Modeling heat conduction in spiral geometries

A two-dimensional energy balance (the 2D model) is reduced to a one-dimensional energy balance (the 1D-Radial-Spiral model) by a coordinate transformation approach. The 1D-Radial-Spiral model, even though one-dimensional, captures both radial and spiral heat conductions over a wide range of design parameters. By comparing the temperature predictions of the 1D-Radial-Sp1D-Radial-Spiraliral model and the 2D model, parameter ranges are identified where spiral conduction is important and where the 1D-Radial-Spiral model holds. The 1D-Radial-Spiral model provides a 60-fold savings in computation time over the two-dimensional model. When coupled to electrochemistry, the 2D model takes approximately 20 hours to simulate a 2C discharge of a Li-ion battery, while the 1D-Radial-Spiral model takes about 20 min.