Answer:
Q = 47.1 kW
Texit = 25.93ºC
Explanation:
The heat transfer is occurring by convection, which means that the heat is flowing from different materials (tube for water). So, by Newton Cooling Law:
Q = h x A x ΔT
The area of the tube will be :
A = πdL
Where d is the diameter and L is the length.
d = 2.5 cm = 0.025 m
A = 3.14x0.025x4 = 0.314 m²
Then
Q = 3000x0.314x50
Q = 47100 W = 47.1 kW
By the heat equation for water, knowing that the specific heat (c) of water is 4.5 kJ/ºC
Q = mcΔT
47.11 = 0.5x4.5x(Texits - Tenters)
47.1 = 2.25x(Texits - 5ºC)
Texits - 5ºC = 20.93 ºC
Texits = 25.93ºC
47.1 kW is the rate of heat transfer and 25.93ºC is the temperature of the water at exit.
We can calculate the rate of heat transfer of the water by using the Newton's cooling law as:
Q = h x A x ΔT, where
h = heat transfer coefficient = 3000 W/m².°C (given)
A = surface area of heat transfer
ΔT = change in temperature = 50°C (given)
First we calculate the area by using the below formula:
A = πdL, where
d = diameter of tube = 2.5cm = 0.025m
L = length of tube = 4m
A = 3.14 x 0.025 x 4 = 0.314 m²
Therefore, rate of heat transfer is:
Q = 3000 x 0.314 x 50 = 47100 W = 47.1 kW
Now we calculate the rise in temperature by using the below formula:
Q = mcΔT
47.11 = 0.5 x 4.5 x (Texits - Tenters)
47.1 = 2.25 x (Texits - 5ºC)
Texits - 5ºC = 20.93 ºC
Texits = 25.93ºC
Hence, 47.1 kW is the rate of heat transfer and 25.93ºC is the temperature of exit water.
To know more about heat transfer, visit the below link:
https://brainly.com/question/16055406
