Thermal stress vs. thermal transpiration: A competition in thermally driven cavity flows

Abstract

The driven cavity flow over the whole range of the Knudsen number Phys. The velocity dependent Maxwell (VDM) model for the boundary condition of a rarefied gas, recently presented by Struchtrup ["Maxwell boundary condition and velocity dependent accommodation coefficient," Phys. Fluids 25, 112001 (2013)], provides the opportunity to control the strength of the thermal transpiration force at a wall with temperature gradient. Molecular simulations of a heated cavity with varying parameters show intricate flow patterns for weak, or inverted transpiration force. Microscopic and macroscopic transport equations for rarefied gases are solved to study the flow patterns and identify the main driving forces for the flow. It turns out that the patterns arise from a competition between thermal transpiration force at the boundary and thermal stresses in the bulk. C 2015 AIP Publishing LLC.

Fundamental solutions to moment equations for the simulation of microscale gas flows

“…The combined effect of the counter-flowing thermal creep and thermal stress effects is a recirculating flow field. A similar competition of thermal stress and thermal creep is discussed in Mohammadzadeh, Rana & Struchtrup (2015) in the context of lid-driven cavity flow. Figure 11 shows the total drag force on the two spheres against Kn (the force on each sphere is equal, and in the same direction; there is no attractive or repulsive component).…”

Evaporation boundary conditions for the R13 equations of rarefied gas dynamics

“…4 and 5 and references therein. The rich interplay between the different rarefaction effects comes into play in particular for multi-dimensional problems 8,37 but is mainly lost in the simple one-dimensional problems discussed above. Since R13 includes the rarefaction effects, and NSF does not, their predictions differ greatly in multidimensional problems.…”

“…12 Even then, the number of boundary conditions required for the solution of the equations differed between the linear and the non-linear equations. 26 For the closure presented (8), the equations were modified such that linear and non-linear equations require the same number of boundary conditions, 37 and this is the preferred version of the R13 equations for slow flows. For non-linear processes such as shock waves, various versions show marked differences in the results.…”

“…3,6,7 While adding jump and slip boundary conditions to NSF introduces some of these effects into classical hydrodynamics, all bulk rarefaction effects remain elusive. 8 A fully accurate description of rarefied flow behavior requires solution of the Boltzmann equation, e.g., by the direct simulation Monte Carlo (DSMC) method 9 or by direct numerical simulation, 10 but typical computational times are often significantly above those for hydrodynamics, in particular, when the degree of rarefaction is mild. Macroscopic models for rarefied flows, such as the R13 equations, extend the equations of hydrodynamics by accounting for a small number of additional flow variables, yet describe bulk a) struchtr@uvic.ca.…”

A moment model for phonon transport at room temperature

“…(24), as well as the production terms Eqs. (27) and (28), provides a closed system of equations that can be solved to describe the thermal behavior of the crystal. We introduce the non-dimensional moments, time and space as…”