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.