An electronic circuit board is the shape of a flat plate 0.3 m × 0.3 m in plan-form and dissipates 15 W. It is placed in operation on an insulated surface in a horizontal position or at an angle of 45 degrees to horizontal, in both cases; it is in still air at 25°C. If the circuit fails above 60°C, determine if the two proposed installations are safe.

Question

GIVEN

• A flat plate with insulated back, horizontal or at an angle of 45 degrees in still air

• Plate size (s × s) = 0.3 m × 0.3m

• Heat generation rate (qG) = 15 W

• Air temperature (T?) = 25°C

• Maximum plate temperature (Ts) = 60°C

FIND

• If the two plate positions are safe

ASSUMPTIONS

• Radiative heat transfer is negligible

SKETCH



PROPERTIES AND CONSTANTS

for dry air at the mean temperature of 43°C

Thermal expansion coefficient (?) = 0.00316 1/K

Thermal conductivity (k) = 0.0267 W/(m K)

Kinematic viscosity (?) = 17.9 × 10–6 m2/s

Prandtl number (Pr) = 0.71

Answer 1

For the horizontal case, the characteristic length



The Grashof and Rayleigh numbers for the flat case at the maximum operating temperature are





For the inclined case, the characteristic length is the length of the inclined side (0.3 m), the Grashof

number for the inclined case is



Case 1: The average Nuselt number is



The rate of heat transfer from the plate at Ts = 60°C is



Since this is larger than the heat generation rate, the actual surface temperature will be less than 60°C.

Case 1 configuration is safe.

Case 2



Therefore, the average heat transfer coefficient is



The rate of heat transfer when Ts = 60°C is



Since this is also greater than the heat generation rate, the actual temperature will be less than 60°C.

Therefore, Case 2 is also safe.