Abstract. A mathematical model is developed to analyse the combined flow and solidification of a liquid in a small pipe or two-dimensional channel. In either case the problem reduces to solving a single equation for the position of the solidification front. Results show that for a large range of flow rates the closure time is approximately constant, and the value depends primarily on the wall temperature and channel width. However, the ice shape at closure will be very different for low and high fluxes. As the flow rate increases the closure time starts to depend on the flow rate until the closure time increases dramatically, subsequently the pipe will never close.

We develop a mathematical model to simulate the solidification process of a non-Newtonian power-law fluid flowing through a circular crosssection microchannel. The initial system consists of three partial differential equations, describing the fluid flow and temperature in the liquid and solid, which are solved over a domain specified by the Stefan condition. This is reduced to solving a partially coupled system consisting of a single partial differential equation and the Stefan condition. Results show qualitative differences, depending on the power law index and imposed flow conditions, between Newtonian and non-Newtonian solidification. The model behaviour is illustrated using power law models for blood and polyethylene oxide.