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which is valid for liquid feed rate of 58-87 kg/h and agitation speed of 150-500 rpm. The correlation obtained for the turbulent-flow regime (Re > 1,000) was

w which is valid for liquid feed rate of 87-133 kg/h and agitation speed of 500-1,300 rpm. The authors found that unstable operation of the evaporator occurred when the speed of the wiper blades was below 150 rpm, and rapid increase in hp was observed for rpm range 250-350. Under similar conditions of evaporation, heat-transfer coefficients were lower for high-viscosity liquids.

A detailed expression for the overall heat-transfer coefficient in multiple-effect falling-film evaporators was worked out (10). This coefficient U was given as a function of the enthalpy and temperature of the liquid and vapor phases, local heat-transfer coefficients, and mass fractions of solute in the inlet and outlet liquid streams. The fundamental mathematical model of multiple-effect evaporators was further applied (11) along with an accurate estimate of U and fouling factor Rd to design a five-effect evaporation unit capable of treating the input citrus juice flow rates indicated in (Figure 3). Results of the calculations are shown in Table 2 for orange and lemon juices that were concentrated from 11.7 to 65°Brix, and from 9.3 to 40°Brix, respectively.

According to one study (12), factors influencing the rate of heat transfer can be summarized as

1. Temperature difference between the steam and the boiling liquid.

2. Fouling of evaporator surfaces.

3. Boundary film thickness.

Factors influencing the economics of evaporation include

1. Loss of concentrate due to foaming and entrainment.

### 2. Energy expenditure.

The total evaporation depends on the steam consumption and the specific surface area of the evaporator. Capital costs increase with the size of the evaporator whereas energy cost decrease with it. If the fouling of the heating surface is expressed as specific product losses and is reduced from 1.0 to 0.2 kg thin milk/m2, for modern evaporators with a specific surface area of 0.12-0.14 m2(kg/h), the production costs will decrease by about 40% for whole milk evaporation and 30% for skim milk evaporation (13). Increased fouling is caused by a nonuniform distribution of liquid to individual heating tubes in falling-film evaporators such that some groups of tubes have more deposit than the others.

Steam economy, defined as the mass of water evaporated per unit mass of steam utilized, is often used as a measure of evaporator performance. A similar definition could be used if another condensing vapor (ammonia, Freon, or diphenyl) is employed as the heating medium.

Steam requirement for double-effect is computed directly from solving the heat and mass balances presented earlier. Equations 1-6 can be used to compute the heat-transfer surface area after the overall heat-transfer coefficients Uj and U2 have been evaluated for both effects. The usual procedures for computing steam requirement involve assumptions, such as equal heat flux, equal heat-transfer area, or equal temperature gradient in each effect of the system.

For plants with increasing number of effects resulting in decreased potential temperature difference in each effect, the boiling point rise is of importance when calculating the temperature program of an evaporation plant. For well-defined solutions such as water, the elevation of boiling points is proportional to the molar concentration of the solute, thus

Food liquids are normally more complicated and the boiling point rise has to be determined experimentally. For milk, the following values have been given (8):

Concentration % DM 16 27.5 39 49 62 69 73 Temperature °C 0.5 1 1.5 2 3 4 5

The Duhring plot for sucrose for various conditions are presented in Figure 4.

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