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A computer cooled by a fan contains eight PCBs, each dissipating 10 W power. The cooling air is supplied by a 25-W fan mounted at the inlet. If the temperature rise of air as it flows through the case of the computer is not to exceed 10 oC, determine (a) the flow rate of the air that the fan needs to deliver and (b) the fraction of the temperature rise of air that is due to the heat generated by the fan and its motor.

Answer :

Given Information:  

Qin = 8*10 = 80 W

Win = 25 W

Temperature = T2-T1 = 10°C

Required Information:  

(a) flow rate of the air = m = ?

(b) fraction of the temperature rise of air = f = ?

Answer:  

(a) flow rate of the air m = 0.01044 kg/s

(b) fraction of the temperature rise of air f = 23.8 %

Solution:

(a) The flow rate of the air that fan needs to deliver can be found by

[tex]m = Q_{in} + W_{in} /C_{p} (T_{2} -T_{1} )[/tex]

Where the value of specific heat of air is 1005 j/kg.C

m = (80 + 25)/1005*10

m = 0.01044 kg/s

(b) fraction of the temperature rise of air due to fan

ΔT = Q/mCp

ΔT = 25/0.01044*1005

ΔT = 2.38°C

So the fan causes a temperature rise of 2.38°C

f = ΔT/T2-T1

f = 2.38/10

f = 0.238 = 23.8 %

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