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 40oC.
  • The ambient pressure is 1 bar, and the ambient temperature is 25oC.

  • 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

    Xdestroyed = T0Sgen

  • The entropy balance for the gearbox is:

    Sin - Sout + Sgen = ΔSsystem