Analysis and simplification of a mathematical model for high-pressure food processes

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) [3], Infante et al. (2009) [5], Knoerzer et al. (2007) [6], Otero et al. (2007) [9]). 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) [5], Knoerzer et al. (2007) [6]). 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.