A dimensionless study on thermal control of positive temperature coefficient (PTC) materials

Abstract

Positive temperature coefficient (PTC) material is widely used in the field of thermal control due to its unique temperature sensitive characteristics. However, there is no general criterion about PTC material thermal control at present due to the lack of theoretical analysis in the previous works. Thus, in this paper, the dimensionless method is used to study PTC material adaptive thermal control and finally, a fitting formula is obtained to estimate the equilibrium temperature of controlled device. First, a one-dimensional and steady-state heat transfer model was proposed to calculate the equilibrium temperature of controlled device under thermal control of PTC materials, and it was verified by experiment. Then, the model has been nondimensionalized and four dimensionless numbers are introduced by Buckingham theorem, in which the Wr number is presented to represent the heating characteristics of PTC materials. Finally, by fitting all the data, a form of fitting equation of equilibrium temperature of controlled device is obtained. The results show that this form proposed in this paper can be applied to the widely used ceramic PTC materials. The criterion equation fitted by this form can effectively estimate the equilibrium temperature of the controlled devices with good accuracy and wide application.