Consider a 2-m-high electric hot-water heater that has a diameter of 40cm and maintains the hot water at 55C. The tank is located in a small room whose average temperature is 27C, and the heat transfer coefficients on the inner and outer surfaces of the heater are 50 and 12W/m2K, respectively. The tank is placed in another 46cm-diameter sheet metal tank of negligible thickness, and the space between the two tanks is filled with foam insulation (k=0.03W/mK). The thermal resistances of the water tank and the outer thin sheet metal shell are very small and can be neglected. The price of electricity is $0.08/kWh, and the home owner pays $280 a year for water heating. Determine the fraction of the hot-water energy cost of this household that is due to the heat loss from the tank. Hot-water tank insulation kits consisting of 3cm thick fiberglass insulation (k=0.035W/mK) large enough to wrap the entire tank are available in the market for about $30. If such an insulation is installed on this water tank by the home owner himself, how long will it take for this additional insulation to pay for itself? |Answers: 17.2 percent, 19 months]