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

This article presents an inverse problem to determine the apparent thermal conductivity of carrot puree 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 puree 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 degrees C, 0 degrees C] and stay approximately a constant value for temperatures bigger than 0 degrees C.