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3.162 Heat transfer from a transistor may be enhanced by inserting it in an aluminum sleeve (k = 200 W/m · K) having 12 integrally machined longitudinal fins on its outer surface. The transistor radius and height are r1 =
2.5 mm and H = 4 mm, respectively, while the fins are
of length L = r3 – r2 = 8 mm and uniform thickness t = 0.8 mm. The thickness of the sleeve base is r2 – r1 = 1 mm, and the contact resistance of the sleeve-transistor interface is Rt”,c = 0.6 X 10-3 m2 · K/W. Air at Too = 20°C flows over the fin surface, providing an approximately uniform convection coeffficient of h = 30 W/m2 · K.


Cylinder wall

Aluminum casing

T1 Tb


R” , T

T¥, h

t,c 1


t = 2 mm
d = 2 mm H

ri = 60 mm
r1 = 66 mm

T¥, h
Sleeve with longitudinal fins r1

r2 = 70 mm
ro = 95 mm
The air is at 320 K and the corresponding convection coefficient is 100 W/m2 · K. Although heating at the inner surface is periodic, it is reasonable to assume steady-state conditions with a time-averaged heat flux of
(a) When the transistor case temperature is 80°C, what
is the rate of heat transfer from the sleeve?
(b) Identify all of the measures that could be taken to improve design and/or operating conditions, such that heat dissipation may be increased while still maintaining a case temperature of 80°C. In words, assess the relative merits of each measure. Choose
what you believe to be the three most promising measures, and numerically assess the effect of cor- responding changes in design and/or operating con- ditions on thermal performance.

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