8.3. OVERALL HEAT-TRANSFER COEFFICIENTS IN EVAPORATORS

The overall heat-transfer coefficient U in an evaporator is composed of the steam-side condensing coefficient, which has a value of about 5700 W/m2 · K (1000 btu/h · ft2 · °F); the metal wall, which has a high thermal conductivity and usually a negligible resistance; the resistance of the scale on the liquid side; and the liquid film coefficient, which is usually inside the tubes.

The steam-side condensing coefficient outside the tubes can be estimated using Eq. (4.8-20) through (4.8-26). The resistance due to scale formation usually cannot be predicted. Increasing the velocity of the liquid in the tubes greatly decreases the rate of scale formation, which is one important advantage of forced-circulation evaporators. The scale may be salts, such as calcium sulfate or sodium sulfate, which decrease in solubility with an increase in temperature and hence tend to deposit on the hot tubes.

For forced-circulation evaporators the coefficient h inside the tubes can be predicted if there is little or no vaporization inside the tube. The liquid hydrostatic head in the tubes prevents most boiling in the tubes. The standard equations for predicting the h value of liquids inside tubes can be used. Velocities used often range from 2 to 5 m/s (7 to 15 ft/s). The heat-transfer coefficient can be predicted from Eq. (4.5-8), using a constant of 0.028 instead of 0.027 (B1). If there is some or appreciable boiling in part or all of the tubes, use of the equation assuming no boiling will give conservative safe results (P1).

For long-tube vertical natural-circulation evaporators the heat-transfer coefficient is more difficult to predict, since there is a nonboiling zone in the bottom of the tubes and a boiling zone in the top. The length of the nonboiling zone depends on the heat transfer in the two zones and the pressure drop in the boiling two-phase zone. The film heat-transfer coefficient in the nonboiling zone can be estimated using Eq. (4.5-8) with a constant of 0.028. For the boiling two-phase zone, a number of equations are given by Perry and Green (P2).

For short-tube vertical evaporators the heat-transfer coefficients can be estimated by using the same methods as for long-tube vertical natural-circulation evaporators. Horizontal-tube evaporators have heat-transfer coefficients on the same order of magnitude as short-tube vertical evaporators.

For the agitated-film evaporator, the heat-transfer coefficient may be estimated using Eq. (4.13-4) for a scraped surface heat exchanger.

The methods given above are useful for actual evaporator design and/or for evaluating the effects of changes in operating conditions on the coefficients. In making preliminary designs or cost estimates, it is helpful to have available overall heat-transfer coefficients usually encountered in commercial practice. Some preliminary values and ranges of values for various types of evaporators are given in Table 8.3-1.

Table 8.3-1. Typical Heat-Transfer Coefficients for Various Evaporators[*] (B3, B4, L1, P1)
 Overall U
Type of EvaporatorW/m2 · Kbtu/h · ft2 · °F
Short-tube vertical, natural circulation1100-2800200-500
Horizontal-tube, natural circulation1100-2800200-500
Long-tube vertical, natural circulation1100-4000200-700
Long-tube vertical, forced circulation2300-11 000400-2000
Agitated film680-2300120-400

[*] Generally, nonviscous liquids have the higher coefficients and viscous liquids the lower coefficients in the ranges given.

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