Estimation of apparent thermal conductivity of carrot purée during freezing using inverse problem

• Published in: International journal of food science & technology 2009-07, Vol.44 (7), p.1292-1303
• Main Authors: Mariani, Viviana Cocco, do Amarante, Álvaro Cesar Camargo, dos Santos Coelho, Leandro
• Format: Article
• Language: English
• Subjects: Apparent thermal conductivity; Biological and medical sciences; carrot purée; differential evolution; Food engineering; food freezing; Food industries; Fruit and vegetable industries; Fundamental and applied biological sciences. Psychology; General aspects; heat transfer; inverse problem; optimization
• ISSN: 0950-5423; 1365-2621
• DOI: 10.1111/j.1365-2621.2009.01958.x

This article presents an inverse problem to determine the apparent thermal conductivity of carrot purée during the freezing process. The heat diffusion equation with the enthalpy model is solved to estimate the thermal conductivity. A modern meta-heuristic of evolutionary computation field called Differential Evolution (DE) is applied for the solution of inverse problem. Experiments were performed to estimate the thermal conductivity of the carrot purée as a function of temperature, using two piecewise functions. A best least square fitting between the experimental and predicted temperature curves during freezing conditions is obtained using DE. Statistical analysis are considered with Gaussian error of 0.05 and zero mean showing than the results for one piecewise function are more stable than with another piecewise function. Good agreement between the reported and estimated temperature curves was obtained. The apparent thermal conductivity was observed to decrease asymptotically with temperature in the range [-40 °C, 0 °C] and stay approximately a constant value for temperatures bigger than 0 °C.