Prediction of chilling rates for food product packages : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Food Engineering at Massey University, Palmerston North, New Zealand
Many food product packages contain significant air void fractions in which natural convection and radiation heat transfer occurs. This may significantly affect the cooling rate of the package as a whole. Voids tend to be either rectangular (at the top of the package), approximately triangular (e.g. in comers of the package), or can be represented as a combination of both shapes. For widely used meat cartons containing voids the bulk of the heat transfer can be modelled two-dimensionally, ignoring end effects. Empirical Nu vs. Ra correlations for horizontal rectangular air voids were available from the technical literature. Since corresponding published data were not obtainable for right-angled isosceles triangular air voids cooled from above with a hypotenuse-down orientation, temperature-time data were collected from twenty-eight transient chilling trials using analogue food packages that contained different sized voids (up to 50mm high) with this shape and orientation. A reliable finite element package was used to model the heat transfer as a conduction process throughout the entire analogue package. The effective thermal conductivities that best-fitted modelled and measured temperature-time profiles within each of five sequential time intervals during cooling were determined. The results were then curve-fitted to generate Nu vs. Ra correlations. New two-dimensional finite element models were developed for predicting chilling rates of food packages that contained combinations of isosceles triangular and/or horizontal rectangular air voids. The models were solved by using a customised heat conduction program called FINELX, in which the effective thermal conductivity in the voids was recalculated at the start of every time-step from the Nu vs. Ra correlations, but the heat transfer was otherwise modelled as conduction. The finite element model was tested against twenty independent transient chilling trials using an analogue food package that contained rectangular and triangular voids of various heights. Predictions from the finite element model agreed to within ±7% and ±12% (at the 95% level of confidence) of the measured data for packages containing rectangular voids and packages containing combined rectangular and triangular voids respectively. This indicated that the model was an accurate simulator of the overall heat transfer occurring in packages that contained significant air void fractions. Previously available simple methods for the prediction of chilling rates of such packages assumed that the contents were homogeneous solids with 'effective' thermal properties based upon the packaging arrangement and the relative amounts of solid and air. These methods were shown to be inaccurate. A simple model based on the semi-infinite slab shape was developed for predicting chilling rates of food packages that contained combinations of isosceles triangular and/or horizontal rectangular void shapes. The simple model accounted for the presence of air voids by the use of effective heat transfer coefficients. Several types of solution method were possible: from analytical methods to simple numerical methods with a run-time of only a few seconds on a 350MHz Pentium II computer, which was significantly less than the 3 hours preparation and 5 hours run-time for the finite element model. Testing of the simple model against measured data from forty-eight transient chilling trials yielded 95% confidence intervals of (-6, +12)%, (-15, +11)%, and (-9, +17)% for packages containing rectangular voids, triangular voids, and combined voids respectively. The quality of prediction indicated that the assumptions employed during the development of the simple model did not worsen its accuracy beyond a level that was likely to be acceptable in industry. Although the simple model gave relatively accurate results for much less computational effort, the customised finite element approach would allow researchers to extend the applicability of the model to any void shape, provided that natural convection and radiation heat transfer data within that particular void shape were available.
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North, M.F., Cleland, A.C. and Lovatt, S.J. (1996). Prediction of Chilling and Freezing Rates of Cartoned Meat (a technical note). Proc. 3rd NZ Conf. of Postgraduate Students in Engng and Tech., University of Canterbury, Christchurch: 493-494.
North, M .F., Lovatt, S J . and Cleland, A.C. (1998). Methods for Evaluating the Effect of Large Voids on Food Package Cooling Times. Proc. Int. Symp. 'Model-It', Acta Horticulturae, ISHS, No. 476 : 95- 103.
North, M.F., Lovatt, S.J. and Cleland, A.C. ( 1999). The Effect of Void Space on Chilling Times for Food Product Packages. Proc. 20th Int. Congr. Refrig. (in press).