Modelling the solidification of a power-law fluid flowing through a narrow pipe

•A mathematical model for describing solidification of a power law fluid in a circular cross-section pipe is developed.•The work has applications to phase change micro-valves and cryopreservation.•Results indicate shear thinning fluids solidify more rapidly than Newtonian fluids.•For low flow rates solidification times are relatively constant, at high flow rates the solidification time increases.

We develop a mathematical model to simulate the solidification process of a non-Newtonian power-law fluid flowing through a circular cross-section 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.