Consider the electronic elements that are cooled by forced convection in Problem 6.31. The cooling system is designed and tested at sea level (p ≈ 1 atm), but the circuit board is sold to a customer in Mexico City, with an elevation of 2250 m and atmospheric pressure of 76.5 kPa. (a) Estimate the surface temperature of the chip located 120 mm from the leading edge of the board when the board is operated in Mexico City. The dependence of various thermophysical properties on pressure is noted in Problem 6.19.

surface temperature of the chip located 120 mm Ts=42.5°C

surface temperature of the chip in Mexico Ts=46.9°C

Explanation:

from the energy balance equation we have to:

q=E=30W

from Newton's law:

Ts=Tα + (q / (h*A)), where A=l^2

N=h/k=0.04 * (Vl/V) ^0.85*Pr^1/3

data given:

l=0.12 m

v=10 m/s

k=0.0269 W / (m*K)

Pr=0.703

Replacing:

h=0.04 * (0.0269/0.12) * (10*0.12) / ((16*69x10^-6)) ^0.85 * (0.703^1/3) = 107 W/m^2*K

The surface temperature at sea level is equal to:

Ts=25 + (30x10^-3/107*0.004^2) = 42.5°C

h=0.04 * (0.0269/0.12) * ((10*0.12) / (21*81x10^-6)) ^0.85 * (0.705^1/3) = 85.32 W / (m*K)

the surface temperature at Mexico City is equal to:

Ts=25 + (30x10^-3/85.32*0.004^2) = 46.9°C