| Insulating packaging is used in a variety of applications to protect temperature-sensitive products from thermal damage. Several factors affect the performance of insulating packages. These factors include (i) heat transfer through the packaging material (conduction, convection and radiation), (ii) the configuration of the insulating package, and (iii) the choice of phase change materials. In this research, a comprehensive model, including all of these factors, was developed to effectively design and analyze the performance of the insulating package.Nine one-dimensional heat transfer models, each consider only conduction, are reviewed and explored as candidates to be used for predicting the performance of insulating packages. Comparing calculated results from various models with experimental data, one spherical shell model (with the inside volume of the spherical shell equaling the inside volume of the rectangular container and the thickness of spherical shell equaling the thickness of the rectangular container) is identified most suitable for use in the following research.Several versions of the spherical shell model which respectively consider conduction only, both conduction and external convection, multi-layered wall, and finally external convection and radiation and enclosed radiation together, were developed. Relationships among wall thickness, inside radius, package duration, ambient temperature, convection coefficients, emissivity of insulated material surface and product size are developed and discussed. General conclusions are reached as to these variables and input parameters.The spherical shell model offers a unique basis for packaging analysis and design due to the closed-form solutions of heat transfer through this spherical shell configuration. Based on this model, the insulating packaging solution is achieved by using 'minimum packaging cost' as an optimization target. This optimized design on the spherical shell model can be then transformed to rectangular configurations by using the same rule used for transforming rectangular configurations to the spherical shell configuration.The comparison of results predicted from the present model with benchmark experimental data shows satisfactory agreement in terms of package duration. As a result, this research work offers not only an effective mathematical model for insulating package system, but also a unique transformation between the spherical and rectangular configurations, providing a straightforward tool, validated by benchmark experiments, for making insulating package design for the packaging industry. |
