Your company sells and installs ground source heat pump in the Northeast region. A ground source...

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Your company sells and installs ground source heat pump in the Northeast region. A ground source heat pump is a renewable heating and cooling system that uses the earth's relatively constant temperature to provide heating and hot water for buildings. For these heat pumps, water from the heat pump is discharged into a tubing placed into the soil and then is retuned back to the heat pump (see the figure). For your next job assignment, your boss has recommended circulating water using a 70% efficient pump through a high-density polyethylene tubing of D₁ = 25 mm, thickness t = 8 mm, and thermal conductivity k = 0.47 W/m K. He has asked you to determine minimum power required to achieve a tube outlet temperature (heat pump inlet temperature), Tm,o, of 7°C. Hint: Find Tm,o as a function of the tube length L and water mass flow rate. Variables: Water mass flow rate: 0.01 ≤ m < 0.05 (kg/s) with increments of 0.005 kg/s; Tube length: 10 L ≤ 50 m with increments of 5 m. Constants: Tube inlet temperature (heat pump outlet temperature), Tm,i = 0°C; Tube constant outer surface temperature T, = 10°C. Assumptions: Tm = 277K; Thermal entry length problem For rough estimate of pump power: Powerpump = mghf/n; hf = 128μLm πρ2gD4 (for laminar flows) Your company sells and installs ground source heat pump in the Northeast region. A ground source heat pump is a renewable heating and cooling system that uses the earth's relatively constant temperature to provide heating and hot water for buildings. For these heat pumps, water from the heat pump is discharged into a tubing placed into the soil and then is retuned back to the heat pump (see the figure). For your next job assignment, your boss has recommended circulating water using a 70% efficient pump through a high-density polyethylene tubing of D₁ = 25 mm, thickness t = 8 mm, and thermal conductivity k = 0.47 W/m K. He has asked you to determine minimum power required to achieve a tube outlet temperature (heat pump inlet temperature), Tm,o, of 7°C. Hint: Find Tm,o as a function of the tube length L and water mass flow rate. Variables: Water mass flow rate: 0.01 ≤ m < 0.05 (kg/s) with increments of 0.005 kg/s; Tube length: 10 L ≤ 50 m with increments of 5 m. Constants: Tube inlet temperature (heat pump outlet temperature), Tm,i = 0°C; Tube constant outer surface temperature T, = 10°C. Assumptions: Tm = 277K; Thermal entry length problem For rough estimate of pump power: Powerpump = mghf/n; hf = 128μLm πρ2gD4 (for laminar flows)

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To determine the minimum power required to achieve a tube outlet temperature Tmo of 7C we can follow ... View the full answer