A model to design high-pressure processes towards an uniform temperature distribution
ABSTRACT A mathematical model has been developed to describe the phenomena of heat and mass transfer taking place during the high-pressure treatment of foods. It has proved that convection currents in the pressure medium play an important role in the thermal evolution of the processed samples especially when the filling ratio in the pressure vessel is low.This model shows to be an extremely useful tool to design high-pressure processes seeking a uniform temperature distribution.
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ABSTRACT: This paper deals with an inverse problem concerning the identification of the heat exchange coefficient H (assumed depending on the temperature) between a certain material with the external environment (see, e.g., (2), (4) for real applications modelled with equations involving this coefficient). Only experimental measurements of the temperature are supposed to be known. The goal is to identify H in order to get a solution for the corresponding model, approximating same given temperature measurements. We begin by setting several scenarios for the inverse problem. For each scenario, we know the initial and ambient temperatures, identify function H through different methods and obtain error bounds in adequate norms (uniform and square integrable). Finally, we study the inverse problem in the framework of the classical theory for Hilbert spaces. Several methods are used (Tikhonov, Morozov, Landweber,. . . ) and the approximations obtained, as well as the one provided by the previous algorithm, are shown.01/2008;
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ABSTRACT: Cooling is an important task in the food industry. Harvested agricultural produce is subjected to precooling before packaging, processing and transportation. Heat moves to surface of product in a mixed-mode of conduction and convection, and from surface to environment by convection. Therefore, estimation of thermal properties (like thermal diffusivity) is important to analyze heat transfer phenomena and design of refrigeration and processing equipments. This work presents a simple method to estimate thermal diffusivity variations of selected regular shaped food products subjected to natural convection cooling. Experimental investigations were carried out on fruits and vegetables. Samples chosen were melon, orange and potato (spherical) and bottle gourd (cylindrical). The experimental setup consists of a deep-freezer maintained at -10˚C and 1 atm. The variation of temperature within a product is measured along the radial direction using copper-constantan thermocouples. The output of thermocouples is read on a digital microvolt meter. The temperature of thermocouples was recorded at regular intervals of 5 minutes. Variation of surface temperature is obtained based on radial temperature profiles. Thermal diffusivity (α) variation is calculated for each time interval using one-dimensional Fourier's equation. Correlation for thermal diffusivity as a function of surface temperature is developed for each of the sample.The 3rd International Symposium on Processing of Foods, Vegetables and Fruits, The University of Nottingham Teaching Centre Level 2, Chulan Tower No 3 Jalan Conlay 50450 Kuala Lumpur, Malaysia; 08/2014
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ABSTRACT: Nowadays, consumers look for minimally processed, additive-free food products that maintain their organoleptic properties. This has led to the development of new technologies for food processing. One emerging technology is high hydrostatic pressure, as it proves to be very effective in prolonging the shelf life of foods without losing its properties. Recent research has involved modelling and simulating the effect of combining thermal and high pressure processes (see Denys et al. (2000) , Infante et al. (2009) , Knoerzer et al. (2007) , Otero et al. (2007) ). The focus is mainly on the inactivation of certain enzymes and microorganisms that are harmful to food. Various mathematical models that study the behaviour of these enzymes and microorganisms during a high pressure process have been proposed (see Infante et al. (2009) , Knoerzer et al. (2007) ). Such models need the temperature and pressure profiles of the whole process as an input. In this paper we present two dimensional models, with different types of boundary conditions, to calculate the temperature profile for solid type foods. We give an exact solution and propose several simplifications, in both two and one dimensions. The temperature profile of these simplified two and one dimensional models is calculated both numerically and analytically, and the solutions are compared. Our results show a very good agreement for all the approximations proposed, and so we can conclude that the simplifications and dimensional reduction are reasonable for certain parameter values, which are specified in this work.Applied Mathematics and Computation 01/2014; 226:20–37. · 1.35 Impact Factor