Three-dimensional temperature field in a line-heater embedded by a spiral electric resistor

In this study, three-dimensional temperature fields induced by AC and DC through a spiral electric resistor in a line-heater are numerically investigated. Electric heaters have been widely found, for example, in houses as dryers, stoves, and water heaters, and in industrial and research institutions as elements of equipments. The line-heater in the present model is realistically considered to have multiple regions composed of a spiral electric resistor, electrically insulated region, covering outer layer, and two terminal pins with distinct thermal and electrical properties. Solving unsteady three-dimensional heat conduction equations in distinct regions, the surface temperatures predicted as a function of time in this model are confirmed by the measured data. The calculated results quantitatively show that high surface temperatures of the heater can be reached by increasing dimensionless joule heat parameter, radius of the spiral electric resistor or pins, thermal diffusivity of the insulation region, and decreasing Biot number and radius of insulation region. The effects of the pins on surface temperature are also studied. Aside from showing that DC produces higher temperature than AC, the results indicate that the effects of current frequency on temperature fields are insignificant. The findings can be generalized to a curved heater, because any local location can be considered as a small line-segment. The present work provides general and quantitative data valuable for designing an efficient heater/furnace.