  A Maxwell gas confined within a micro cavity with non-isothermal walls is
investigated in the slip and early transition regimes using the classical and
extended continuum theories. The vertical sides of the cavity are kept at the
uniform and environmental temperature T_0, while the upper and bottom ones are
linearly heated in opposite directions from the cold value T_0 to the hot
oneT_H. The gas flow is, therefore, induced only by the temperature gradient
created along the longitudinal walls. The problem is treated from a macroscopic
point of view by solving numerically the so-called regularized 13-moment
equations (R13) recently developed as an extension of Grad 13-moments theory to
the third order of the Knudsen number powers in the Chapman-Enskog expansion.
The gas macroscopic properties obtained by this method are compared with the
classical continuum theory results (NSF) using the first and second order of
velocity slip and temperature jump boundary conditions. The gas flow behavior
is studied as a function of the Knudsen number (Kn), nonlinear effects, for
different heating ratesT_0/T_H . The micro cavity aspect ratio effect is also
evaluated on the flow fields in this study.
