Ohmic processing of solid-liquid mixtures: Heat generation and convection effects

Fryer, P.J.; Alwis, A.A.P. de; Koury, E.; Stapley, A.G.F.; Zhang, L.

doi:10.1016/0260-8774(93)90031-e

Cited by 94 publications

(54 citation statements)

References 10 publications

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“…[24], who looked at the stability of models allowing for different types of flow. More background on this type of process can be found in [5], [12], [15], [26], [27] and [29]. Lacey et al .…”

Section: Introductionmentioning

confidence: 99%

Estimates of Blow-Up Time for a Non-Local Reactive–convective Problem Modelling Ohmic Heating of Foods

Nikolopoulos¹,

Tzanetis²

2006

Proceedings of the Edinburgh Mathematical Society

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In this work, we estimate the blow-up time for the non-local hyperbolic equation of ohmic type, ut + ux = λf (u)/( 1 0 f (u) dx) 2 , together with initial and boundary conditions. It is known that, for f (s), −f (s) positive and ∞ 0 f (s) ds < ∞, there exists a critical value of the parameter λ > 0, say λ * , such that for λ > λ * there is no stationary solution and the solution u(x, t) blows up globally in finite time t * , while for λ λ * there exist stationary solutions. Moreover, the solution u(x, t) also blows up for large enough initial data and λ λ * . Thus, estimates for t * were found either for λ greater than the critical value λ * and fixed initial data u 0 (x) 0, or for u 0 (x) greater than the greatest steadystate solution (denoted by w 2 w * ) and fixed λ λ * . The estimates are obtained by comparison, by asymptotic and by numerical methods. Finally, amongst the other results, for given λ, λ * and 0 < λ − λ * 1, estimates of the following form were found: upper bound + c 1 ln[c 2 (λ − λ * ) −1 ]; lower bound c 3 (λ − λ * ) −1/2 ; asymptotic estimate t * ∼ c 4 (λ − λ * ) −1/2 for f (s) = e −s . Moreover, for 0 < λ λ * and given initial data u 0 (x) greater than the greatest steady-state solution w 2 (x), we have upper estimates: either c 5 ln(c 6 A −1 0 + 1) or + c 7 ln(c 8 ζ −1 ), where A 0 , ζ measure, in some sense, the difference u 0 − w 2 (if u 0 → w 2 +, then A 0 , ζ → 0+). c i > 0 are some constants and 0 < 1, 0 < A 0 , ζ. Some numerical results are also given.

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Section: Introductionmentioning

confidence: 99%

Estimates of Blow-Up Time for a Non-Local Reactive–convective Problem Modelling Ohmic Heating of Foods

Nikolopoulos¹,

Tzanetis²

2006

Proceedings of the Edinburgh Mathematical Society

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“…It is assumed that in each section of the tube, heat generation rates in the solid and liquid, the temperatures of the phases, and velocities of the phases are uniform and known. Fryer et al (1993) show that uniform heating in the liquid is possible, and Zhang and Fryer (1993) show that a rotating particle can heat uniformly.…”

Section: Electrical Heating Modelmentioning

confidence: 98%

Food sterilization by electrical heating: Sensitivity to process parameters

Zhang

Fryer

1994

AIChE Journal

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Food SterilizationThe aim of food sterilization is to produce a sterile product of the highest possible quality. The classical method is canning, in which the product is sealed and then processed until it has reached the correct level of sterility. This may result in a lowquality product; the kinetics of sterilization and quality loss reactions are such that a better product is obtained by heating to higher temperatures for shorter times. This is best done in a continuous process with three sections: (i) a heating section in which product is first heated to the required temperature; (ii) a holding section in which it is held at temperature long enough to ensure sterility; and (iii) a cooling section prior to packaging. The holding section is generally a horizontal or slightly inclined tube.Continuous processes are capable of producing a higherquality product than canning. It is possible to process liquids, using forced convective heat transfer, at much higher heating and cooling rates, on the order of l"C/s, than is possible in processes which rely on thermal conduction or natural convection in the can. A number of commercial food sterilization processes involve the transport and heating of solid-liquid food mixtures of high solids fractions (Holdsworth, 1993). These flows can consist of up to 50-60% solids, particle diameters up to 25 mm in diameter, and carrier fluids which are generally non-Newtonian. Fluid velocities are restricted by the requirement to cause as little damage as possible to the mixture. It is difficult to process solid-liquid mixtures rapidly as solids heating is thermal-conduction-controlled; however, new volumetric heating technologies, such as microwave (Ayappa et al., 1991) and electrical (ohmic) heating (Biss et a]., 1989; Parrott, 1992) allow solids to be heated at the same rates as liquids.Volumetric processes potentially remove heat-transfer limitations on processing particles during the heating stage. Despite this, Zhang and Fryer (1993) demonstrate that significant quality loss can still accumulate during cooling. It is thus vital to study the whole process. To design processes and confirm the sterility of the final product, the temperatures of solidliquid mixtures must be known. Little information is available on the heating rates of the particles and the liquid and of the flow patterns of the food mixture; the design of plant is thus largely empirical. Food will have a range of residence times in any flow situation, and so the process must be designed so that the fastest moving piece of fluid must be sterilized while the slowest moving part is not overcooked.The APV Baker ohmic heater forms the basis for the electrical heating system modeled here. As described by Parrott (1992), the heater consists of a vertical or near-vertical tube up to 10 m in length and 75 mm in diameter, containing a series of up to seven electrode housings, each containing a single cantilever electrode across the tube. Up to 3 ton/h of flood flow upward through the tube past the electrodes; current density ...

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“…The problem was considered initially in [19] where the stability of models allowing for different types of flow is studied. More background on this type of process can be found in [5,4,9,20,22,24]. In [15] problem (1.1) is also studied and it is found that for f decreasing with for instance either f (s) = e −s or f (s) = (1 + s) −p , p > 1, satisfy (1.2).…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of a Nonlocal Problem Modelling Ohmic Heating of Foods

Nikolopoulos

2009

Comput. Methods Appl. Math.

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-An upwind and a Lax-Wendroff scheme are introduced for the solution of a one dimensional non-local problem modelling Ohmic heating of Foods. The schemes are studied regarding their consistency, stability and the rate of convergence for the cases that the problem attains a global solution in time. A high resolution scheme is also introduced and it is shown that it is total-variation-stable. Finally some numerical experiments are presented in support of the theoretical results.

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Ohmic processing of solid-liquid mixtures: Heat generation and convection effects

Cited by 94 publications

References 10 publications

Estimates of Blow-Up Time for a Non-Local Reactive–convective Problem Modelling Ohmic Heating of Foods

Estimates of Blow-Up Time for a Non-Local Reactive–convective Problem Modelling Ohmic Heating of Foods

Food sterilization by electrical heating: Sensitivity to process parameters

Numerical Solution of a Nonlocal Problem Modelling Ohmic Heating of Foods

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