Microwave cooking of thin potato discs

We consider the cooking of thin potato slices in a microwave oven. It has been observed that this cooking method leads to under-cooking at the edges of the disc. For a uni-modal field the under-cooking occurs on the edge tangential to the direction of the applied field, while for a multi-modal field, the under-cooking occurs around the entire circumference. We develop a mathematical model for the electric field in both these situations, modelling the electric field using the Helmholtz equations. Using asymptotic analysis, we exploit the small aspect ratio and large dielectric constant in the disc, and are able to predict cooking patterns consistent with experimental observations in both cases. We also consider a simplified 2D electrostatic model, in order to explore the possible asymptotic structure of the solution in more detail.