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Fluid-flow theory
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Heat-transfer theory

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1. For heat exchangers:

                       q = UA DTm
DTm = (DT1 - DT2) / ln (DT1/ DT2)

2. For jacketed pans:

                       q = UA DT
(T2 - Ta)/(T1Ta) = exp(-hsA t/c
rV )

3. For sterilization of cans:
(a) thermal death time is the time taken to reduce bacterial spore counts by a factor of 1012

(b) F value is the thermal death time at 121°C. For Clostridium botulinum, it is about 2.8 min.
(c) z is the temperature difference corresponding to a ten-fold change in the thermal death time
(d)       t121 = tT x 10-(121-T)/z or

       tT = t121 x 10(121-T)/z

4. The coefficient of performance of refrigeration plant is:
        (heat energy extracted in evaporator)/(heat equivalent of theoretical energy input to compressor).

5. Freezing times can be calculated from:

       tf  =      lr   (P a/hs + R a2/k)

where for a slab P = 1/2 and R = 1/8 and for a sphere P = 1/6 and R = 1/24. An improved approximation is to substitute DH over the whole range, for l. In addition for brick shapes a multiplier of around 1.2 is needed.


1. A stream of milk is being cooled by water in a counter flow heat exchanger. If the milk flowing at a rate of 2 kg s-1, is to be cooled from 50°C to 10°C, estimate the rate of flow of the water if it is found to rise 22°C in temperature. Calculate the log mean temperature difference across the heat exchanger, if the water enters the exchanger at 5 °C.
[ 11.8 °C ]

2. A flow of 9.2 kg s-1 of milk is to be heated from 65°C to 150°C in a heat exchanger, using 16.7 kg s-1 of water entering at 95°C. If the overall heat-transfer coefficient is 1300 J m-2 s-1 °C-1, calculate the area of heat exchanger required if the flows are (a) parallel and (b) counter flow.
[(a) 53 m2 ;(b) 34 m2 ]

3. In the heat exchanger of worked Example 6.2 it is desired to cool the water by a further 3°C. Estimate the increase in the flow rate of the brine that would be necessary to achieve this. Assume that: the surface heat transfer rate on the brine side is proportional to v0.8, the surface coefficients under the conditions of Example 6.2 are equal on both sides of the heat-transfer surface and they control the overall heat-transfer coefficient.
[ Flow rate increase of 33% required ]

4. A counter flow regenerative heat exchanger is to be incorporated into a pasteurization plant for milk, with a heat-exchange area of 23 m2 and an estimated overall heat-transfer coefficient of 950 J m-2 s-1 °C-1. Regenerative flow implies that the milk passes from the heat exchanger through further heating and processing and then proceeds back through the same heat exchanger so that the outgoing hot stream transfers heat to the incoming cold stream. Calculate the temperature at which the incoming colder milk leaves the exchanger if it enters at 10°C and if the hot milk enters the exchanger at 72°C.
[ Milk, originally colder, leaves the exchanger at 55.7 °C ]

5. Olive oil is to be heated in a hemispherical steam-jacketed pan, which is 0.85 m in diameter. If the pan is filled with oil at room temperature (21°C), and steam at a pressure of 200 kPa above atmospheric is admitted to the jacket, which covers the whole of the surface of the hemisphere, estimate the time required for the oil to heat to 115°C. Assume an overall heat-transfer coefficient of 550 J m-2 s-1 °C-1 and no heat losses to the surroundings.
[ 14 min. ]

6. The milk pasteurizing plant, using the programme calculated in worked Example 6.6, was found in practice to have a 1°C error in its thermometers so that temperatures thought to be 65°C were in fact 64°C and so on. Under these circumstances what would the holding time at the highest temperature (a true 65°C) need to be?
[ 4 min 41 s ]

7. The contents of the can of pumpkin, whose heating curve was to be calculated in Problem 9 of Chapter 5, has to be processed to give the equivalent at the centre of the can of a 1012 reduction in the spore count of C. botulinum. Assuming a z value of 10°C and that a 1012 reduction is effected after 2.5 min at 121°C, calculate the holding time that would be needed at 115°C. Take the effect of the heating curve previously calculated into consideration but ignore any cooling effects.
[ 79 s ]

8. A cold store is to be erected to maintain an internal temperature of -18°C with a surrounding air temperature of 25°C. It is to be constructed of concrete blocks 20 cm thick and then 15 cm of polystyrene foam. The external surface coefficient of heat transfer is 10 J m-2 s-1 °C-1 and the internal one is 6 J m-2 s-1 °C-1, and the store is 40 x 20 x 7 m high. Determine the refrigeration load due to building heat gains from its surrounding air. Assume that ceiling and floor loss rates per m2 are one-half of those for the walls. Determine also the distance from the inside face of the walls of the 0°C plane, assuming that the concrete blocks are on the outside.
[ Refrigeration load 14.82 kJ s-1; distance 5.7 cm from inside face of wall ]

9. For a refrigeration system with a coefficient of performance of 2.8, if you measure the power of the driving motor and find it to be producing 8.3 horsepower, estimate the refrigeration capacity available at the evaporator, the tons of refrigeration extracted per kW of electricity consumed, and the rate of heat extraction in the condenser. Assume the mechanical and electrical efficiency of the drive to be 74%.
[ Refrigeration capacity 12.82 kW, tons refrigeration; 0.59 per kW; rate of heat extraction 17.4 kW

10. A refrigeration plant using ammonia as refrigerant is evaporating at -30°C and condensing at 38°C, and extracting 25 tons of refrigeration at the evaporator. For this plant, assuming a theoretical cycle, calculate the:
(a) rate of circulation of ammonia, kg s-1
(b) theoretical power required for compression, kW
(c) rate of heat rejection to the cooling water, kW
(d) COP,
(e) volume of ammonia entering the compressor per unit time, m3 s-1
[(a) 0.0842
kg s-1 ;(b) 31.6 kW ;(c) 0.12 MJ s-1 ;(d) 2.8 ;(e) 0.08 m3 s-1 ]

11. It is wished to consider the possibility of chilling the apples of worked Example 6.10 in chilled water instead of in air. If water is available at 1°C and is to be pumped past the apples at 0.5 m s-1 estimate the time needed for the chilling process.
[ 30.8 min ]

12. Estimate the time needed to freeze a meat sausage, initially at 15°C, in an air blast whose velocity across the sausage is 3 m s-1 and temperature is -18°C. The sausage can be described as a finite cylinder 2 cm in diameter and 15 cm long.
[ 37 min ]

13. If the velocity of the air blast in the previous example were doubled, what would be the new freezing time? Management then decide to pack the sausages in individual tight-fitting cardboard wraps. What would be the maximum thickness of the cardboard permissible if the freezing time using the higher velocity of 6 m s-1 were to be no more than it had been originally in the 3 m s-1 air blast.
[ New freezing time 26 min ; maximum cardboard thickness 0.5 mm ]

14. If you found by measurements that a roughly spherical thin plastic bag, measuring 30 cm in diameter, full of wet fish fillets, froze in a -30°C air blast in 16 h, what would you estimate to be the surface heat-transfer coefficient from the air to the surface of the bag?
[ 13.5 J m-2 s-1 °C-1 ]


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Unit Operations in Food Processing. Copyright © 1983, R. L. Earle. :: Published by NZIFST (Inc.)
NZIFST - The New Zealand Institute of Food Science & Technology