Applying a heat transfer mathematical model for the cryopreservation of rainbow trout (Oncorhynchus mykiss) sperm: How straw location over liquid nitrogen level affects freezing rate and fertilization yield.

Cryopreservation of rainbow trout semen under field conditions was analyzed. Straw location over liquid nitrogen level is a crucial variable that affects freezing rate and fertilization yield due to changes in nitrogen vapor external temperature. The objectives were: to analyze cryopreservation protocols by experimentally measuring the cooling rates and fertilization yield of 0.5 ml plastic straws located in nitrogen vapor at different heights corresponding to different external temperatures; to numerically simulate the freezing process, by solving the heat transfer partial differential equations with the corresponding thermo-physical properties of the biological system and the plastic straw; to evaluate and analyze the surface heat transfer coefficient (h) during the freezing process of the straws; to introduce a new variable, the characteristic freezing time (tc), that enables comparison between protocols; this variable was defined as the elapsed period between the initial freezing temperature and a final reference temperature of -40 °C (temperature in which more than 80 % of the water is in a frozen state). The mathematical model predicted the temperature distribution inside the straw, showing a low effect of straw plastic materials (polyethylene-terephthalate glycol, polyvinyl-chloride, and polypropylene) on freezing rates. The average h value obtained from numerical simulations was 25.5 W/m 2 K, close to that obtained from the analytical Nusselt correlation for natural convection. An improvement on fertilization trials was observed when the average external nitrogen temperature was -129.6 °C (temperature range: -94 to -171 °C) with an average tc of 56.8 s (ranging between 47 and 72 s). These results corresponded to a height above the level of liquid nitrogen of 2 cm. Comparison with literature reported data showed satisfactory results. Applying mathematical models in the cryobiology field achieved results that are relevant for cryopreservation activities.