Modeling Heat Conduction in Spiral Geometries

A two-dimensional ~2-D! energy balance ~the 2D model! is reduced to a one-dimensioanl ~1-D! energy balance ~the 1D-radialspiral model! by a coordinate transformation approach. The 1D-radial-spiral model, even though 1-D, captures both radial and spiral heat conductions over a wide range of design parameters. By comparing the temperature predictions of the 1D-radial-spiral model and the 2D model, parameter ranges were identified where spiral conduction was important and where the 1D-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. © 2003 The Electrochemical Society. @DOI: 10.1149/1.1605743# All rights reserved.