Milk and Vegetables

Abstract

The majority of foods are perishables that deteriorate in terms of quality short after being left unattended. We use sterilization of milk as an example to quantitatively elaborate heat sterilization as the most widely used operation for improving storage stability of food. We then discuss the basics of heat transfer and the design of heat exchanger which is a device used for heat sterilization. Refrigeration and freezing are other common practices for extending the shelf life of food. This chapter therefore also documents these operations as well as thawing of frozen food. In view of the close influences water activity has on food storage, the chapter finally closes with discussions on water activity and intermediate-moisture foods using jam as an example.

Exercise

• 6.1 Table 6.6 shows the heating time, t, and survival rate, N/N ₀, during a sterilization process to eliminate a certain type of microorganism at 110 °C. Determine the D-value under this condition.

  Table 6.6 Thermal death process of a microorganism

• 6.2 The relationship between time, t, and the unoxidized fraction, Y, described by Eq. (6.51) holds for the autoxidation of methyl linoleate:

  $$ \ln \frac{1-Y}{Y}=kt+ \ln \frac{1-{Y}_0}{Y_0} $$

  (6.51)

  Here, k [h⁻¹] denotes the rate constant. The two parameters of the oxidation process of methyl linoleate at 65 °C are tabulated in Table 6.7. Determine the rate constant, k.

  Table 6.7 Oxidation of methyl linoleate

• 6.3 The oxidation rate constants of methyl linoleate are measured at various temperatures (Table 6.8). Determine the activation energy and frequency factor for the autoxidation of methyl linoleate.

  Table 6.8 Temperature dependence of oxidation rate constant, k, of methyl linoleate

• 6.4 One liter of water of 15 °C is heated to 95 °C in an electric kettle with a 1250-W heating element. The kettle weighs 0.7 kg and has an average specific heat of 0.75 kJ/(kg · °C). Let the specific heat of water be 4.18 kJ/(kg · °C). (a) Determine the time required for heating assuming that there is no heat loss from the kettle. (b) Letting the electricity rate be 20 cents per kWh, how much does it cost to bring this hot water to a boil?

• 6.5 A foam container with a thickness of 2.0 cm contains 600 g of water of 0 °C and 400 g of ice of 0 °C. Determine the time needed for all the ice to melt when the container is placed in the atmosphere with an ambient temperature of 30 °C. The external dimension of the container is 20 cm × 25 cm × 40 cm, the latent heat of melting of ice is 335 kJ/kg, and the overall heat transfer coefficient referenced to the outer surface area of the container is 5.0 W/(m² · K).

• 6.6 A heat flux meter mounted on the inner wall of the door 3-cm thick of a refrigerator reads 58 W/m². The temperatures of the inner and outer walls of the door are 5 °C and 24 °C, respectively. What is the thermal conductivity of the door?

• 6.7 A liquid food is heated by means of a double-pipe heat exchanger using hot water as the heat source. The food is flowing through the inner pipe at the rate of 2 kg/s and heated from 10 to 60 °C. Meanwhile, the hot water experiences a temperature drop from 90 to 70 °C while flowing countercurrent to the liquid food through the annular space. Let the overall heat transfer coefficient of the heat exchanger be 200 W/(m² · K); determine the flow rate of hot water and the required heat transfer area. Also, determine the flow rate of hot water and the required heat transfer area in the case where the hot water and the liquid food are flowed cocurrent to each other. Compare these values with those determined earlier for the case of countercurrent flow. Let the respective specific heats of the liquid food and water be 4.30 and 4.19 kJ/(kg · K).

• 6.8 One thousand kilograms of broccoli is precooled with cold water down to 5 °C and then loaded into a refrigerated container with a storage temperature of 2 °C before being transported to a destination located 20 h away from the loading point. In the first 1.5 h, the broccoli loaded into the container is cooled from 5 to 2 °C. The total surface area of the container walls is 30 m², and the overall heat transfer coefficient between the external atmosphere and the walls is 0.3 W/(m² · K). The specific heat of broccoli is 4.02 kJ/(kg · K) and the respiratory heat of broccoli is 35 kW/kg. If the external ambient temperature is 30 °C, what is the total quantity of heat removed by the refrigerator of the container throughout the entire transportation process, and what is the maximum rate for the heat removal?

• 6.9 When an asparagus of 1 cm in diameter with an initial temperature of 30 °C is cooled in an atmosphere of 3 °C, how much time is required for its center to reach 8 °C? The thermal conductivity of the asparagus is 0.604 W/(m · K), the density is 1040 kg/m³, and the specific heat is 3.31 kJ/(kg · K). In addition, consider the asparagus as an infinite cylinder, and assume that the heat transfer coefficient between it and the surrounding atmosphere is 20 W/(m² · K).

• 6.10 Detrimental quality changes in mandarin oranges resulted from them getting frozen on trees by cold air on winter nights pose a problem for the growers. When a mandarin orange of 11 cm in diameter with an initial temperature of 20 °C is stored in cold air of −2 °C, what will the center temperature be after 6 h? Assume that the fruit does not get frozen, and let its thermal conductivity be 0.55 W/(m · K), its density be 1030 kg/m³, its specific heat be 3.77 kJ/(kg · K), and the heat transfer coefficient between it and the surrounding atmosphere be 10 W/(m² · K).

• 6.11 Peas of 7 mm in diameter are spread in a layer on top of a stainless steel perforated plate, and cold air of −30 °C is blown from below the plate to suspend the peas in the air while freezing them (referred to as fluidized-bed freezing method). Assume the initial temperature of the peas is 15 °C, the wet basis moisture content is 80 % (w/w), and the freezing point is −1.0 °C, determine the length of time needed to completely freeze the peas. In addition, how much time is further required for cooling the completely frozen peas to an average product temperature of −20 °C using the same freezing equipment? Let the heat transfer coefficient between the peas and the cold air be 150 W/(m² · K), the thermal conductivity of the frozen phase in the peas be 0.5 W/(m · K), the respective specific heats of the unfrozen and frozen phases in the peas be 3.31 kJ/(kg · K) and 1.76 kJ/(kg · K), the density be 1050 kg/m³, and the latent heat of freezing of water be 334 kJ/kg.

• 6.12 Meatballs of 10 °C measuring 15 mm in diameter with an initial wet basis moisture content of 60 % (w/w) are placed on the conveyor belt of a tunnel freezer (Fig. 6.18b). The inlet temperature of the cooling air blown from the top through nozzles onto the meatballs is −40 °C. The air is then discharged from the freezer at −30 °C. The freezing point of the meatballs is −2 °C, at which all the water contained therein is frozen. The meatballs are further cooled after being frozen and they come out of the freezer at −20 °C. Now, find the answers to the questions below:

  • (a) Determine the amount of heat energy removed from 1 kg of unprocessed meatballs through the entire process of refrigerating them from the initial temperature, freezing all the water present in them at −2 °C and subsequently further cooling them down to −20 °C. Assume the specific heats of the unfrozen and frozen meatballs are 2.85 kJ/(kg · K) and 1.72 kJ/(kg · K), respectively, and the latent heat of freezing of water is 334 kJ/kg.

  • (b) Let the heat transfer coefficient between air and the meatballs be 15 W/(m² · K), the thermal conductivity of the frozen meatballs be 1.17 W/(m · K), and the density be 1000 kg/m³. Determine using Plank’s equation the time required for refrigerating the meatballs from the initial temperature to −2 °C and then freezing them completely at the same temperature.

  • (c) As refrigeration further progresses, the temperature of the meatballs completely frozen at −2 °C decreases further to an average value of −20 °C. How long does this cooling process take to complete? Assume the specific heat of the frozen meatballs is 1.34 kJ/(kg · K) and the density is 980 kg/m³.

  • (d) Let the throughput of the freezer for the meatballs be 500 kg/h, and determine the minimum flow rate of cold air of −40 °C. Assume the specific heat of air is 1 kJ/(kg · K).

  • (e) Cooling of air is performed by heat exchange between air of 30 °C and a refrigerant of −60 °C through a heat exchanger to obtain the cold air of −40 °C. Assume the overall heat transfer coefficient of the heat exchanger is 100 W/(m² · K); determine the required heat transfer area. Also, assume that the refrigerant temperature stays constant throughout the heat exchange process and the refrigerant and air are flowing countercurrent to each other.

• 6.13 A 15 % (w/w) sugar solution and a salt solution of the same concentration have water vapor pressure of 3.138 kPa and 2.825 kPa, respectively, at 25 °C. What are the respective water activity values of the solutions? The vapor pressure of pure water at 25 °C is 3.167 kPa.