Time-Dependent Base Temperature Estimation in a Porous Fin via Conjugate Gradient

This research examines the use of the conjugate gradient technique to determine the time-varying base temperature of a porous fin, leveraging temperature data collected at the fin’s tip. The analysis focuses on the impact of measurement errors, porosity, initial guess, and sensor location on the accuracy of the inverse solution. Results demonstrate that the present algorithm accurately reconstructs the base temperature under various scenarios, including cases with and without measurement noise. It is observed that while the inverse solution remains stable and insensitive to the choice of initial guess, its accuracy deteriorates with increasing porosity. Moreover, although acceptable accuracy is achieved when the sensor is placed at the fin tip, relocating the sensor slightly toward the fin base significantly enhances the reconstruction precision. Overall, the results confirm the robustness, stability, and effectiveness of the proposed method for solving inverse heat transfer problems in porous fin.