Inverse problem methodology for thermal-physical properties estimation of frozen green beans

Frozen green beans (Phaseolus vulgaris, L.) thermal conductivity (k) and heat capacity (Cp) were determined experimentally by a one dimensional finite difference (transient method) and differential scanning calorimetry, respectively. Thermal properties were also estimated by the inverse problem methodology (IPM). Heat capacity and thermal conductivity behaviour with temperature were modelled by the Schwartzberg equations and linear relationship, respectively below and above the melting point. These equations were used inside a finite element model (FEM) to simulate green beans phase transition under thawing conditions. The sequential simplex method was used to minimise the error vector of the FEM inverse problem, to estimate thermal capacity and thermal conductivity. The accuracy of thermal-physical properties estimated by the two methodologies was compared with data from literature. The thermo-physical properties estimated by the IPM converged for physically meaningful values. Important conclusions were obtained about errors in model predictions. Furthermore, the IPM thermal properties increased the accuracy of simulations, especially during phase transition. One of the most difficult part of frozen foods phase change modelling problems is the characterisation of non-linear thermal properties in time and space, such as, thermal conductivity (k) and thermal capacitance (Cp). Frozen foods do not exhibit a sharp liquid/solid interface that characterises Stefan problems. Foods are multi-component materials that present a phase transition region, where thermal-physical properties can be described by smooth non-linear curves, near the melting point (Voller, 1997). Heat conductivity (k) and capacitance (Cp) inside the phase transition region depends upon ice crystallisation or melting during freezing and thawing, respectively. Inside this region, thermal-properties can be modelled as functions of temperature. Introduction Corresponding author. Tel.: +351-22-5580058; fax: +351-22-