A Novel Transient PDE Model for Development of Highly Sensitive Microthermal Expansion-Based Angular Motion Sensor

We propose a novel transient partial differential equation (PDE) model for the development of highly sensitive microthermal expansion-based angular motion (
$\mu $
TEAM) sensors based on the study of time-dependent response. With the efficient prediction of thermal time constant (
$\tau ^{\ast} $
) based on the PDE model, which is >2200 times faster than 3-D CFD simulation (32.67 s versus >20 h) and was validated by the experimental results, the parametric analysis has been conducted for design optimization. The
$\mu $
TEAM sensors with three pairs of temperature detectors (TDs) were adopted for the systematic study of the PWM frequency (
${f} _{\text {PWM}}$
) effect on the sensor performance to identify the optimal
${f} _{\text {PWM}}$
(
${f} _{\text {o}}$
), which can optimize the sensitivity by >11%. Based on the time-dependent analysis of our PDE model,
${f} _{\text {o}}$
was verified to be dominated by the thermal response of the sensor. A generalized “Phase Diagram” regarding the normalized sensitivity (
$S^{\ast} $
) was presented, for the first time, as a function of
${f} _{\text {PWM}}$
and the normalized heater-to-detector distance (
${D} _{x}/{L} _{x}$
). Accordingly, an optimal region, where
$S^{\ast} \ge0.95$
, was identified to successfully develop an SF 6-based
$\mu $
TEAM sensor with a high sensitivity of 1.5631 mV/°/s, which was >3.5 times as large as that of the N2-based sensor (0.4203 mV/°/s). In particular, the SF6-based sensor reveals an excellent normalized sensitivity of 0.0487 mV/°/s/mW compared to the reported thermal angular motion sensors (AMSs); thus, the comprehensive study based on the PDE model enables the significant improvement of sensor sensitivity and would be useful for system-level integration in the future.