Question

A disk-shaped transistor, which is mounted in an insulating medium, dissipates 0.25 W during steady state operation. To reduce the temperature of the transistor, it is proposed that a hollow copper tube (k = 400 W/m · K) be attached to the transistor as shown. The outer surface of the tube is exposed to ambient air at T? = 25 °C with a convection coefficient of h = 50 W/m² K. As a first approximation, heat transfer from the interior surface of the tube and from the exposed surface of the transistor may be neglected. Since r_i >> t, the tube may be treaded as a rectangular fin. (a) What is the temperature of the transistor with the fin? (b) What is the temperature of the transistor without fin if h and T? remain the same? (c) What is the temperature of the transistor if using infinite fin approximation? r_o = 7.75 mm t = 0.25 mm r_i = 7.5 mm L = 15mm Air h = 50 W/m²·K T? = 25°C Copper tube Transistor

          A disk-shaped transistor, which is mounted in an insulating medium, dissipates 0.25 W during steady state operation. To reduce the temperature of the transistor, it is proposed that a hollow copper tube (k = 400 W/m · K) be attached to the transistor as shown. The outer surface of the tube is exposed to ambient air at T? = 25 °C with a convection coefficient of h = 50 W/m² K. As a first approximation, heat transfer from the interior surface of the tube and from the exposed surface of the transistor may be neglected. Since r_i >> t, the tube may be treaded as a rectangular fin.
(a) What is the temperature of the transistor with the fin?
(b) What is the temperature of the transistor without fin if h and T? remain the same?
(c) What is the temperature of the transistor if using infinite fin approximation?
r_o = 7.75 mm
t = 0.25 mm
r_i = 7.5 mm
L = 15mm
Air
h = 50 W/m²·K
T? = 25°C
Copper tube
Transistor

A disk-shaped transistor, which is mounted in an insulating medium, dissipates 0.25 W during steady state operation. To reduce the temperature of the transistor, it is proposed that a hollow copper tube (k = 400 W/m · K) be attached to the transistor as shown. The outer surface of the tube is exposed to ambient air at T? = 25 °C with a convection coefficient of h = 50 W/m² K. As a first approximation, heat transfer from the interior surface of the tube and from the exposed surface of the transistor may be neglected. Since ri >> t, the tube may be treaded as a rectangular fin.
(a) What is the temperature of the transistor with the fin?
(b) What is the temperature of the transistor without fin if h and T? remain the same?
(c) What is the temperature of the transistor if using infinite fin approximation?
ro = 7.75 mm
t = 0.25 mm
ri = 7.5 mm
L = 15mm
Air
h = 50 W/m²·K
T? = 25°C
Copper tube
Transistor

Added by Jacob B.

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