Steady-periodic heating in parallel-plate microchannel flow with participating walls

Simulations are presented for thermal sensing of steady laminar flow in a parallel-plate microchannel. Steady-periodic heating is introduced at the channel wall and temperatures are reported at upstream and downstream locations to represent temperature sensors. Exact analytical expressions for the temperature are given in the form of integrals, and numerical values are found by quadrature. Because axial conduction is prominent, there is a well-defined measurable flow range associated with each thermal-sensor geometry. Various fluid-flow rates, heating frequencies, sensor locations, and wall properties are explored. The results are given as a design correlation which shows the extent to which a given sensor can be tuned, by adjusting the heating frequency, to the flow-measurement range of interest.