## Theory And Calculations

The operating principle of scraped-surface heat exchange is based on the constant movement of a product away from the heat-exchange surface in order to minimize the formation of films that resist heat transfer.

In considering the scraped-surface heat exchanger, four types of thermal exchange are taken into account:

• Sensible Heat. The heat produced by the increase or decrease in temperature of a product (without change of state).

• Latent Heat. Heat exchange associated with a physical change in the material being processed.

• Heat of Reaction. The heat given off (exothermic) or taken up (endothermic) when two or more chemicals react.

• Mechanical Heat. Power is consumed in turning the dasher of a SSHE. Most of this energy is absorbed as heat energy into the product within the heat exchanger.

The ideal form of heat transfer occurs when one product at an elevated temperature is brought into direct contact with another material at a lower temperature. The warmer product gives up its heat without loss of energy and at a rate equivalent to the ability to mix or disperse the two materials.

In practice, however, it is rare that two materials may be brought into direct contact. As a general rule, there is an intervening heat-transfer surface such as a tank or tube

Freezing jacket

Product

Pilot regulator (suction pressure control)

High pressure û relief valve

High pressure û relief valve

Ammonia gauge

Gas operated pressure suction valve regulator

Ammonia gauge

Freezing jacket

Product

Pilot regulator (suction pressure control)

Ammonia gas valve-open

Ammonia float valve

Ammonia liquid line

Nickel chrome freezing cylinder

Suction line

Ammonia gas valve-open

Ammonia float valve

Ammonia liquid line

Nickel chrome freezing cylinder

Suction line

Figure 8. Full flooded SSHE refrigeration system (a) shown in operation, (b) shown shut down.

wall. This surface presents problems to heat transfer because it resists the passage of heat. It further induces resistances related to hydraulic drag and the buildup of deposits or other films that further retard the passage of heat. Figure 9 illustrates the various resistances that may be encountered.

Since these resistances are in series, they are additive. The adverse effect, however, may be reduced by agitating the fluids on both sides of the wall. Since the SSHE eliminates buildup of deposits on the product side of the tube wall, the resistance to heat transfer is minimized.

The total resistance to heat transfer then is

The difference in temperatures between the product and the media is the driving force to push across this resistance. Therefore, the equation for heat transfer is

resistance

This equation can be developed into a useful form by letting the temperature difference be AT and resistance be J?. Therefore

Scraped surface heat exchanger

No product film of insulating layer

Rj product resistance R;, tube resistance R; media resistance

Shell and tube heat exchanger

Insulating layer on heat transfer wall

Rj product resistance R;, tube resistance R; media resistance

Temp, hot fluid (inside tube) Temp, loss turbulent region

Temp, loss viscous layer

Ternp_ loss tubewa 11

Temp, hot fluid (inside tube) Temp, loss turbulent region

Temp, loss viscous layer

Ternp_ loss tubewa 11

Shell and tube heat exchanger

Insulating layer on heat transfer wall

Tern p _loss_dtte_ to_foulin£ _ Temp, loss viscous layer

Temp, loss turbulent region

Temp, of cold fluid

Figure 9. Comparison of scraped surface and shell and tube heat transfer profiles.

Tern p _loss_dtte_ to_foulin£ _ Temp, loss viscous layer

Temp, loss turbulent region

Temp, of cold fluid

Figure 9. Comparison of scraped surface and shell and tube heat transfer profiles.

heat-transfer rate = AT/R

Furthermore, by taking the inverse of resistance, which is conductance, 1 /R = U. The heat-transfer equation now is heat-transfer rate = UAT.

Heat-exchange U values in a scraped-surface heat exchanger consist of three parts as shown in this formula:

where hp is the heat-transfer coefficient for the product and ranges from 200 to 800 Btu/h • ft2 • °F, t/k is the heat-transfer coefficient through the cylinder wall (t usually is between 1/4 and 1/8 in. and k varies depending on the material, and hm is the heat-transfer coefficient for the media and ranges from 800 (water media) to 2000 (steam or ammonia) Btu/h • ft2 • °F. The overall U value then varies from 150 to 420 Btu/h • ft2 • °F. Unfortunately, the hp is difficult to determine theoretically and, because hp tends to influence the overall U value much more than hm and t/k, manufacturers size the heat exchangers using a TJ that is determined from lab test data or from production runs. Attempts have been made to predetermine the expected TJ value, but many factors influence the heat-transfer rate:

the smaller the annular space in which the product travels. A small annular spacing will improve heat transfer.

Viscosity: SSHE units normally can handle viscosities of up to 1,000,000 cP. The greater the viscosity, the lower the TJ value. Products with viscosities that vary greatly at different temperatures; eg, peanut butter and cooking—cooling starch for salad dressings, usually produce lower TJ values. This is due to mass rotation. It normally is encountered in cooling applications where the low-viscosity warm product short-circuits through the heat-exchange cylinder while the cooler, thicker product rotates with the dasher.

Dasher speed: high dasher speeds improve heat transfer but heat generated by high rpm is counter-productive in cooling applications.

Number of scraper blades: dashers typically are equipped with two or four rows of scraper blades. Units with four rows of blades provide higher heat-transfer rates at any given dasher rpm. When supplying two rows of blades, many manufacturers compensate by increasing the dasher speed.

Specific heat: the lower the specific heat, the lower the U values.

SSHE geometry: an SSHE can be equipped with different diameter dashers. The larger the dasher diameter,

Thermal conductivity: the lower the thermal conductivity, the lower the TJ value.

Flow rate: the higher the product flow rate, the higher the U value. Flow rates below 5 gpm are considered low. See Figure 10.

Applications: heating applications produce higher U values than do cooling applications. Cylinder materials: the cylinder materials, as mentioned previously, can be nickel, stainless steel or bimetallic. Figure 11 charts the differences in overall U values when cylinder thickness or materials are changed. Nickel is the most efficient and is used as the basis to compare the other materials commonly available.

Once a U value for an application has been determined, a calculation to size the heat exchanger can be made.

50 100 150 200 250 300 350 400 450 500 1/4" Nickel V value

Figure 10. Comparison of nickel and other materials.

50 100 150 200 250 300 350 400 450 500 1/4" Nickel V value

Figure 10. Comparison of nickel and other materials.