Chapter 4, Problem 4.35P

An electronic device, in the form of a disk 20 mm in diameter, dissipates 100 W when mounted flush on a large aluminum alloy (2024) block whose temperature is maintained at 27°C. The mounting arrangement is such that a contact resistance of $R_{t,c}^n=5\times {10}^{-5}{\text{m}}^{\text{2}}\cdot \text{K/W}$ exists at the interface between the device and the block.

1. Calculate the temperature the device will reach, assuming that all the power generated by the device must be transferred by conduction to the block.
2. To operate the device at a higher power level, a circuit designer proposes to attach a tinned heat sink to the top of the device. The pin fins and base material are fabricated from copper $\left(k=400\text{W/m}\cdot \text{K}\right)$ and are exposed to an airstream at 27°C for which the convection coefficient is $1000{\text{W/m}}^{\text{2}}\cdot \text{K}.$ For the device temperature computed in part (a), what is the permissible operating power?