# Interdisciplinary Applied Mathematics

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Re=80, Kno=0.05, Mi=0.55, Pr=0.7

FIGURE 6.14. Temperature contours and streamlines obtained by the DSMC and continuum slip flow simulations.

obtained (see Figure 6.14). Such temperature decrease indicates large heat transfer to the channel surfaces, which are kept at isothermal conditions (at 300 K). Relatively large temperature jump and velocity slip occur in this region.

After the entrance section, the pressure drops very rapidly with corresponding fluid acceleration. The pressure drop in this section (1.2 < x/h < 1.5) is almost uniform across the channel, as seen in Figure 6.15. We also identify that the velocity increases along the channel, similar to a compressible straight channel flow. In this section the fluid temperature at the center of the entrance region (CE) decreases substantially, reaching a minimum at around x/h = 2.0. This is accompanied with acceleration of fluid in the streamwise direction, representing transformation of thermal energy into kinetic energy. Around the step expansion we also observe an increase in the cross-flow component of velocity. Therefore, the thermal energy transformation affects both the streamwise and the cross-flow velocities.

The sudden expansion in the geometry creates adverse pressure gradients across the    entire    cross    section    (see    Figure    6.15)    until    x/h = 3.25    at    BW,

and x/h = 3.65 at TW. Due to the adverse pressure gradients, the flow at the bottom wall (BW) separates and reattaches at x/h = 2.8, before

FIGURE 6.15. Pressure distribution along backward-facing channel at five selected locations. Predictions of both DSMC (symbol) and pFlow (lines) are presented (see Table 6.1 for description of the symbols).

the pressure gradient at the bottom wall becomes zero (at x/h = 3.25). The early reattachment under slightly adverse pressure gradients is due to the compressibility effects, where conversion of thermal energy into kinetic energy enhanced the tangential momentum of the fluid.

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