Blast-cooling of beef-in-sauce catering meals: numerical results based on a dynamic zero-order model

Abstract

Beef-in-sauce catering meals under blast-cooling have been investigated in a research project which aims at quantitative HACCP (hazard analysis critical control point). In view of its prospective coupling to a predictive microbiology model proposed in the project, zero-order spatial dependence has proved to suitably predict meal temperatures in response to temperature variations in the cooling air. This approach has modelled heat transfer rates via the a priori unknown convective coefficient h_c which is allowed to vary due to uncertainty and variability in the actual modus operandi of the chosen case study hospital kitchen. Implemented in MS Excel®, the numerical procedure has successfully combined the 4^th order Runge-Kutta method, to solve the governing equation, with non-linear optimization, via the built-in Solver, to determine the coefficient h_c. In this work, the coefficient h_c was assessed for 119 distinct recently-cooked meal samples whose temperature-time profiles were recorded in situ after 17 technical visits to the hospital kitchen over a year. The average value and standard deviation results were h_c = 12.0 ± 4.1 W m^-2 K^-1, whilst the lowest values (associated with the worst cooling scenarios) were about h_c » 6.0 W m^-2 K^-1.