Cooling Time for Preserving Eggs and Stone Fruits

Rapid cooling of stone fruits is common and necessary for extending the shelf life of such products. Cooling and storing eggs at low temperature (or pasteurizing at a temperature around 60 degrees) has been known to suppress the growth of Salmonella. While several studies have been conducted to estimate the cooling time, it has usually been the case that such fruits (olives, dates, etc.) or eggs are modelled as spheres with internal spherical cores. The motive for such simplification is that the governing heat differential equation is easily solved in spherical coordinates. It is obvious that such fruits or eggs are not spherical. They are in the shape of prolate spheroids (i.e. elongated spheres with different major and minor axes). Such simplifications in the geometry of these fruits or eggs, naturally, induce errors in the estimation of the time needed and consequently in the amount of energy used in the cooling process. In this proposal, we accurately determine the cooling time of eggs and stone fruits using their natural prolate spheroidal shapes. To solve the heat conduction over a prolate spheroid, we use a specially fit coordinates system, namely the prolate spheroidal coordinates system. Unlike the well-known coordinates systems (rectangular, cylindrical, and spherical), this system is capable of appropriately hosting such geometry. We consider different cooling conditions through varying the Biot number which is a dimensionless number that combines the effects of the conduction properties of the stone fruits or eggs, and the convection strength of the cooling media. We present the results in terms of isotherms and as the cooling time versus the axis ratio, the stone/yolk size, and Biot number. We also verify and compare the results of this study to the literature available, in particular the asymptotic cases of spherical stone fruits or eggs.