Optimization of the temperature sensor position in a hot wire probe set up for estimation of the thermal properties of foods using optimal experimental design

Abstract

The objective of this work is to determine the optimal sensor in a hot wire probe set up, for accurate and unique estimation of the parameters involved in conduction heated foods. The influence of different parameters of input heat generation profiles, such as the magnitude of the heat generation and the final time, on the optimal sensor location was also investigated. The experimental set up consists of a constantan heating wire impeded in a stainless steel hypodermic needle. A thermocouple is placed at some position in the model food substance. The heat conduction in the probe and its environment was modeled by means of the finite element method and the model has been validated using experimental data. For a given heat generation profile, the influence of the sensor location with respect to the information content of the experiment has been investigated by using an optimal design criterion based on the Fisher information matrix. Simulations indicated that there is an optimal position where the time–temperature measurement should be recorded in order to have an informative experiment such that the parameters are accurately and uniquely estimated. Moreover, it was observed that the choice of the magnitude of heat generation and the final time of the experiment have no significant influence on the information content. Implementation results confirmed that by using the time–temperature data measured around the optimal measurement position, unique and accurate estimates may be obtained.