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

R. C. Martins, C. L.M. Silva*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)383-392
Number of pages10
JournalJournal of Food Engineering
Issue number4
Publication statusPublished - 1 Aug 2004


  • Frozen green beans
  • Inverse problem
  • Thermo-physical properties


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