Alimentos

Journal of Food Engineering 91 (2009) 34–41

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Journal of Food Engineering
journal homepage: www.elsevier.com/locate/jfoodeng

A quick method for thermal diffusivity estimation: Application to several foods
Giampaolo Betta *, Massimiliano Rinaldi, Davide Barbanti, Roberto Massini
Dipartimento di Ingegneria Industriale, Università degli Studi diParma, Via G. Usberti 181/A, 43100 Parma, Italy

a r t i c l e

i n f o

a b s t r a c t
A reliable, quick and userfriendly method for thermal diffusivity estimation has been developed. An appropriate software tool, based on least square optimization of a finite difference solution of Fourier’s equation, has been created and an appropriate measuring cell has been designed and made in order todecrease the systematic error in probe positioning. The method has been experimentally validated and its results have been compared with those obtained by three other available methods. Several foods (tomato products, low-acid pasta sauces, olive pate, confectioner’s custard and apricot jam) were tested and in every case the method proved to be effective. The developed software also allowedestimation of thermal diffusivity via heat penetration curves obtained by variable temperature treatments. So it has been also possible to exclude the contribution of container material from the estimation of thermal diffusivity of liquid packed foods. The proposed method turns out to be a useful tool for scientific design of several processes, such as sterilization and pasteurization, and for correctcontrol of transport, storage and distribution of foods. Ó 2008 Elsevier Ltd. All rights reserved.

Article history: Received 23 March 2008 Received in revised form 31 July 2008 Accepted 2 August 2008 Available online 9 August 2008 Keywords: Thermal diffusivity Modelling Tomato Jam Olive Sauce Mushrooms Cheesy Truffle Bacon&egg Custard

1. Introduction Correct knowledge of thermal properties isessential for efficient and economical design and control of all food processing operations involving heat transfer such as heating, cooling, freezing, thawing, and frying. Precise and reliable values of thermal properties of foods are necessary to simulate temperature during heat treatments, transport, storage and distribution. Conductive heat exchange is an almost simple physical phenomenon: theclassic mathematical model of conduction is Fourier’s equation (1)

q Á cp Á

oT ¼ k Á r2 T ot

ð1Þ

Conductive heat exchange depends on three physical properties: density (q), thermal conductivity (k) and specific heat capacity (cp). These properties can be included in a single parameter called thermal diffusivity, defined by the ratio

a¼

k

q Á cp

ð2Þ

Thermal diffusivity (a)physically relates the ability of a material to conduct heat to the ability to store it. Many methods for determining thermal conductivity and thermal diffusivity were
* Corresponding author. E-mail address: giampaolo.betta@nemo.unipr.it (G. Betta). 0260-8774/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2008.08.003

developed. Apart from non-conventionaltechniques, such as ac method (Calzona et al., 1993), thermal-wave cavity (Balderas-Lopez and Mandelis, 2001), thermal lens technique (Bernal-Alvarado et al., 2003), the majority of available methods were reviewed by Reidy and Rippen (1971) and Choi and Okos (1986). Singh (1992) reported three models based on food composition (Dickerson, 1969; Choi and Okos, 1986; Martens, 1980). Information onthermal properties of porous foods is presented in a review paper by Wallapapan et al. (1983). There are two categories of measurement for thermal conductivity and several experimental techniques have been developed for each category; in some techniques, while thermal conductivity is measured, thermal diffusivity is also obtained: (a) steady-state methods, such as hot plate method (Lentz, 1961),...