Chapter 9, Problem 9.42P

Many laptop computers are equipped with thermal management systems that involve liquid cooling of the central processing unit (CPU), transfer of the heated liquid to the back of the laptop screen assembly, and dissipation of heat from the back of the screen assembly by way of a flat, isothermal heat spreader. The cooled liquid is recirculated to the CPU and the process continues. Consider an aluminum heat spreader that is of width $w=275\text{mm}$ and height $L=175\text{mm}$ . The screen assembly is oriented at an angle $\theta =30°$ from the vertical direction, and the heat spreader is attached to the $t=3\text{-mm}$ -thick plastic housing with a thermally conducting adhesive. The plastic housing has a thermal conductivity of $k=0.21\text{W/m}\cdot \text{k}$ and emissivity of $\epsilon =0.85$ . The contact resistance associated with the heat spreaderhousing interface is $R_{t,c}^n=2.0\times {10}^{-4}{m}^2\cdot \text{K/W}$ . If the CPU generates, on average, 15 W of thermal energy, what is the temperature of the heat spreader when $T_{\infty }=T_{\text{sur}}=23°C$ ? Which thermal resistance (contact, conduction, radiation, or free convection) is the largest?