Three-dimensional modeling of heat transfer during freezing of suspended and in-contact-with-a-surface yellow potatoes and ullucus

The aim of this research was to model the heat transfer during the freezing process of cubed yellow potatoes (Solanum tuberosum L.) and ullucus (Ullucus tuberosus Caldas). A mathematical model was developed using the three-dimensional (3D) finite difference scheme to simulate the freezing process of suspended and in-contact-with-a-surface cubic particles. The thermophysical properties were predicted using the proximal composition and the convective heat transfer coefficient (h) was obtained by optimizing the root mean square error (RMSE) value. A pseudo h was included to simulate the heat transfer of cubic particles in-contact-with-a-surface. Low values of h were found for suspended frozen cubes (17–27 W/m2°C) and high values of pseudo h (295–371 W/m²°C) were determined for frozen cubes in-contact-with-a-surface. An excellent agreement was observed between experimental and predicted temperatures histories (RMSE: 0.6–1.7°C) at different thermocouples positions. In conclusion, the developed model simulated correctly the freezing profile of potato and ullucu in cubic shape. With this model, the possible effects of h and external temperature on freezing times of these vegetables under different positions were evaluated and were represented by polynomial equations that could be used in the industry. Practical Applications: In this research, a simple and easy-to-implement mathematical model was developed to simulate the heat transfer during freezing process of yellow potatoes and ullucus in cubes. The 3D finite difference scheme developed can be used to simulate the freezing of suspended cubed food, as is the case of fluidized bed freezers, or that are in contact with a metal surface, as in plate freezers. In addition, this study presented polynomial equations that allow the quick and precise calculation of the freezing times of cubed yellow potatoes and ullucus.