Q: Japanese honeybees have a unique defensive mechanism against their natural predator, the giant hornet. When threatened by a hornet attacking the nest, worker bees will work together to surround the hornet, and then vibrate to create heat. If enough bees work together, the heat from the vibrations is enough to kill the hornet. The point of death for a hornet is when the internal temperature raises to 47�C. Model the Hornet as a cylinder

Question

Q: Japanese honeybees have a unique defensive mechanism against their natural predator, the giant hornet. When threatened by a hornet attacking the nest, worker bees will work together to surround the hornet, and then vibrate to create heat. If enough bees work together, the heat from the vibrations is enough to kill the hornet. The point of death for a hornet is when the internal temperature raises to 47�C. Model the Hornet as a cylinder

50 mm long with a 5 mm radius and protected by a thin layer (1 mm) of exoskeleton (0.02 W/(m K)), and each of the 500 bees required to cover the hornet can provide 1.8 x 10^-2 J of heat per second;

(a) The fi�rst part of the heating process is the bees' heating the air around the hornet. Using convection heat transfer, calculate the di�erence in temperature between the hornet's outer surface and the heat generating bees. A typical value for forced air convection is somewhere around 200 W=(m2 K).

(b) The second part of the process is conduction. As the outer part of the hornet reaches a temperature of 52�C, the internal temperature also starts to increase due to conduction, with a total amount of 2000 J transferring from the outside of the hornet, to the inside, across the exoskeleton. How long does it take to kill the hornet?

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