Mathematical modeling of a fan heater using a three-dimensional temperature measurement system

Electric heaters are widely used because of their portability, rapid heating, ease of use, and reliability. The widespread use of heaters underscores the importance of selecting the appropriate heater to optimize efficiency and achieve energy savings. To this end, a three-dimensional temperature measurement system was developed to enable a more efficient and purpose-oriented heater design and production in this study. The measurement system included a novel sensor circuit capable of detecting temperature changes with a sensitivity of 0.0489 °C, utilizing a total of 81 sensor circuit boards. These sensors were arranged in a 9 × 9 matrix configuration on the xy-plane and were vertically displaced along the z-axis of the heater to facilitate the development of three-dimensional heating models. Using the heating models obtained from a fan heater in experimental studies, a mathematical model of the heater was derived. The model performance was evaluated using error-based performance metrics for five different heater configurations. Accordingly, the average mean absolute error and R² compatibility value between the mathematical model and the measurement results for all configurations were 0.30 °C and 98.18%, respectively.