Parameters

Short description

$\frac{\partial }{\partial y}$

the divergence operator in a one-dimensional configuration

y

position of the ending point of the converging particle

$y^{\prime }$

position of the starting point of the converging particle

$u\left(y\right)$

mass flow velocity in the point y

$v_T\left(y\right)$

the average magnitude of the thermal velocity of converging particle in point

$Z_V\left(y^{\prime }\right)$

the rate of collisions per unit volume at the point of the collision $y^{\prime }$

$\overrightarrow{v}\left(y\right)$

velocity vector in the ending point y

$Q_i\left(y^{\prime },y\right)$

the probability of free path traveling along the ballistic trajectory of the converging ballistic trajectory starting at $y^{\prime }$ and ending y

${\Psi }_{out}\left(y\right)$

property content of a diverging point y particle

${\Psi }_{in}\left(y^{\prime }\right)$

property content of a diverging point $y^{\prime }$ particle and heading to y

n

incompressible gas particles density

$n_{ef}\left(y^{\prime }\right)$

effective gas-particle density in point $y^{\prime }$ associated with particles carrying transported property

m

particle mass

${\sigma }_c$

the cross-section of collisions

$P_c={\sigma }_{c}n$

the number of particles placed within a collision tube of a unit length

$y_{b1}$

a position of the upper plate of the micro-channel

$y_{b2}$

a position of the lower plate of the micro-channel

V

the volume of integration over space occupied by the model gas

$v_{+}\left(y,y^{\prime }\right)$

the velocity vector of the diverging particle in point $y^{\prime }$

$Q_{+}\left(y,y^{\prime }\right)$

the probability of free path traveling along the ballistic trajectory from y to $y^{\prime }$

$B_{in}^{\Psi \text{\_}FS}\left(y\right)$

the net rate of property influx per unit volume from the model gas system

$B_{in}^{\Psi \text{\_}F}\left(y\right)$

the net rate of property influx per unit volume from the surrounding gas (trajectories 303 and 304)

$B_{in}^{\Psi \text{\_}BD}\left(y\right)$

the net rate of property influx per unit volume from the boundaries (trajectories 315 and 316, diffuse component)

$Q_{21}=\exp \left(-P_{c}H\right)$

the probability of free path traveling along the ballistic trajectory between confining plates in incompressible gas