  Asymptotic homogenisation is used to systematically derive reduced-order
macroscopic models of conductive behaviour in spirally-wound layered materials
in which the layers have very different conductivities. The problem is
motivated by the need for simplified models of the electrical and thermal
behaviour of lithium-ion cells, accounting for the highly conductive metallic
current collectors and relatively poorly conductive electrodes. We identify and
study three distinguished limits, and then describe two composite models which
each provide a uniform approximation spanning two distinguished limits. We
compare the results of the various reduced-order models with calculations of
the full model on a detailed geometry to give a guide to the accuracy of the
approximations.
