Specific Heat Smoothing Methods for Numerical Heat Transfer Analysis Involving Phase Change in a Model Food System

Abstract

For high-moisture foods, the water latent heat of fusion during a phase change process causes a significant discontinuity in the temperature-dependent apparent specific heat of food products, which leads to complications during the numerical solution of heat transfer problems. The discontinuity in the apparent specific heat as a function of temperature can be alleviated by smoothing. Previously, a piecewise approximation smoothing method was developed and extensively used. In this study, different approaches which are based on curve fitting, the use of a sigmoid function, and data interpolation were developed. The performance of these methods in numerical simulations of food freezing and thawing processes was evaluated. The heat transfer model was implemented with the MATLAB PDE Toolbox. Simulated temperature profiles of representative freezing/thawing processes showed a reasonable agreement with experimental values collected from the literature. The optimal smoothing method showed comparatively less numerical oscillation, higher accuracy, faster computation speed, and simplicity in implementation. Recommendations were provided for the utilization of the smoothing methods under different circumstances.