## O

24 32 40 48 54 62 70 Product flow in 100's lb/h

Figure 11. Curves represent a 6-ft2 SSHE margarine cooler with 4-1/2-in.-diameter dasher. Discharge temperature 49-50°F flow rate increased from 2400 to 6200 lb/h; U value increases with flow rate and eventually levels off. Ammonia temperature is lowered to maintain proper exit temperature.

A Practical Formula

Deriving the practical scraped-surface heat exchange formula is achieved as follows:

heat-transfer rate = UAT

Product heat load Q (heat load being transferred from the product to the media) will be equal to the heat-transfer rate times the heat transfer area A. Thus

where A is the area, ft2. The product heat load is equated

Q = (product) lb/h x temperature change x SpHt + latent heat + heat of reaction + mechanical heat

In the majority of applications, heat of reaction does not occur. Therefore, by eliminating this factor and combining equations, the generally accepted formula for calculating scraped-surface heat exchangers is area = [product flow x (Tm - Tout) x SpHt + latent heat + hp x 2545 Btu/h/hp] + U x LMTD

For steam, ammonia, and Freon units,

1 media in

Area: square feet of surface required

Flow: pounds per hour of product

Tin: temperature of product in (°F)

Tout: temperature of product out (°F)

Tmedia in: temperature of media in (°F)

Tmedia out: temperature of media out (°F)

Latent heat: heat removed from ice formation or fat crystallization Btu/h hp: dasher drive horsepower. Use only on cooling applications; disregard on heating. Note that horsepower is converted to Btu by the conversion factor 2545 Btu/ h/HP

LMTD: log mean temperature difference

Sample Calculation

Product: gravy Specific heat: 0.8

Application: cool from 200 to 60°F using 5°F ammonia

U value: 280

Flow rate: 5000 lb/h

Assume 15 hp is required.

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