An electronic device that internally generates 600 mW of heat has a maximum permissible operating temperature of 70°C. It is to be cooled in 25°C air by attaching aluminum fins with a total surface area of 12 cm2 . The convection heat transfer coefficient between the fins and the air is 20 W/(m2 K). Estimate the operating temperature when the fins are attached in such a way that: (a) there exists a contact resistance between the surface of the device and the fin array of approximately 50 K/W, and (b) there is no contact resistance but the construction of the device is more expensive. Comment on the design options.
GIVEN
FIND
Operating temperature (To) for
(a) contact resistance (Ri) = 50 K/W
(b) no contact resistance
ASSUMPTIONS
-One dimensional heat transfer
-Steady state has been reached
-The temperature of the device is uniform
-The temperature of the aluminum fins is uniform (the thermal resistance of the aluminum is
negligible)
-The heat loss from the edges and back of the device is negligible
SKETCH
(a) The thermal circuit for the case with contact resistance is shown below
The value of the convective resistance,
For steady state conditions, the heat loss from the device (q) must be equal to the heat generated by
the device
(b) Similarly, the operating temperature of the device with no contact resistance is
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