Need help regarding heat transfer questions

[wattsie10]

Please can someone show me how to work out the following questions.

1) A hot water cylinder holds 500 litres. If the primary heat source is 30kW and the supply water inlet to the cylinder is 12°C, how long will it take to heat the whole tank to 60°C?

2) The primary side of a plate heat exchanger rated at 400kW has an inlet temperature of 85°C and the outlet temperature is 40°C. What is the mass flow rate?

3) To achieve a water flow rate of 5kg/s at 20°C from a 210kW source, what would be the temperature of the water as it enters the heat exchanger?

Many thanks

 

[tiny-tim]

Welcome to PF!

Hi wattsie10! Welcome to PF!

Show us what you've tried, and where you're stuck, and then we'll know how to help!

 

[Mene]

for reaching out for help with your heat transfer questions. I understand that these problems can be challenging, but with the right approach and understanding of heat transfer principles, they can be solved easily.

For question 1, we can use the formula Q = mcΔT, where Q is the heat energy, m is the mass of water in the cylinder, c is the specific heat capacity of water, and ΔT is the change in temperature. We know that the heat energy supplied (Q) is 30kW, the mass (m) is 500 litres, and the change in temperature (ΔT) is 60°C - 12°C = 48°C. We can convert the volume of water to mass using the density of water (1 liter = 1kg). Solving for time (t), we get:

Q = mcΔT
30kW = (500kg)(4.18 kJ/kg°C)(48°C)
t = 5.09 hours

Therefore, it will take approximately 5.09 hours to heat the whole tank to 60°C.

For question 2, we can use the formula Q = mcΔT, where Q is the heat energy, m is the mass of water in the heat exchanger, c is the specific heat capacity of water, and ΔT is the change in temperature. We know that the heat energy supplied (Q) is 400kW, the inlet temperature (T1) is 85°C, and the outlet temperature (T2) is 40°C. Solving for mass (m), we get:

Q = mcΔT
400kW = (m)(4.18 kJ/kg°C)(85°C - 40°C)
m = 14.83 kg/s

Therefore, the mass flow rate is 14.83 kg/s.

For question 3, we can use the formula Q = mcΔT, where Q is the heat energy, m is the mass of water in the heat exchanger, c is the specific heat capacity of water, and ΔT is the change in temperature. We know that the heat energy supplied (Q) is 210kW, the flow rate (m) is 5kg/s, and the inlet temperature (T1) is what we need to find. Solving for ΔT and T1, we get:

Q = mc