The water in the elevated reservoir is used for general duties around the station (drinking, bathing, cooking, watering Dr. Smith's avocado plant that is not doing well, etc.). Unfortunately, the elevated reservoir is outside and exposed to -62°C. To keep the water from freezing, it is cycled continuously through an electric heater, but calcium deposits have diminished the efficiency of this system and the bulk temperature of the water is dropping precariously close to 0°C. A double-pipe heat exchanger is proposed as the replacement. For this exchanger, assume that the water flows through the annular region of the exchanger and has a heat transfer coefficient of 5.618 kW/m^2-K. The temperature as the water enters the exchanger is 10°C. 500 kW must be supplied to the water in order to keep the bulk water temperature in the tank stable at 10°C. Assume that the volume of the elevated tank is 3000 gallons and that the pump feeding the heat exchanger turns that volume over every 15 minutes (meaning that a volume of water equivalent to the volume of the tank is pumped through the exchanger every 15 minutes).
Water: p = 1000 kg/m^3, u = 0.001308 kg/m s, Cp = 4.192 kJ/kgK
A natural gas turbine is used to generate power for the plant, and the hot exhaust from the turbine is used as the hot side of the heat exchanger, which is to flow through the center pipe of the exchanger in a counterflow direction. The pipe inside diameter is 15 cm. This exhaust has a volume flow rate of 2.83 m^3/s and a gas temperature of 350°C. Assume the following properties for the fully developed exhaust gas flow are the same as for air:
p = 0.56 kg/m^3, μ = 3.017 x 10^-5 kg/m s, Cp = 1.0511 kJ/kg.K, k = 46.61 mW/mK
Calculate the length of heat exchanger required, assuming the overall heat transfer coefficient is constant, and that the thermal resistance of the wall can be neglected.
Hint: Calculate the heat transfer coefficient for the exhaust gas and use that and the given heat transfer coefficient to determine an overall heat transfer coefficient, then find the length.
