Mathematical modeling of unsteady heating of a chicken egg under forced convection

Abstract

The temperature regime is a key factor determining the success of poultry egg incubation. Deviations from optimal parameters lead to decreased hatchability and deterioration of chick viability. Despite the existence of fundamental works on heat transfer, the complex influence of hydrodynamic and geometric factors on unsteady heat transfer under commercial incubation conditions is understudied. The research goal is to quantify the influence of air flow velocity and egg geometric dimensions on the dynamics of egg heating in an incubator. The study was performed by mathematical modeling of unsteady heat transfer. The egg is approximated by a spherical body filled with water taking into account six accepted assumptions. The solution of the Fourier heat conduction equation is obtained with boundary conditions of the third kind. Parametric analysis is performed for egg diameters ranging from 37 to 41 mm and air flow velocities from 0 to 2 m s. The calculation of heat transfer coefficients and the Biot number is based on empirical relationships. It was found that the convective heat transfer coefficient increased from 2.05 to 12.45 W (m²·°C) at increasing flow velocity from 0 to 2 m s. The Biot number was in the range of 0.13–0.86 which corresponded to the transient heat transfer regime. The time to reach an egg temperature of 35°C varied from 45 to 70 minutes depending on the diameter; the difference between the extreme values was 35%. The most significant reduction in heating time (35–40%) was achieved by increasing the velocity from 0 to 1.0 m s. The recommended air flow velocity for a mixed batch of eggs with a diameter of 37–41 mm is 1.0 m s which provides a balance between heat transfer intensity and energy consumption. The obtained quantitative relationships may be used for the engineering design of energy-efficient incubation systems.