Q6: Say we have a heat exchanger made to heat 150 liters/minute from 20 degrees celsius to 80 degrees celsius. Each section of the heat exchanger, which is a circular pipe, is 10m long. The outer diameter is 2in, and the thickness of the pipe is 1 / 8 inch. As the heat exchanger is operated, lime is built up known as fouling. The heat exahnger uses N number of pipes, where water passes through the pipe and hot gas is on the outside.

k(foul) = 0.5 W/mK, K(foul) increases at 1mm/year, however there is no lime build up initially because the heat exchanger is new.

Steel thermal conductivity is k(steel) = 50 W/mK while the convection coefficient between the water in the tube and the inside wall of the pipe is 1000 W/m^2K, and the convection coefficient of the outside pipe and hot gas is 100 W/m^2K.

1. Calculate duty of the aforementioned heat exchanger

2. Calculate new overall heat transfer coefficient for the pipe (when heat exchanger is brand new, no fouling) use the expressions (for cylinders) where needed. Use outer surface of the pipe as the reference

3. Calculate the time in years for the heat exchanger over heat transfer coefficient to become exactly half its initial value

4. Find the thickness of lime layer when overall heat transfer coefficient is exactly half its original value.

5. Can the loss of performance due to lime build up be counteracted by making the steel pipes thinner?

6. Assuming the temperature difference is a constant 100 degrees celsius between the hot gas outside of the pipe and the water inside of the pipe., use the overall heat coefficient to find the number of pipes needed to operate the heat exchanger. Find the total area first to do this.