Knowledge of temperature distributions in laminar flow of power law liquids heated
by electric current (direct ohmic heating) enables to asses the effect of thermal treatment of
liquid foods (rapid sterilization). This paper extends existing analytical solutions of
temperature fields to arbitrary flow behavior index and suggests simple formulas for
evaluation of influence of temperature upon the electrical conductivity of heated liquids.
1. Introduction
Advanced continuous processes of thermal
treatment of liquid or heterogeneous foods make
use of either microwave or direct ohmic heating.
E.g. continuous sterilizer APV consists of a
stainless steel tube coated by an electrical
insulator with the circular electrodes (fed by three
phase alternating current 50 Hz), which are fitted
at the tube ends. This arrangement enables
internal heating of processed liquids by electrical current, which flows in the direction of
electrical intensity vector, i.e. in the direction of the tube axis. Another possibility is to use
the channel walls as electrodes, e.g. in a plate heater, where the electrical intensity is
perpendicular to the flow direction.
The basic advantage of both arrangements is more uniform heating of liquid or
particles in the liquid suspended, than by using classical methods of indirect heating. Thus
it is possible to improve the ratio between the desired effects of sterilization (the lethality of
microbes) and undesired reactions which impair quality of processed food [3]. To evaluate
the kinetics of reactions properly, a rather accurate description of residence time distribution
and temperature distribution in a processed liquid must be known. Typical materials heated
in ohmic sterilizers are heterogeneous and highly non Newtonian liquids. Our effort is
concentrated upon the heating of homogeneous liquids, because it is prerequisite for the final
and technologically most important step: finding the temperature field in a particle surrounded
by a liquid of known temperature - time course and in an electrical field of known intensity.
2. Ohmic heating in a circular tube and between parallel plates -
formulation
We shall analyze ohmic heating of a homogeneous non-Newtonian power law liquid,
characterized by flow behavior index n. The heater is either a circular tube with electrodes
at the tube ends or a narrow channel between parallel plates which serve as electrodes; in
both geometries we shall assume fully developed laminar flow.
3. Power consumption - evaluation of Joule heating term
4. Temperature dependent electrical conductivity - integral approach
5. Radial temperature profiles - analytical and numerical solution
6. Lethality evaluation in an ohmic sterilizer
7. Conclusions
The outlined analysis enables to evaluate power consumption of tubular and plate
ohmic heaters, including the effects of temperature dependent electrical conductivity. The
temperature distribution was obtained in an analytical form for power law liquids and for
uniform heating rate.
REFERENCES
[1] BIRD, R.B.: Viscous heat effects in extrusion of molten plastics, SPE J., 1955, 11,
No.9, pp.35
[2] DE ALWIS, A.A.P. - FRYER,P.J.: The use of direct resistance heating in the food
industry, Journal of Food Engineering, 1992, 15, pp. 21-48
[3] FRYER, P.J. et al: Ohmic processing of solid-liquid mixtures: heat generation and
convection effects. Journal of Food Engineering, 1993, 18, pp.101-125
[4] GILL, W.N.: Heat transfer in laminar power law flows with energy sources, AIChE
J., 1962, 8, pp. 137-138
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