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THERMODYNAMICS - CASE STUDY SOLUTION


 

The heat transfer between the printed circuit boards (PCBs) and the air passing through the computer needs to be calculated to determine how many PCBs can be installed in the computer.

Assumptions:

  • Air is an ideal gas with cP = 1.005 kJ/kg-K
  • Heat transfer from the box to the surroundings is negligible
  • No change in potential energy
  • For noise control, the air velocity is relatively low. Hence the kinetic energy is negligible
  • The temperature change of the computer components is negligible
     


Consider the Whole Enclosure as a Control Volume

(1) Method 1:

If the whole enclosure is a control volume, the heat transfer term is zero due to the assumptions. Thus, under the stated assumptions, the energy balance can be expressed as:

If air enters at 20 oC and exits at 32 oC, the enthalpy change is:

      

       = -120.6 W

The power equals the sum of the power of the fan, the power of CPU and other components, and the power supplied to the PCBs. It is negative since it is done to the system.

       =PCBs - 80 W

      

PCBs is negative because power needs to supply to the system.

Each PCB can dissipate 10 W power. It means 10 W power needs to supply to each PCBs. The number of the PCBs is given by

      40.6/10 = 4

   

Heat Transfer and Work of
Control Volume A and B

(2) Method 2:

Consider air as control volume A and the computer components as control volume B.

Control Volume A:

Heat transfer occurs between the air and the electric components, Hence, the heat transfer term is not zero. No work is done by the air or to the air. The energy balance is:

      

From method 1, the enthalpy change is determined to be 120.6 W. Hence, the heat transfer is given by

       = 120.6 W

The positive sign means that the heat transfer is from the computer components to the air.

Control Volume B:

Heat transfer occurs between the air and the computer components. Hence, the heat transfer term is not zero. Work is done to the components, and given by the sum of the power of the fan, the CPU and other components, and the the PCBs. According to the assumptions, no enthalpy change occurs in control volume B. Thus, the energy balance is:

The amount of heat transfer from the PCBs to the air is the same as the heat transfer from the air to the PCBs, hence,

       = -120.6 W

The negative sign indicates that heat is transferred from the system.

The power supplied to the PCBs can be determined by

      PCBs = -120.6 - (-20 - 60) = -40.6 W

Note that fan and CPU have negative sign since power is applied to them.

The result ob is the obtained same as in method 1, hence the number of PCBs is 4.

Based on the results from both methods, for the given fan, Alex can only install up to 4 PCBs.