A sequential technique for solving the inverse problem associated with the assessment of time-dependent surface heat flux in a porous fin

Abstract

In this research, an inverse algorithm utilizing the sequential method is implemented to estimate the unknown time-dependent base heat flux in a porous fin, based on temperature readings collected from within the medium. The direct problem is resolved using the finite difference method to ascertain the temperature distribution. To illustrate the effectiveness of the inverse method in estimating the unknown base heat flux, two particular cases are analyzed. The study investigates how the number of future time points, measurement inaccuracies, and sensor locations affect the inverse solution. The results confirm that the inverse method can achieve accurate and stable estimations of the time-dependent base heat flux, even when measurement errors are present. It is observed that, for achieving an accurate heat flux estimation, the sensor location should be positioned as close to the base of the fin as possible. The findings reveal that an increase in the porosity parameter results in a diminished accuracy of heat flux estimation.