Problem Description

A parallel-shaft gearbox is planned to be installed on a new exercise machine. This gearbox receives work through a high-speed shaft and then delivers work through a low-speed shaft. The gearbox is cooled on its outer surface by convection with the surrounding air. A test is needed to exam the performance of this gearbox.

What is known:

• The gearbox receives 60 kW through a high-speed shaft.
• The outer surface of the gearbox is 0.8 m².
• Heat transfer coefficient between the gearbox and its surrounding air is 1.8 kW/m²-K
• Temperature of the outer surface of the gearbox is 40^oC.
• The ambient pressure is 1 bar, and the ambient temperature is 25^oC.

• Determine the work delivered by this gearbox.
• Explore the exergy transfer of the gearbox and the exergy destruction.

• Take the gear box as a closed system.
• Use the energy balance of the gear box to determine the work output through the low-speed shaft.
• The exergy is transferred by heat and work.
• Exergy destruction is given as
  
  X_destroyed = T₀S_gen
  
  
• The entropy balance for the gearbox is:
  
  S_in - S_out + S_gen = ΔS_system