A 1.5-mm-thick plate is to be cooled by gas flow through microchannels with square cross sections. Assuming gas mean temperature and pressure of 300 K and 100 kPa, respectively, estimate the...

A 1.5-mm-thick plate is to be cooled by gas flow through microchannels with square cross sections. Assuming gas mean temperature and pressure of 300 K and 100 kPa, respectively, estimate the microchannel cross-section size for the following thresholds:

(a) continuum with negligible slip at walls,

(b) continuum with slip at walls,

(c) free molecular flow.

Perform these calculations for air and helium.