A power transistor mounted on a circuit board generates of thermal energy that must…
PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter
Problem
A power transistor mounted on a circuit board generates 12W of thermal energy that must be conducted through a rectangular alumina (ceramic) spacer into an aluminum heat sink maintained at 25∘C. The junction of the transistor can safely reach a maximum steady-state temperature of 105∘C. Alumina has a thermal conductivity of 24Wm−1∘C−1. The spacer is 1.2mm thick.
(a) Derive an expression for the minimum cross-sectional area of the spacer that will ensure the junction temperature does not exceed the specified maximum under steady-state conditions.
(b) Calculate the numerical value of that minimum area.
(c) Standard spacers are manufactured in square shapes. Determine the minimum side length of a square spacer that satisfies the requirement.
(d) If the spacer side length calculated in part (c) were reduced by 15% while all other parameters remained unchanged, compute the new steady-state junction temperature and comment on whether it would remain within safe limits.