Experimental transfer functions identification: Thermal impedance and transmittance in a channel heated by an upstream unsteady volumetric heat source

- Linear differential system with time constant coefficients get convolutive solution.
- Experimental identification of transfer function (thermal impedance, transmittance).
- Experimental calibration with regularized identification.
- Experimentally identified transfer function integrates effects difficult to model.

Linear Time Invariant (LTI) systems can be modeled by transfer functions linking inputs to outputs through convolution products. This concept is experimentally validated in the case of an upstream heated channel with thick walls and steady liquid flowrate using two calibration experiments with different unsteady upstream heating powers. Proper identification of transfer functions (impedances and transmittances) requires the inversion of experimental temperature measurement through regularization techniques. Truncated Singular Value Decomposition (TSVD) and Zero-order Tikhonov regularization are tested and compared for this application.