By Thomas O. Maginnis, Ph.D.
Thermal mass flow sensing is well established commercially for measurement and control of low gas flows in the semiconductor industry and elsewhere. Yet the basic theory of this critical flow sensing technology still remains poorly developed. The author has discovered a class of closed form exact solutions to the governing differential equations for this kind of sensor. Though these exact solutions unfortunately do not include the most common commercial sensor design, they still provide considerable insight into the physics of these sensors, and the exact solutions can be used to test Blackett’s hypothesis directly for these special cases. For these simple special cases the low flow sensor slope can evaluated exactly in closed form. These special solutions can therefore be used to provide estimates and bounds for the low flow slope in real commercial sensors. They can also be used to begin the kind of fundamental uncertainty analysis needed to assess the potential of the capillary tube thermal flow sensing technology for future development as a low flow primary mass flow standard.