Question

Design a scalding unit for slaughtered chickens to loosen their feathers before they are routed to feather-picking machines with a capacity of 1200 chickens per hour under the following conditions: The unit will be of an immersion type filled with hot water at an average temperature of \(53^{\circ} \mathrm{C}\) at all times. Chicken with an average mass of \(2.2 \mathrm{kg}\) and an average temperature of \(36^{\circ} \mathrm{C}\) will be dipped into the tank, held in the water for \(1.5 \mathrm{min}\), and taken out by a slow-moving conveyor. The chicken is expected to leave the tank 15 percent heavier as a result of the water that sticks to its surface. The center-to-center distance between chickens in any direction will be at least \(30 \mathrm{cm} .\) The tank can be as wide as \(3 \mathrm{m}\) and as high as \(60 \mathrm{cm} .\) The water is to be circulated through and heated by a natural gas furnace, but the temperature rise of water will not exceed \(5^{\circ} \mathrm{C}\) as it passes through the furnace. The water loss is to be made up by the city water at an average temperature of \(16^{\circ} \mathrm{C}\). The walls and the floor of the tank are well-insulated. The unit operates \(24 \mathrm{h}\) a day and 6 days a week. Assuming reasonable values for the average properties, recommend reasonable values for \((a)\) the mass flow rate of the makeup water that must be supplied to the tank, (b) the rate of heat transfer from the water to the chicken, in \(\mathrm{kW},(c)\) the size of the heating system in \(\mathrm{kJ} / \mathrm{h},\) and \((d)\) the operating cost of the scalding unit per month for a unit cost of \(\$ 1.12 /\) therm of natural gas.

Short answer

The mass flow rate of the makeup water that must be supplied to the tank is 396 kg/h. b) What is the rate of heat transfer from the water to the chicken? The rate of heat transfer from the water to the chicken is 25.91 kW. c) What is the size of the heating system? The size of the heating system is 93.26 MJ/h. d) What is the operating cost of the scalding unit per month for a unit cost of $1.12/therm of natural gas? The operating cost of the scalding unit per month is $572,137.33.

Step-by-step solution

Calculate the mass of the water sticking to the chicken

We are given that after dipping, the chicken is expected to be 15% heavier due to the water sticking to its surface. So, we'll first calculate the mass of the water sticking to the chicken by using the following relation: Mass of water sticking to the chicken = Mass of chicken x 0.15 Mass of water sticking to the chicken = \(2.2 \mathrm{kg}\) x 0.15 = \(0.33 \mathrm{kg}\)

Calculate the mass flow rate of the makeup water

We are given that 1200 chickens are processed per hour. So, the total mass of water sticking to 1200 chickens per hour is given by the following relation: Total mass of water sticking to 1200 chickens per hour = Mass of water sticking to the chicken x 1200 Total mass of water sticking to 1200 chickens = \(0.33 \mathrm{kg}\) x 1200 chickens = \(396 \mathrm{kg}\) per hour So, the mass flow rate of the makeup water that must be supplied to the tank is \(396 \mathrm{kg/h}\).

Calculate the heat required to raise the chicken's temperature

Using the specific heat of chicken meat (assuming it to be the same as water: \(4186 \mathrm{J/kg} \cdot \mathrm{C}\)), we can calculate the heat required to raise the chicken's temperature from \(36^{\circ} \mathrm{C}\) to \(53^{\circ} \mathrm{C}\): Heat required = Mass of chicken x Specific heat x \(\Delta T\) Heat required = \(2.2 \mathrm{kg}\) x \(4186 \mathrm{J/kg}\cdot \mathrm{C}\) x (\(53^{\circ}\mathrm{C} - 36^{\circ}\mathrm{C}\)) = \(77719.6 \mathrm{J}\) per chicken Now, we need to find the rate of heat transfer. Since there are 1200 chickens per hour, we can calculate the rate of heat transfer as follows: Rate of heat transfer = Heat required per chicken x Number of chickens per hour / 3600 seconds per hour Rate of heat transfer = \(77719.6 \mathrm{J} \) x 1200 / 3600 = \(25906.53 \mathrm{W}\) or \(25.91 \mathrm{kW}\)

Calculate the size of the heating system

The heating system should be able to provide the heat required by the total number of chickens processed in an hour. So, we can calculate the size of the heating system as follows: Size of the heating system = Heat required per chicken x 1200 chickens Size of the heating system = \(77719.6 \mathrm{J}\) x 1200 = \(93,263,520 \mathrm{J/h}\) or \(93.26 \mathrm{MJ/h}\)

Calculate the operating cost of the scalding unit per month

The given unit cost of natural gas is \(\$1.12 /\) therm. There are 105,500 \(\mathrm{kJ}\) in one therm. The scalding unit operates for 24 hours a day and 6 days a week. First, we need to find the number of therms required for the heating system per hour: Number of therms required per hour = Heating system size / Energy in one therm Number of therms required per hour = \(93,263,520 \mathrm{J/h}/105,500 \mathrm{J/therm}\) = 883.29 therms/h Now, let's find the total cost per month: Operating hours per month = 24 hours/day x 6 days/week x 4 weeks/month = 576 hours/month Operating cost per month = Number of therms required per hour x Unit cost of natural gas x Operating hours per month Operating cost per month = 883.29 therms/h x \(\$ 1.12 /\) therm x 576 hours/month = \(\$ 572,137.33\) per month In conclusion, the mass flow rate of the makeup water that must be supplied to the tank is 396 \(\mathrm{kg/h}\), the rate of heat transfer from the water to the chicken is 25.91 \(\mathrm{kW}\), the size of the heating system is 93.26 \(\mathrm{MJ/h}\), and the operating cost of the scalding unit per month is \(\$ 572,137.33\).