Analysis of the melt phase of a rotating polymer disc supporting a diffusion flame

When a laminar diffusion flame is established over a spinning, thermoplastic, polymer fuel disc in a quiescent, oxidizing environment, the polymer melts and flows radially outwards, causing some fuel to be lost and not transported to the diffusion flame. The viscosity of the liquid in the melt layer retards the radial flow, thereby determining the amount of fuel lost. The melt layer is analysed here for two limiting cases, namely one in which the liquid viscosity depends strongly on temperature, leading to an asymptotic analysis involving two zones in the liquid, and one in which the liquid viscosity is constant, independent of temperature, so that there is only one zone in the liquid. The utility of these two limits is assessed by comparing their predictions with those of full numerical integrations for poly(methyl methacrylate) (PMMA) discs burning in air at atmospheric pressure.