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

Smith, Nadia; Mitchell, Sarah; Ramos, Ángel

doi:10.1016/j.amc.2013.10.030

Cited by 5 publications

(5 citation statements)

References 13 publications

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“…Parameter setup. We have used parameters and dimensions as described in [17] 3.1. Sensitivity analysis Figure 1 illustrates that perturbations in the thermal conductivity coefficient k = k(t), given by equation (17), lead to rather small variance in the corresponding temperature T = T (r, t) at r = 0 and r = R. Left column has signal to noise ratio SN R = 10 and right column has signal to noise ration SN R = 10 3 .…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…According to Smith et al [17], a mathematical model of the high pressure food preserving method under consideration can be cast as an initial and boundary value problem for a parabolic partial differential equation as follows…”

Section: Direct Problem or Forward Mappingmentioning

confidence: 99%

“…We have used Tylose parameters, a setup of parameter values and dimensions described in Table 1. This parameter set has already been used as a valid synthetic setting in [17]. We have solved the direct problem (1) approximating the polar Laplacian and the derivatives in the boundary conditions by means of standard centered order two finite differences and using the classical Crank-Nicolson time stepping, resulting in a second order method, both in time and space.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…According to Infante et al [9] "...In high-pressure processes, food is treated with mild temperatures and high pressures in order to inactivate enzymes and preserve as many of its organoleptic properties as possible...". Consequently, there are several research efforts to model the dynamics of food preservation processes which rely on high pressures away from thermal equilibrium [1,3,5,7,9,[13][14][15][16][17]. A related problem is to infer the thermal conductivity coefficient associated to food preservation processes given measurements of the temperature, see [8].…”

Section: Introductionmentioning

confidence: 99%

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Estimating a pressure dependent thermal conductivity coefficient with applications in food technology

Capistrán

Río

2019

Inverse Problems in Science and Engineering

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In this paper we introduce a method to estimate a pressure dependent thermal conductivity coefficient arising in a heat diffusion model with applications in food technology. To address the known smoothing effect of the direct problem, we model the uncertainty of the conductivity coefficient as a hierarchical Gaussian Markov random field (GMRF) restricted to uniqueness conditions for the solution of the inverse problem established in Fraguela et al. [6]. Furthermore, we propose a Single Variable Exchange Metropolis-Hastings algorithm to sample the corresponding conditional probability distribution of the conductivity coefficient given observations of the temperature. Sensitivity analysis of the direct problem suggests that large integration times are necessary to identify the thermal conductivity coefficient. Numerical evidence indicates that a signal to noise ratio of roughly 10 3 suffices to reliably retrieve the thermal conductivity coefficient.

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Section: Numerical Experimentsmentioning

confidence: 99%

Section: Direct Problem or Forward Mappingmentioning

confidence: 99%

Section: Numerical Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Estimating a pressure dependent thermal conductivity coefficient with applications in food technology

Capistrán

Río

2019

Inverse Problems in Science and Engineering

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“…When a cylindrical domain is considered, under suitable conditions (see [16]) a onedimensional radial model can be a good approximation of the model. Then, the model can be written in Cartesian coordinates (for convenience in this paper) as…”

Section: Introductionmentioning

confidence: 99%

A uniqueness result for the identification of a time-dependent diffusion coefficient

et al. 2013

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This paper deals with the problem of determining the time-dependent thermal diffusivity coefficient of a medium, when the evolution of the temperature in a part of it is known. Such situations arise in the context of food technology, when thermal processes at high pressures are used for extending the shelf life of the food, in order to preserve its nutritional and organoleptic properties (Infante et al 2009 On the Modelling and Simulation of High Pressure Processes and Inactivation of Enzymes in Food Engineering pp 2203-29 and Otero et al 2007 J. Food Eng. 78 1463-70). The phenomenon is modeled by the heat equation involving a term which depends on the source temperature and pressure increase, and appropriate initial and boundary conditions. We study the inverse problem of determining time-dependent thermal diffusivities k, when some temperature measurements at the border and inside the medium are known. We prove the uniqueness of the inverse problem solution under suitable a priori assumptions on regularity, size and growth of k.

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High hydrostatic pressure processing of foods

Tsevdou

Gogou

Taoukis

2019

Green Food Processing Techniques

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

Cited by 5 publications

References 13 publications

Estimating a pressure dependent thermal conductivity coefficient with applications in food technology

Estimating a pressure dependent thermal conductivity coefficient with applications in food technology

A uniqueness result for the identification of a time-dependent diffusion coefficient

High hydrostatic pressure processing of foods

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