Chapter 3, Problem 3.160P

An electronic device, such as a power transistor mounted on a finned heat sink, can be modeled as a spatially isothermal object with internal heat generation and an external convection resistance.

(a) Consider such a system of mass M, specific heat c, and surface area $A_s$, which is initially in equilibrium with the environment at $T_{\infty }$. Suddenly, the electronic device is energized such that a constant heat generation ${\stackrel{\dot{}}{E}}_g\left(W\right)$ occurs. Show that the temperature response of the device is $\frac{\theta }{{\theta }_i}=\exp \left(-\frac{t}{RC}\right)$ where $\theta \equiv T-T\left(\infty \right)$ and $T\left(\infty \right)$ is the steady-state temperature corresponding to $t\to \infty ;{\theta }_i=T_i-T\left(\infty \right)$; $T_i=$, initial temperature of device; $R=$ thermal resistance $1/\bar{h}{A}_s$; and $C=$ thermal capacitance Mc.

(b) An electronic device, which generates 60 W of heat, is mounted on an aluminum heat sink weighing 0.31 kg and reaches a temperature of 100°C in ambient air at 20°C under steady-state conditions. If the device is initially at 20°C, what temperature will it reach 5 min after the power is switched on?