Question

2.9 A young engineer is asked to design a thermal protec- tion 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 charac- teristics, the engineer specifies use of a nanostructured aerogel, characterized by a thermal conductivity of ka % 0.005 W/m! K, for the protective barrier. The engi- neer’s boss questions the wisdom of selecting the aero- gel 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 + 106 W/m2 . The absorptivities of the materials are ' % 0.2, 0.9, and 0.8 for the aluminum, glass, and aerogel, respectively, and the initial temperature of the barrier is Ti % 300 K. 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.

Answer 1

Answer:

attached

Explanation:

From Table A-1 for pure aluminum at 300 K

k_al = 238 Wm • K

From Table A-3 for pure glass at 300 K

k_gl = 1.4 Wm•K

Applying the energy balance.  

q_s'' =   q_abs''

Hence,  

formula is attached find the first attachment

Substituting for all cases we get  

formula is attached find the second attachment

So that, using the aerogel material as an insulation will be accompanied by high therms stresses in the protection layer which results in a rapid damage for this layer and thus the device will face the thermal hazard.