Inverse problem estimation of internal heat transfer coefficients in ducts through a time-dependent reciprocity functional method

The reciprocity function method is presented in this work as a powerful tool for the transient inverse estimation of steady internal heat transfer coefficients in ducts, using only external boundary data. This paper extends our previous results in a sense that transient measurements can now be used to recover a steady heat transfer coefficient without the need to reach the steady-state regime. In this method, only data from the external (accessible) surface are necessary to estimate the unknown function on the internal (inaccessible) surface. Transient temperature measurements taken on the outer surface are used to estimate internal steady heat transfer coefficients in a non-iterative and non-intrusive process. Different profiles for the internal heat transfer coefficient are considered and noisy synthetic measurements are used to verify the method. Results show that the methodology is able to recover these functions in a short computational time, with good accuracy.