Consider a 1.5-m-high electric hot-water heater that has a diameter of 40 cm and maintains the hot water at 60°C. The tank is located in a small room whose average temperature is 27°C, and the heat transfer coefficients on the inner and outer surfaces of the heater are 50 and 12 W/ m² ⋅K, respectively. The tank is placed in another 46-cm-diameter sheet metal tank of negligible thickness, and the space between the two tanks is filled with foam insulation (k = 0.03 W/m⋅K). 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 homeowner 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 3-cm-thick fiberglass insulation (k = 0.035 W/m⋅K) 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 homeowner himself, how long will it take for this additional insulation to pay for itself?

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27°C 3 cm H 40 cm T₁ = 60°C Water heater Foam insulation FIGURE P17-77 1.5 m