Mathematical approaches for use of analytical solutions in experimental determination of heat and mass transfer parameters

Calculation of the convective heat transfer coefficient and thermal diffusivity of cucumbers using numerical simulation and the inverse method

Cooling of fruits and vegetables, immediately after the harvest, has been a widely used method for maximizing post-harvest life. In this paper, an optimization algorithm and a numerical solution are used to determine simultaneously the convective heat transfer coefficient, hH, and the thermal diffusivity, α, for an individual solid with cylindrical shape, using experimental data obtained during its cooling. To this end, the one-dimensional diffusion equation in cylindrical coordinates is discretized and numerically solved through the finite volume method, with a fully implicit formulation. This solution is coupled to an optimizer based on the inverse method, in which the chi-square referring to the fit of the numerical simulation to the experimental data is used as objective function. The optimizer coupled to the numerical solution was applied to experimental data relative to the cooling of a cucumber. The obtained results for α and hH were coherent with the values available in the literature. With the results obtained in the optimization process, the cooling kinetics of cucumbers was described in details.

Numerical evaluation of spherical geometry approximation for heating and cooling of irregular shaped food products

Irregular shapes of food products add difficulties in modeling of food processes, and using actual geometries might be in expense of computing time without offering any advantages in heating and cooling processes. In this study, a three-dimensional scanner was used to obtain geometrical description of strawberry, pear, and potato, and cooling-heating simulations were carried out in a computational heat transfer program. Then, spherical assumption was applied to compare center and volume average temperature changes using volume to surface area ratios of these samples to define their characteristic length. In addition, spherical assumption for a finite cylinder and a cube was also applied to demonstrate the effect of sphericity. Geometries with sphericity values above 0.9 were determined to hold the spherical assumption.

PRACTICAL APPLICATIONS

Irregular shapes of food products add difficulties in modeling of heating and cooling processes of food products. In addition, using actual geometries are in expense of computational time without offering any advantages. Hence, spherical approximation for irregular geometries was demonstrated under sphericity values of 0.9. This approach might help in developing better heating and cooling processes.