An engineer wishing to live off the grid has devised a scheme for heating a residence.
The system is a small engine that directly drives a heat pump. This system is shown schematically in Figure P3.19. The engine receives heat from a combustion process at 1500°F and rejects heat to the house which is at a temperature of 72°F.
All of the power delivered by the engine drives the heat pump, which receives heat from the environment at 20°F and rejects it to the house. The total heat transfer rate required to maintain the house at 72°F is 65,000 Btu/h. This is provided by the engine and the heat pump. To determine the best possible performance for this system, consider the case where both the engine and the heat pump are operating at the maximum possible thermal efficiency. For this ideal heating system determine the,

a. Heat transfer rate from the combustion source to the engine (Btu/h)

b. Heat transfer rate from the outdoor source to the heat pump (Btu/h)

c. Heat transfer rate from the engine to the house (Btu/h)

d. Heat transfer rate from the heat pump to the house (Btu/h)

e. Power required to run the heat pump (hp)

f. Devise and calculate the overall thermal efficiency of this system keeping in mind that the energy transfer from the environment to the heat pump is a “free” energy source.
In an effort to make a more realistic estimation of this system’s performance recalculate parts (a) through (f) assuming that the engine has a thermal efficiency of 36% and the heat pump has a coefficient of performance of 3.50. What is your engineering assessment of this off-the-grid heating system?

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T, = 1500F FIGURE P3.19 An off-the-grid residential heating system. T = 72F QHP T, = 20F