Hot water is transported from building A to building B through a500-m-long, 2-inches steel-pipeline. The hot water is heated up to90oC by an electric hot water boiler located in building A. Theefficiency of the boiler is 95% while the average ambienttemperature 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 ofinsulation to be used.
1. Find the pipeline heat losses as a function of the insulationthickness (assume any variable required for the calculation such asconvection heat transfer coefficients, surface finishing of theinsulation, etc.). Then, find the annual cost of the electricityrequired to compensate the heat losses in the pipeline as afunction of the insulation thickness (again, assume any variablerequired such as electricity cost).
2. Find the investment cost of the insulation as a function ofthe insulation thickness (you can assume that the installedfiberglass cost per unit volume is $150/m3 and multiply that costtimes the total insulation volume required, if you find a moreprecise way to calculate the investment, it would be welcome).Then, annualize the investment cost by dividing total investment in15 years of lifetime for the insulation (that way you aredisregarding any elaborated financial calculation including, forexample, interest rate, expected profit for the investment,residual cost, etc. Again, if you want to use a more precise way tocalculate the annualized investment, it would be welcome).
3. Graph the total annual cost of the project against thethickness. The total annual cost can be found by adding the annualenergy cost and the annualized investment cost. The graph shouldhave a minimum value for some given thickness. Find such thickness(this is the optimal insulation thickness) and the correspondingtotal annual cost (this is the minimum total annual cost of theproject).
4. For the optimal insulation thickness, find the temperature ofthe hot water reaching building B
5. What happens to the optimal thickness, the minimum totalcost, and the temperature at building B if the average ambienttemperature drops to -20oC?
6. What happens if the electric hot water boiler is replacedwith a natural-gas-fueled hot water boiler with 85% efficiency(assume any required variable such as LHV or price for the naturalgas)?
