Comparison of heat transfer in liquid and slush nitrogen by numerical simulation of cooling rates for French straws used for sperm cryopreservation

Slush nitrogen (SN₂) is a mixture of solid nitrogen and liquid nitrogen, with an average temperature of −207 °C. To investigate whether plunging a French plastic straw (commonly used for sperm cryopreservation) in SN₂ substantially increases cooling rates with respect to liquid nitrogen (LN₂), a numerical simulation of the heat conduction equation with convective boundary condition was used to predict cooling rates. Calculations performed using heat transfer coefficients in the range of film boiling confirmed the main benefit of plunging a straw in slush over LN₂ did not arise from their temperature difference (−207 vs. −196 °C), but rather from an increase in the external heat transfer coefficient. Numerical simulations using high heat transfer (h) coefficients (assumed to prevail in SN₂) suggested that plunging in SN₂ would increase cooling rates of French straw. This increase of cooling rates was attributed to a less or null film boiling responsible for low heat transfer coefficients in liquid nitrogen when the straw is placed in the solid-liquid mixture or slush. In addition, predicted cooling rates of French straws in SN₂ tended to level-off for high h values, suggesting heat transfer was dictated by heat conduction within the liquid filled plastic straw.