Question

A company owns a refrigeration system whose refrigeration capacity is 200 tons ( 1 ton of refrigeration = \(211 \mathrm{~kJ} / \mathrm{min}\) ), and you are to design a forced-air cooling system for fruits whose diameters do not exceed \(7 \mathrm{~cm}\) under the following conditions: The fruits are to be cooled from \(28^{\circ} \mathrm{C}\) to an average temperature of \(8^{\circ} \mathrm{C}\). The air temperature is to remain above \(-2^{\circ} \mathrm{C}\) and below \(10^{\circ} \mathrm{C}\) at all times, and the velocity of air approaching the fruits must remain under \(2 \mathrm{~m} / \mathrm{s}\). The cooling section can be as wide as \(3.5 \mathrm{~m}\) and as high as \(2 \mathrm{~m}\). Assuming reasonable values for the average fruit density, specific heat, and porosity (the fraction of air volume in a box), recommend reasonable values for the quantities related to the thermal aspects of the forced-air cooling, including (a) how long the fruits need to remain in the cooling section, \((b)\) the length of the cooling section, \((c)\) the air velocity approaching the cooling section, \((d)\) the product cooling capacity of the system, in \(\mathrm{kg}\) fruit/h, \((e)\) the volume flow rate of air, and \((f)\) the type of heat exchanger for the evaporator and the surface area on the air side.

Short answer

The fruits need to remain in the cooling section for a duration (t) which can be calculated using the relation between the mass flow rate (M) and the time required: \(t = \frac{m}{M}\) b) What is the length of the cooling section? The length of the cooling section (L) can be determined using the following formula: \(L = vt\) Where L represents the length of the cooling section, v represents the air velocity (assuming \(2 \mathrm{~m / s}\)), and t represents the cooling duration. c) What is the air velocity approaching the cooling section? The air velocity approaching the cooling section should be under \(2 \mathrm{~m / s}\) to satisfy the given constraints. d) What is the product cooling capacity of the system, in kg of fruit per hour? The product cooling capacity (P) of the system in \(\mathrm{kg}\) fruit/h can be calculated using the mass flow rate (M) of the fruits found in step 2: \(P = M \times 60 \mathrm{~min / h}\) e) What is the volume flow rate of air? The volume flow rate of air (V) can be calculated based on the length of the cooling section (L) and the cross-sectional area (A_section): \(V = \frac{A_\text{section} \times L}{t}\) f) What type of heat exchanger should be used for the evaporator, and what is the surface area on the air side? A plate-fin heat exchanger with a large surface area on the air side is recommended to ensure effective cooling. The required surface area can be determined by considering the air-side heat transfer equation and the desired fruit cooling rate. It is difficult to provide an exact value without more detailed information, but the surface area should be maximized within the given area constraints to promote efficient heat transfer between the refrigerant and the air.

Step-by-step solution

Calculate the required cooling energy

To determine how long the fruits need to remain in the cooling section, we need to find the required cooling energy. Let's assume an average fruit density of \(500 \mathrm{~kg / m}^3\), specific heat of \(3.6 \mathrm{~kJ / kg} \cdot \mathrm{K}\), and porosity of \(0.4\). The cooling energy (Q) is calculated using the formula: \(Q = mc \Delta T\) Where m is the mass of the fruit, c is the specific heat, and \(\Delta T = T_\text{initial} - T_\text{final}\).

Calculate mass flow rate of fruits

The refrigeration system has a capacity of \(200 \mathrm{~tons}\), which is equal to \((200 \cdot 211) \mathrm{~kJ / min}\). We can now find the mass flow rate (M) of the fruits entering the system by dividing the cooling energy (Q) by the refrigeration capacity: \(M = \frac{Q}{(200 \cdot 211) \mathrm{~kJ / min}}\)

Calculate cooling duration

To find the cooling duration (t), we can use the relation between the mass flow rate (M) and the time required: \(t = \frac{m}{M}\)

Determine the length of the cooling section

The cooling section can be as wide as \(3.5 \mathrm{~m}\) and as high as \(2 \mathrm{~m}\), resulting in a cross-sectional area of \(A_\text{section} = (3.5 \cdot 2) \mathrm{~m^2}\). Based on the constraint that the velocity of air approaching the fruits must remain under \(2 \mathrm{~m / s}\), we can find the length of the cooling section (L): \(L = vt\) Where v is the air velocity (assuming \(2 \mathrm{~m / s}\)).

Determine product cooling capacity

Using the mass flow rate (M) of the fruits found in step 2, we can now calculate the product cooling capacity (P) of the system in \(\mathrm{kg}\) fruit/h: \(P = M \times 60 \mathrm{~min / h}\)

Calculate the volume flow rate of air

The volume flow rate of air (V) can be calculated based on the length of the cooling section (L) and the cross-sectional area (A_section): \(V = \frac{A_\text{section} \times L}{t}\)

Recommend the type of heat exchanger and surface area on the air side

Based on the constraints given, a plate-fin heat exchanger with a large surface area on the air side is recommended to ensure effective cooling. The required surface area can be determined by considering the air-side heat transfer equation and the desired fruit cooling rate. It is difficult to provide an exact value without more detailed information, but the surface area should be maximized within the given area constraints to promote efficient heat transfer between the refrigerant and the air.

Key concepts

Refrigeration Capacity

Understanding refrigeration capacity is crucial when designing a forced-air cooling system. It determines how much heat can be removed from the stored items within a certain period. In this exercise, a capacity of 200 tons was given. Remember, one ton of refrigeration is equivalent to 211 kJ per minute, which means a 200-ton system will provide 42,200 kJ per minute.

This capacity ensures that the fruits are efficiently cooled within the required timeframe. It's essential to match the system's capacity with the cooling needs for maximum efficiency and to avoid energy wastage.

Cooling Section Dimensions

The dimensions of the cooling section play a significant role in the design of a forced-air cooling system. This exercise specifies a maximum width of 3.5 meters and a height of 2 meters. The cross-sectional area is important, as airflow characteristics within these dimensions impact the cooling efficiency.

A well-designed cooling section ensures adequate exposure to the cooled air, allowing heat to transfer from the fruit to the air efficiently. The layout must accommodate the required air flow while maintaining structural integrity and ease of access for maintenance and loading operations.

Mass Flow Rate

Mass flow rate refers to the mass of fruit that moves through the cooling system per unit time. Calculating this is vital to ensure that the system is capable of cooling the expected amount of fruit efficiently.

In the presented exercise, the mass flow rate is derived from the available refrigeration capacity. Knowing the specific heat and initial and final temperatures helps determine how quickly fruits need to absorb cooling energy. The formula used to calculate this is grounded in basic heat transfer principles, where the required energy for cooling is divided by the refrigeration system's total capacity. This gives students insight into balancing the refrigeration power with the practical needs of their system.

Heat Exchanger Selection

A key component in forced-air cooling systems is the heat exchanger. It facilitates heat removal from the air, making the system more effective. For this specific exercise, a plate-fin heat exchanger is recommended due to its large surface area on the air side.

The surface area plays a pivotal role in the heat exchanger's performance. A larger surface area foster efficient heat transfer from the air, ensuring that the refrigeration system's potential is fully utilized. Although the exact surface area isn't specified, maximizing it within the system's constraints ensures optimal cooling of the fruits. Consideration of the heat exchanger's design directly influences the cooling effectiveness, highlighting the importance of careful selection and design integration.