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 H.B. Nahor a, * , N. Scheerlinck a , J.F. Van Impe b , B.M. Nicola € ı a a Flanders Center, Laboratory of Postharvest Technology, Department of Agro-Engineering and Economics, Faculty Agriculture and Applied Biological Sciences, Katholieke Universiteit Leuven, W. de Croylaan 42, B-3001 Leuven, Belgium b BioTec-Bioprocess Technology and Control, Department of Chemical Engineering, Katholieke Universiteit Leuven, W. de Croylaan 46, B-3001 Leuven, Belgium Received 21 December 2001; accepted 27 May 2002 Abstract Theobjectiveofthisworkistodeterminetheoptimalsensorinahotwireprobesetup,foraccurateanduniqueestimationofthe 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. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Heat transfer; Finite element method; Parameter estimation; Optimal experimental design; Hot wire probe; Modified E-criterion 1. Introduction Model-based predictions for the design of food pro- cessequipmentorimprovementsinprocessefficiencyare highly dependent on the reliability of the model pa- rameters. The parameters involved in conduction heat transfer are the thermophysical properties, namely, the thermal conductivity, k, and the volumetric heat ca- pacity, qc. Besides the estimation of these parameters based on the chemical composition of the food using empirical equations, various steady and transient state measurement methods exist. Among others, the tran- sient hotwire probe method has emerged as the method of choice owing to its accuracy and thus is the most extensively used (Bristow, Kluitenberg, & Horton, 1994). In this method, a needle with a heating wire is inserted in the food and the heating is started. The thermal conductivity (and with some modification, the volumetric heat capacity) can then be calculated from the time–temperature data measured in the probe or at some position in the food. Recent interests are directed towards estimation of the thermophysical properties of various biological materialsandsoilsbymeansofsingleordualheatprobe methods (Moysey, Shaw, & Lampman, 1977; Chang, Lai, & Miller, 1980; Bristow et al., 1994; Tagawa, Kitamura, Muramatsu, Fusakaz, & Murata, 1996; Fontana, Wacker, Campbell, & Campbell, 2001). Since Journal of Food Engineering 57 (2003) 103–110 www.elsevier.com/locate/jfoodeng * Corresponding author. Tel.: +32-16-32-26-68; fax: +32-16-32-29- 55. E-mail address: nahor.haddish@agr.kuleuven.ac.be (H.B. Nahor). 0260-8774/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII:S0260-8774(02)00278-9