corresponding numerical solutions are obtained using the Direct Simulation Monte Carlo (DSMC) method of Bird. The thermal conductivity, the viscosity, and the Sonine-polynomial coefficients of the velocity distribution function from DSMC agree with CE results at small Knudsen numbers and with MH results at finite Knudsen numbers. Subtle differences between inverse-power-law, variable-soft-sphere, and variable-hard-sphere representations of Maxwell molecules are observed. The MH and DSMC results both indicate that the effective thermal conductivity and the effective viscosity for Maxwell molecules are independent of the heat-flux Knudsen number, and additional DSMC simulations indicate that these transport properties for hard-sphere molecules decrease slightly as the heat-flux Knudsen number is increased. Similarly, the MH and DSMC results indicate that the effective thermal conductivity and the effective viscosity for Maxwell molecules decrease as the shear-stress Knudsen number is increased, and additional DSMC simulations indicate the same behavior for hard-sphere molecules. These results provide strong evidence that the DSMC method can be used to determine the state of a gas under highly nonequilibrium conditionsComment: 33 pages (preprint format) + 15 figures + 3 tables; to be published in Physics of Fluids; v2: Abstract in the abstract web page has been corrected, but otherwise the paper remains the same as in v

Non-Newtonian Couette-Poiseuille flow of a dilute gas

The steady state of a dilute gas enclosed between two infinite parallel plates in relative motion and under the action of a uniform body force parallel to the plates is considered. The Bhatnagar-Gross-Krook model kinetic equation is analytically solved for this Couette-Poiseuille flow to first order in the force and for arbitrary values of the Knudsen number associated with the shear rate. This allows us to investigate the influence of the external force on the non-Newtonian properties of the Couette flow. Moreover, the Couette-Poiseuille flow is analyzed when the shear-rate Knudsen number and the scaled force are of the same order and terms up to second order are retained. In this way, the transition from the bimodal temperature profile characteristic of the pure force-driven Poiseuille flow to the parabolic profile characteristic of the pure Couette flow through several intermediate stages in the Couette-Poiseuille flow are described. A critical comparison with the Navier-Stokes solution of the problem is carried out.Comment: 24 pages, 5 figures; v2: discussion on boundary conditions added; 10 additional references. Published in a special issue of the journal "Kinetic and Related Models" dedicated to the memory of Carlo Cercignan

Express Assessment of Population Health in Environmentally Unfriendly Region of Kazakhstan

The article shows that the proximity of houses to Lake Balkhash affects somatic health – more than 80 % of inhabitants of nearby area had low level, while about the same number of people – 75 % of the inhabitants of more remote areas from the lake showed "average" and "below average" level of healt

Experimental investigation of hydrodynamics of melt layer during laser cutting of steel

In laser cutting process, understanding of hydrodynamics of melt layer is significant, because it is an important factor which controls the final quality. In this work, we observed hydrodynamics of melt layer on kerf front in the case of laser cutting of steel with inert gas. The observation shows that the melt flow on the kerf front exhibits strong instability, depending on cutting velocity. In intermediate range of velocity, the flow on the central part of the kerf front is continuous, whereas the flow along the sides is discontinuous. It is firstly confirmed that the instability in the side flow is the cause of the striation initiation from the top part of the kerf. The origin of the instability is discussed in terms of instabilities in thermal dynamics and hydrodynamics. The proposed model shows reasonable agreement with experimental results