Chapter 2, Problem 2.9P

A young engineer is asked to design a thermal protection barrier for a sensitive electronic device that might be exposed to irradiation from a high-powered infrared laser. Having learned as a student that a low thermal conductivity material provides good insulating characteristics, the engineer specifies use of a nanostructured aerogel. characterized by a thermal conductivity of $k_a=0.005\text{W/m}\cdot \text{K,}$ for the protective barrier. The engineer's boss questions the wisdom of selecting the aerogel because it has a low thermal conductivity. Consider the sudden laser irradiation of (a) pure aluminum, (b) glass. and (c) aerogel. The laser provides irradiation of $G=10\times {10}^6{\text{W/m}}^{\text{2}}.$ The absorptivities of the materials are $\alpha =0.2,0.9,$ and 0.8 for the aluminum, glass. and aerogel, respectively, and the initial temperature of the barrier is $T_i=300\text{K}\text{.}$ Explain why the boss is concerned. Hint: All materials experience thermal expansion (or contraction), and local stresses that develop within a material are. to a first approximation, proportional to the local temperature gradient.