Modeling heat conduction in spiral geometries

A two-dimensional (2-D) energy balance (the 2D model) is reduced to a one-dimensional (1-D) energy balance (the ID-radial-spiral model) by a coordinate transformation approach. The ID-radial-spiral model, even though t-D, captures both radial and spiral heat conductions over a wide range of design parameters. By comparing the temperature predictions of the ID-radial-spiral model and the 2D model, parameter ranges were identified where spiral conduction was important and where the 1 D-radial-spiral model held. The 1D-radial-spiral model provided a sixtyfold savings in computation time over the 2D model. When coupled to electrochemistry, the 2D model took approximately 20 h to simulate a 2C discharge of a Li-ion battery, while the 1D-radial-spiral model took about 20 min.