You run a zoo and you've decided the best attraction to increase the number of visitors...

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You run a zoo and you've decided the best attraction to increase the number of visitors are flamingoes! Specifically, Deb the Flamingo! You've designed a flamingo-sized hamster-style ball that Deb can run around in throughout the park, and directly interact with families. This idea cannot possibly be a disaster. Good job! The main problem with inventing a ball that a flamingo can run around in is that flamingoes are known particularly for their stink. So you need to coat the ball with material that will prevent the aroma from escaping and repelling zoo visitors. On the other hand, the flamingo inside the ball is naturally producing heat from its exercise, and if the aroma-reduction coating is too thick, then it will effectively form a layer of insulation, the poor flamingo will overheat and then have not just a natural stink but also a post-natural stink, if you understand. The flamingo ball consists of a layer of Plexiglas to contain the flamingo (kflamingo = 0.35 W/m-K), a layer of aroma reduction material, and another layer of Plexiglas to hold everything together. The interior has a 1 meter diameter for the flamingo. The inner Plexiglas layer (kplexigias = 0.33 W/m-K) has a thickness of 0.01 m, the aroma material thickness is 0.01 m, and outer Plexiglas layer is 0.01 m thick. The interior ball walls that the flamingo can touch should not go higher than a temperature of 30 C, or Deb will become even more uncomfortable. Because the ball is moving, there is an effective convective heat transfer coefficient surrounding the exterior of the ball of 50 W/mK, where the temperature is usually 20C. If the flamingo does not have a heat flux of at least 20 W/m, it will overheat and die. You may assume the flamingo is perfectly spherical and completely fills the 1 m diameter inner space. Starting with the heat equation, determine the thermal conductivity that the aroma reduction material should have to not kill the flamingo inside. Show your work. Deb Interior Plexiglas Aroma reduction material Outer Plexiglas You run a zoo and you've decided the best attraction to increase the number of visitors are flamingoes! Specifically, Deb the Flamingo! You've designed a flamingo-sized hamster-style ball that Deb can run around in throughout the park, and directly interact with families. This idea cannot possibly be a disaster. Good job! The main problem with inventing a ball that a flamingo can run around in is that flamingoes are known particularly for their stink. So you need to coat the ball with material that will prevent the aroma from escaping and repelling zoo visitors. On the other hand, the flamingo inside the ball is naturally producing heat from its exercise, and if the aroma-reduction coating is too thick, then it will effectively form a layer of insulation, the poor flamingo will overheat and then have not just a natural stink but also a post-natural stink, if you understand. The flamingo ball consists of a layer of Plexiglas to contain the flamingo (kflamingo = 0.35 W/m-K), a layer of aroma reduction material, and another layer of Plexiglas to hold everything together. The interior has a 1 meter diameter for the flamingo. The inner Plexiglas layer (kplexigias = 0.33 W/m-K) has a thickness of 0.01 m, the aroma material thickness is 0.01 m, and outer Plexiglas layer is 0.01 m thick. The interior ball walls that the flamingo can touch should not go higher than a temperature of 30 C, or Deb will become even more uncomfortable. Because the ball is moving, there is an effective convective heat transfer coefficient surrounding the exterior of the ball of 50 W/mK, where the temperature is usually 20C. If the flamingo does not have a heat flux of at least 20 W/m, it will overheat and die. You may assume the flamingo is perfectly spherical and completely fills the 1 m diameter inner space. Starting with the heat equation, determine the thermal conductivity that the aroma reduction material should have to not kill the flamingo inside. Show your work. Deb Interior Plexiglas Aroma reduction material Outer Plexiglas