Question

1. Heat Pump Operation Heat pumps can be used to heat a house in the winter and when run in reverse, they can cool a house in the summer. As shown in the figure below, the evaporator section of a heat pump can be connected to a pond or a lake which can be used as a heat source in the winter and used for air conditioning in the summer. Consider summer cooling operation where air is passed through a series of copper pipes submerged in the bath. You can ignore the thermal resistance of the copper pipes and assume that the inside surface of the pipe is fixed at the temperature of the pond water at T,-10 C. The air in the pipe enters the pond with an initial temperature of T,-30 C and leaves with a desired exit temperature of T,-15 C. For a pipe with an inner diameter of D=50mm and a mass flow rate of m= 0.001 kg/s, the goal is to determine what length of pipe is needed to obtain the desired cooling T,-30°C _ T10 C Pond Water Thermophysical Properties Air k 0.026 W/m K c,-1.00kJkgK p-1.16kg/m Water k 0.569 W/mK c, -4.2kJ/kgk ρ-1000 kg/m3 Pr-12.99 Pr 0.707 v 15.89x10 m'/s

1. Is the floe within the pipe turbulent or laminar? Justify your answer

2. What is the average Nusselt number and heat transfer coefficient in the pipe? You can assume that the flow is fully developed

3. What length of pipe is required to achieve the desired exit temperature?

4. Was your assumption of fully developed flow justified? Explain why or why not. How much error did this assumption introduce into calculation of nusselt number? Do you need more or less pipe to achieve the desired exit temperature?

Answer 1

Oy For waler Cir 8.43243 o Deterinhe Flod is in the turblort 9t dedde By the Renvood No. evoorotion (Pe) 4xo.ool 2 miher .333 Mv-HD)91.992 fir PIT