  The behaviour of a miniature calorimetric sensor, which is under
consideration for catheter-based coronary artery flow assessment, is
investigated in both steady and pulsatile tube flow. The sensor is composed of
a heating element operated at constant power, and two thermopiles that measure
flow-induced temperature differences over the sensor surface.
  An analytical sensor model is developed, which includes axial heat conduction
in the fluid and a simple representation of the solid wall, assuming a
quasi-steady sensor response to the pulsatile flow. To reduce the mathematical
problem, described by a two-dimensional advection-diffusion equation, a
spectral method is applied. A Fourier transform is then used to solve the
resulting set of ordinary differential equations and an analytical expression
for the fluid temperature is found. To validate the analytical model,
experiments with the sensor mounted in a tube have been performed in steady and
pulsatile water flow with various amplitudes and Strouhal numbers. Experimental
results are generally in good agreement with theory and show a quasi-steady
sensor response in the coronary flow regime. The model can therefore be used to
optimize the sensor design for coronary flow assessment.
