The realization of a three-dimensional temperature measurement system with a two-dimensional sensor array and the demonstration of the deformation effect of gravity on the heating patterns

Abstract

Electric heaters are widely used owing to their portability, fast heating, single-focus heating, and energy efficiency advantages. Manufacturers provide customers with information on the power consumption and energy efficiency classes of heaters but do not provide any information on heating patterns. Knowing the heating pattern enables users to select the correct heater, which has a significant effect on comfort, health, energy efficiency, industrial process performance, plant growth, and climate change. In previous studies, two-dimensional temperature measurements were performed using sensor arrays. However, the three-dimensional heating patterns of the heaters have not been extracted, and the deformation effect of gravity on the heating patterns has not been demonstrated. In this study, a temperature measurement system with 64 temperature sensors placed at equal intervals in the xz-plane was designed and implemented. Then, the fan heater was moved along the y-axis at intervals of 10 cm from 0 to 100 cm, and three-dimensional heating patterns were obtained for different fan voltages. As part of the research objectives, the deformation effect of gravity on the heating pattern was revealed, and the shift in the maximum temperature point on the +z-axis was measured. The mathematical formula for the maximum temperature value was derived based on the fan voltage and the distance between the heater and the sensor array. The goodness-of-fit statistical values for the derived mathematical formula for the 55 temperature measurements were calculated as the root mean square error of 1.9543 and R-squared of 99.43%, demonstrating the accuracy of the presented model.