Over-all heat-transfer

The temperature of the reactor could theoretically be controlled by changing the flow rate or the temperature of the water in the jacket. It will now be shown that the former is impractical. The over-all heat transfer coefficient is given in the major equipment section as around 50 BTU/hr ft2°F or greater. This means that the major resistance to heat transfer is the film on the inside of the reaction vessel. 

U = over-all heat transfer coefficient for the jacketed vessel... 

The over-all heat transfer coefficient will next be determined for values of the outside heat transfer coefficient that differ by a factor of 2. 

Over-all heat transfer coefficients54 Long tube evaporators... 

Some numerical examples are given. For a semi-infinite copper melt initially at the fusion temperature, losing heat with an over-all heat transfer coefficient of 0.5 B.t.u./(hr.)(ft.2)(°F.) to the surroundings at ambient temperature, after 4 hr. 771 = 0.98, and the estimated thickness of solidified copper is 44 in. with a 12% error. A second example is a steel sheet subjected to a slowly flowing stream of very hot gas, such that a uniform heat flux of 105 B.t.u./(hr,)(ft.2)(°F.) is imposed at the surface with negligible motion of the melt. After 200 sec., 771 = 0.68, and the melt thickness is estimated to be 1.26 in., with a possible error of 8.6%. 

The requirements for approximating the radial heat transfer in a packed reactor with a constant over-all heat-transfer coefficient are discussed in Section III, above. When these requirements are met, Eqs. (3-32), (3-33), and (3-34) are used to describe conditions in the reactor. With the substitution of Eq. (7-1), these equations take the form... 

Tw temperature of wall of a tube (T) U over-all heat-transfer coefficient... 

No. 4 was later modified to a flat rotor which gave better performance because of better spreading on the surface. No. 5 was a pilot-plant size with a total of 600 sq. feet of evaporating surface. The nominal capacity is generally stated to be 25,000 gallons per day, but this varies with conditions and especially with At (temperature difference). Assuming an over-all heat-transfer coefficient of 2500 in the usual units, the calculated capacities would be... 

Calculation of Over-all Heat Transfer Coefficient. The rate of production of jacket condensate is used to calculate the heat transferred across the evaporator test section. The calculated value is adjusted for known heat losses and a value of over-all heat transfer coefficient is derived from the equation... 

Promotion of Dropwise Condensation. Preliminary heat transfer experiments, using distilled water as feed, gave values of over-all heat transfer coefficient around 1000 B.t.u./sq. ft hr. ° F. and analysis indicated that the jacket condensate film provided the main resistance to heat transfer, due to filmwise condensation of the jacket steam. Following reports by Garrett (4) of successful tests using drop-wise condensation promoters, it was decided to use oleic acid for this purpose in the present experiments. The resulting improvement in jacketside coefficients enabled over-all heat transfer coefficients in excess of 5000 B.t.u./sq. ft hr ° F. to be achieved. 

The usual method of promotion was to wipe the oleic acid onto the cleaned outside of the tube before the experiment commenced, although it was also found possible to add the promoter to the jacket steam line via a two-valve arrangement. Tests showed that the original wiped-on film remained effective for at least 8 hours, but some improvement in over-all heat transfer coefficient resulted from the use of additional promoter after 30 to 40 hours operation. 

Standard Operating Conditions. During preliminary experiments, it was found that, although the value of the over-all heat transfer coefficient varied with rate of flow and other operating conditions, the variation due to high rate of scale formation predominated under all conditions. Standard conditions for the scaling experiments were selected as shown in Table II. These were chosen in such a way that at least 20 pounds per hour of jacket condensate was produced (to permit accurate measurement) and the initial wetness of steam was adequate to initiate the spray evaporation regime at the bottom of the tube. 

As the initial over-all heat transfer coefficient was approximately 4000 B.t.u./ sq. ft hr. ° F. in all cases, the effect of scaling in first hour reduced the initial coefficient by a factor in excess of 2. 

Figure 2. Over-all heat transfer coefficient vs. time for untreated sea water...

High average over-all heat transfer coefficients were obtained over several runs, but, in view of the rapidly changing rate of heat transfer due to alternate scale formation and stripping, it was impossible to calculate instantaneous values of over-all heat transfer coefficient. However, it would appear that the curve of over-all heat transfer coefficient against time takes the form shown as broken lines in Figure 3. 

Preheating of Sea Water. Sea water was preheated to about 300° F. in a pressure vessel, with a noncondensable gas vent, having a holdup time of about half an hour. The preheated feed water was then passed to the spray evaporator, where evaporation took place at the usual temperature of approximately 240° F. A white Mg (OH) 2 scale formed fairly rapidly in the evaporator, producing a rate of fall of over-all heat transfer coefficient similar to that for untreated sea water. 

In one run, sodium sulfate and calcium chloride were added to a 200-gallon batch of sea water to give a sulfate concentration of 5200 p.p.m. and a calcium concentration of 640 p.p.m. An addition was made of 5 p.p.m. of low molecular weight polyacrylic acid and the treated sea water was evaporated under standard conditions. The over-all heat transfer coefficient averaged 3600 B.t.u./sq. ft. hr. ° F. for a 5-hour period, with no detectable falloff during the period, and the tube was found to be clean, except for the plastic film. In contrast, evaporation of a similar batch of calcium sulfate-enriched sea water, with no polyacrylic acid, resulted in a marked decrease in heat transfer coefficient to less than 800 B.t.u./sq. ft. hr. ° F. after 2 hours. 

Similar results were found by Jackson (4), who reported a maximum increase of 20% in over-all heat transfer coefficients at a Reynolds number of 2100, when... 

The net results of this first single-stage evaluation are summarized in Figure 5 in the form of condenser performance vs. reservoir temperature level and reservoir-condenser temperature difference. The curves shown are valid for distillation at atmospheric pressure, a constant disk speed of 60 r.p.m., and an air-vapor gap of 3/s2 inch. Since the test condenser was water-cooled at high flow rates, the over-all heat transfer coefficients shown are considered to be maximum values controlled by the resistance on the diffusion side. 

The over-all heat-transfer coefficients for the fixed-bed and hot-gas-recycle systems were calculated from a correlation of heat transfi through packed beds. A relatively high transfer coefficient of 50 Btu/(hr) (sq ft) ( F) is obtained for the hot-gas-recycle system because of the high linear velocity of the gas. A uniform amount of reaction has been assumed through the catalyst bed. When the reaction occurs nonuniformly and a large amount of conversion takes place in a limited area, as is often the case near the point of entry of the fresh gas, the gradients are higher. 

In accordance with the two-film theory, the two phases are considered to have uniform, though different, bulk temperatures. The over-all heat-transfer coefficient through the combined films U is defined by... 

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