Your Question:

1. In a meat processing plant, 2 cm thick steaks (k=0.45 W/m.°C and a=0.91 x107 m²/s) that are initially at 25 °C are to be cooled by passing them through a refrigeration room at -11 °C. The heat transfer coefficient on both sides of the steaks is 9 W/m².°C. If both surfaces of the steaks are to be cooled to 2 °C, determine how long the steaks should be kept in the refrigeration room.

Step By Step Answers with Explanation

The heat flux is the rate of heat transfer per unit area. It can be calculated using the following formula:

q = hΔT

In this case, the heat flux is:

q = (9 W/m²·°C) (-36 °C) = -324 W/m²

• Q̇ is the heat transfer rate (W)

• A is the area of the steak (m²)

• W is the width of the steak (m)

Since the thickness of the steak is given in centimeters, we need to convert it to meters:

Q̇ = 2qA = 2 × (-324 W/m²) × (4 × 10^-4 m²) = -25.92 W

Step 4: Calculate the amount of heat to be removed

• m is the mass of the steak (kg)

• c is the specific heat capacity of the steak (J/kg·°C)

The time required to remove the heat can be calculated using the following formula:

t = Q / Q̇

In this case, the time required is:

t = (-118800 J) / (-25.92 W) = 4583.11 s