Sensitivity of the food centre temperature with respect to the air velocity and the turbulence kinetic energy P. Verboven * , N. Scheerlinck, J. De Baerdemaeker, B.M. Nicola  õ Katholieke Universiteit Leuven, Department of Agro-Engineering and Economics, W. de Croylaan 42, Kardinaal Mercierlaan 92 E, B-3001 Leuven, Belgium Accepted 28 August 2000 Abstract The surface heat transfer coecient is an important parameter to characterise forced convection heating and cooling processes. It expresses the in¯uence of ¯ow phenomena on the heat transfer rate to foods. For thermal process calculations, one often relies on dimensionless correlations that contain the ¯ow properties, namely the free stream air velocity and the turbulence kinetic energy. This paper discusses the sensitivity of the food temperature with respect to these variables for dierent food geometries and con- ditions. The study is based on the ®nite element analysis of the product temperature deviations as a result from deviations of the surface heat transfer coecient, combined with existing dimensionless correlations for the surface heat transfer coecient. Sensi- tivity charts are constructed, which relate the temperature sensitivity with respect to the free stream air velocity and the turbulence kinetic energy to dierent air ¯ow conditions as a function of time. By constructing sensitivity charts, it is shown that small velocity deviations can lead to large food temperature deviations. The eect of small deviations of the turbulence intensity is not as sig- ni®cant. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: Surface heat transfer coecient; Modelling; Finite element analysis; Air ¯ow 1. Introduction The concept of the surface heat transfer coecient h W=m 2 °C originates from Newton's law of cooling, which expresses the surface heat ¯ux q W=m 2  as q  hT s   T 1 ; 1 with T s °C the surface temperature and T 1 °C the processing temperature. In the case of a constant h (for example, during forced convection heating or cooling), it serves as a linear boundary condition for conductive food heat transfer models based on the Fourier equation and therefore oers computational bene®ts, which ex- plains its popularity. Eq. (1) is not a real law, but rather a de®ning equation for h. The value of h is related to the surface gradient of the thermal boundary layer in the ¯uid, which in turn depends to a large extent on the velocity boundary layer (see, for example, Bird, Stewart, & Lightfoot, 1960). Obviously, the value of h varies along the surface as the boundary layers develop. The boundary layers are in¯uenced by the solid surface ge- ometry, the ¯ow regime and properties and an assort- ment of ¯uid properties (density, viscosity, heat capacity, thermal conductivity). The local distribution of h may be important to a number of food processes, as was shown by Kondjoyan and Daudin (1995) and Ver- boven, Nicola  õ, Scheerlinck, and De Baerdemaeker (1997). One way to obtain the distribution of h along the solid surface is to resolve the governing Navier±Stokes equations in the boundary layers. However, complex aerodynamic phenomena such as boundary layer sepa- ration, reattachment, vortex shedding and turbulence do in general not allow an analytical solution for complex shapes such as food products. The numerical solution of the Navier±Stokes equations is then required but this remains an active area of research in thermal analysis (Verboven et al., 1997; Kondjoyan & Boisson, 1997; for example, Rhee & Sung, 1996). Also, experimental techniques continue to contribute to the analysis and understanding of the boundary layers and the surface heat transfer coecient (Kondjoyan & Daudin, 1995; Meinders, Martinuzzi, & Hanjalic, 1998). However, currently it is still common practice in thermal food process analysis to determine only a Journal of Food Engineering 48 (2001) 53±60 www.elsevier.com/locate/jfoodeng * Corresponding author. Tel.: +32-16-32-14-53; fax: +32-16-32-29-55. E-mail address: pieter.verboven@agr.kuleuven.ac.be (P. Verboven). 0260-8774/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 0 - 8 7 7 4 ( 0 0 ) 0 0 1 4 5 - X