Hot water is transported from building A to building B through a 500-m-long, 2-inches steel-pipeline. The...

Hot water is transported from building A to building B through a 500-m-long, 2-inches steel-pipeline. The hot water is heated up to 90oC by an electric hot water boiler located in building A. The efficiency of the boiler is 95% while the average ambient temperature of the place is 20oC. In order to keep the water warm, thermal insulation (fiberglass) can be installed around the pipe. The purpose of this analysis is to determine the right amount of insulation to be used.

1. Find the pipeline heat losses as a function of the insulation thickness (assume any variable required for the calculation such as convection heat transfer coefficients, surface finishing of the insulation, etc.). Then, find the annual cost of the electricity required to compensate the heat losses in the pipeline as a function of the insulation thickness (again, assume any variable required such as electricity cost).

2. Find the investment cost of the insulation as a function of the insulation thickness (you can assume that the installed fiberglass cost per unit volume is $150/m3 and multiply that cost times the total insulation volume required, if you find a more precise way to calculate the investment, it would be welcome). Then, annualize the investment cost by dividing total investment in 15 years of lifetime for the insulation (that way you are disregarding any elaborated financial calculation including, for example, interest rate, expected profit for the investment, residual cost, etc. Again, if you want to use a more precise way to calculate the annualized investment, it would be welcome).

3. Graph the total annual cost of the project against the thickness. The total annual cost can be found by adding the annual energy cost and the annualized investment cost. The graph should have a minimum value for some given thickness. Find such thickness (this is the optimal insulation thickness) and the corresponding total annual cost (this is the minimum total annual cost of the project).

4. For the optimal insulation thickness, find the temperature of the hot water reaching building B

5. What happens to the optimal thickness, the minimum total cost, and the temperature at building B if the average ambient temperature drops to -20oC?

6. What happens if the electric hot water boiler is replaced with a natural-gas-fueled hot water boiler with 85% efficiency (assume any required variable such as LHV or price for the natural gas)?

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Expert Solution

samet mamat answered 1 year ago

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