An analytic model for transient heat conduction in bi-layered structures with flexible serpentine heaters

Uniform heating of complex surfaces, especially non-developable surfaces, is a crucial problem that traditional rigid heaters cannot solve. Inspired by flexible electronic devices, a novel design for the stretchable heating film is proposed with the flexible serpentine wire embedded in the soft polymer film, which can be attached to non-developable surfaces conformally. It provides a new way for the stretchable heaters to realize uniform heating of complex surfaces. However, the thermal field of flexible serpentine heaters (FSHs) depends on the configurations of the embedded serpentine heating wire, which requires accurate theoretical prediction of real-time temperature distribution. Therefore, the analytical model for the transient heat conduction in FSHs is solved by the separation of variables method and validated by the finite element analysis (FEA) in this paper. Based on this model, the effects of the geometric parameters, such as the radius and the length of the serpentine heaters, on the thermal uniformity are systematically investigated. This study can help to design and fabricate flexible heaters with uniform heating in the future.