Analytical and experimental characterization of a miniature calorimetric   sensor in pulsatile flow
  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. 
H. Gelderblom, A. van der Horst, J.R. Haartsen, M.C.M. Rutten, A.A.F.   van de Ven, F. N. van de Vosse
physics.flu-dyn