A thin electronic circuit board, 0.1 m by 0.1 m in size, is to be cooled in air at 25°C. The board is placed in a vertical position and the back side is well insulated. If the heat dissipation is uniform at 200 W/m2, determine the average temperature of the surface of the board cover.

Question

GIVEN

• Vertical circuit board in air

• Back is well insulated

• Board dimensions (L × H) = 0.1 m × 0.1 m

• Air temperature (T ?) = 25°C

• Uniform heat dissipation rate ( q G/A) = 200 W/m2

FIND

• The average temperature of the surface of the board (Ts)

ASSUMPTIONS

• Ambient air is still

• The board has reached steady state

• Radiation is negligible

SKETCH

Answer 1

Since the fluid properties must be evaluated at the average of the surface and ambient temperatures,an iterative procedure is required to calculate the average surface temperature of the cover. For the first iteration, let Ts = 55°C

for dry air at the mean temperature of 40°C

Thermal expansion coefficient (?) = 0.00319 1/K

Thermal conductivity (k) = 0.0265 W/(m K)

Kinematic viscosity (?) = 17.6 × 10–6 m2/s

Prandtl number (Pr) = 0.71

The Grashof number is



For a laminar boundary layer, Equation (8.12a) gives the average heat transfer coefficient



The rate of heat generation must equal the rate of convection heat transfer for steady state



Solving for the surface temperature



For the second try, let Ts = (55°C + 57.9°C/2 = 56.5°C, i.e. halfway between the first guess and the result of the first interation. This gives Tmean = 40.7°C so the property values will change very little. For the second iteration.



Therefore, the average surface temperature is about 58°C.