Chapter 5, Problem 5.20P

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.

1. 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 ${\stackrel{.}{E}}_g\left(\text{W}\right)$ 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 $t\to \infty ;{\theta }_i=T_i-T\left(\infty \right);T=$ initial temperature of device; $R=$ thermal resistance $1/\bar{h}{A}_s;$ and $C=$ thermal capacitance $Mc.$
2. 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 $100°\text{C}$ in ambient air at $20°\text{C}$ under steady-state conditions. If the device is initially at $20°\text{C,}$ what temperature will it reach 5 min after the power is switched on?