A thermal protection system for a space vehicle consists of a 0.1 meterthick outer ceramic foam and a 0.1 meterthick inner metal foam, as shown in figure 4.11. The thermal conductivities of the ceramic and metal foams, respectively, are 0.05 and 0.025 \(\mathrm{W} / \mathrm{m} / \mathrm{K}\). A fluid is passed through the metal foam, which absorbs heat at the rate of 1,000 \(\mathrm{W} / \mathrm{m}^{3}\). The metal foam is attached to the vehicle structure and is insulated. The outside temperature of the ceramic foam is estimated to be \(1,000 \mathrm{~K}\). Use onedimensional finite elements to determine the temperature distribution in the foams. What is the temperature of the vehicle structure? Calculate the heat entering the system due to aerodynamic heating.

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1,000 K Ceramic foam Metal foam k = 0.05 W/m/K Q=-1,000 W/m Insulated No heat k=0.025 X flow W/m/K 0.1 m 0.1 m Figure 4.11 Heat transfer of a thermal protection system for a space vehicle