A homeowner wants to replace an electric hot-water heater. There are two models in the store. The

Question:

A homeowner wants to replace an electric hot-water heater. There are two models in the store. The inexpensive model costs $280 and has no insulation between the inner and outer walls. Due to natural convection, the space between the inner and outer walls has an effective conductivity of 3 times that of air. The more expensive model costs $310 and has fiberglass insulation in the gap between the walls. Both models are 3.0 m tall and have a cylindrical shape with an inner wall diameter of 0.60 m and a 5 cm gap. The surrounding air is at 25?C, and the convective heat transfer coefficient on the outside is 15 W/(m2 K). The hot water inside the tank results in an inside wall temperature of 60?C.If energy costs 6 cents per kilowatt-hour, estimate how long it will take to pay back the extra investment in the more expensive hot-water heater. State your assumptions.GIVENTwo hot-water heatersHeight (H) = 3.0 mInner wall diameter (Di) = 0.60 mGap between walls (L) = 0.05 mWater heater #1Cost = $280.00Insulation: noneEffective Conductivity between wall (keff) = 3(ka)Water heater #2Cost = $310.00Insulation: FiberglassSurrounding air temperature (T??) = 25?CConvective heat transfer coefficient (hc) = 15 W/(m2 K)Inside wall temperature (Twi) = 60?CEnergy cost = $0.06/kWhASSUMPTIONSSince the diameter is large compared to the wall thickness, one-dimensional heat transfer is assumedTo simplify the analysis, we will assume there is no water drawn from the heater, therefore theinside wall is always at 60?CSteady state conditionsprevail