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In this paper we introduce a method to estimate a pressure dependent thermalconductivity coefficient arising in a heat diffusion model with applications infood technology. To address the known smoothing effect of the direct problem,we model the uncertainty of the conductivity coefficient as a hierarchicalGaussian Markov random field (GMRF) restricted to uniqueness conditions for thesolution of the inverse problem established in Fraguela et al. Furthermore, wepropose a Single Variable Exchange Metropolis-Hastings algorithm to sample thecorresponding conditional probability distribution of the conductivitycoefficient given observations of the temperature. Sensitivity analysis of thedirect problem suggests that large integration times are necessary to identifythe thermal conductivity coefficient. Numerical evidence indicates that asignal to noise ratio of roughly 1000 suffices to reliably retrieve the thermalconductivity coefficient.

Estimating a pressure dependent thermal conductivity coefficient with applications in food technology