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

Abstract: Slush nitrogen (SN2) is a mixture of solid nitrogen and liquid nitrogen coexisting under an average temperature of -207ºC. In order to investigate whether plunging a French plastic straw (commonly used for spermatozoa cryopreservation) in SN2 may substantially increase cooling rates with respect to liquid nitrogen (LN2), a numerical simulation of the heat conduction equation with convective boundary condition was used to predict the 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 does not arise from their temperature difference (-207ºC vs. -196ºC) but 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 the low heat transfer coefficients in liquid nitrogen when the straw is placed in the solidliquid mixture or slush. In addition, it was demonstrated that predicted cooling rates of French straws in SN2 tends to level-off for high h values, suggesting heat transfer is dictated by the heat conduction within the liquid filled plastic stra