Consider the water heater described in Problem 1.48. We now wish to determine the energy needed to compensate for heat losses incurred while the water is stored at the prescribed temperature of 55 C. The cylindrical storage tank (with flat ends) has a capacity of 100 gal, and foamed urethane is used to insulate the side and end walls from ambient air at an annual average temperature of 20 C. The resistance to heat transfer is dominated by conduction in the insulation and by free convection in the air, for which h 2 W/m2 K. If electric resistance heating is used to compensate for the losses and the cost of electric power is $0.18/kWh, specify tank and insulation dimensions for which the annual cost associated with the heat losses is less than $50.