Let's assume that hay bales can be approximated as cylinders with a diameter of D=2m. They are kept in long rows (you can neglect heat transfer from their ends and only need to account for radial conduction along the diameter of the hay as if they were a very long cylinder) and are in steady-state conditions. Air outside is at T∞=0∘C (in the winter) with ℎ=30W/(m2 ⋅K) for convection on the outside of the hay bales. If the thermal conductivity of the tightly packed hay is k=0.03W/(m⋅K)a. First find the maximum temperature in the bales for dry hay, which has a uniform volumetric heat generation of q_dot=2W/m3 from bacterial growth. After finding the maximum temperature of the bales, what is the temperature on the outside of the hay bale (where the hay is touching the air) ?b. Now for the same hay bale properties, find the maximum temperature if the hay is damp and volumetric heat generation from bacteria is q_dot=15W/m3. Also, what is the temperature on the outside of the damp hay bale (where the hay is touching the air)?c. Finally, for the same hay bale properties, find the maximum temperature if the hay is wet and volumetric heat generation from bacteria is q_dot=80W/m3. Once again, what is the temperature on the outside of the wet hay bale (where the hay is touching the air)? What conclusion can you make from this analysis (select all that apply)?Even for the wet hay conditions, it is unlikely that the hay will catch fire. This is because the maximumtemperature remains low in the hay in all three cases.The temperature in the hay bale is parabolic in shape with respect to radial position.The temperature in the hay bale is logarithmic in shape with respect to radial position.One can put their hand onto the outer surface of baled hay and tell if there is excessive bacterial heatgeneration in the hay because if there is, the hay will feel warm to the touch on the outside.It can be difficult to detect the severity of the volumetric heat generation in the hay just by observation,because its outside temperatures remain cold and close to ambient, even when its internal temperatures varywidely and can be hot enough for hay to catch fire. If you have ever baled hay, you know that it is dangerous to bale wet hay and store itin a barn. Why? Because the hay can catch fire! This may seem counterintuitive.Wouldn't wet hay not burn as easily?The danger from baling wet hay comes from microbial heat generation. If there ismoisture in hay when it is baled, it creates the ideal living conditions for bacteria,which feasts on the wet hay and produces heat from the metabolic process ofbreaking it down. This can lead to very high temperatures in hay bales, which caneventually cause the bale (and entire barn in which it is stored) to catch fire.Images taken from ACES_article on how to prevent hay fires.This is why farmers often wrap baled hay in plastic to protect it from the rain andminimize moisture content. This not only prevents the hay from getting moldy, but canalso prevent a catastrophic fire. You can use your knowledge of heat transfer to figureout just how hot hay gets when it is baled wet.

Answered: Image /qna-images/answer/88c16ff4-0cd4-47ef-9de1-71d3b91358c4.jpg

Let's assume that hay bales can be approximated as cylinders with a diameter of D=2m. They are kept in long rows (you can neglect heat transfer from their ends and only need to account for radial conduction along the diameter of the hay as if they were a very long cylinder) and are in steady-state conditions. Air outside is at T∞=0∘C (in the winter) with ℎ=30W/(m2 ⋅K) for convection on the outside of the hay bales. If the thermal conductivity of the tightly packed hay is k=0.03W/(m⋅K) a. First find the maximum temperature in the bales for dry hay, which has a uniform volumetric heat generation of q_dot=2W/m3 from bacterial growth. After finding the maximum temperature of the bales, what is the temperature on the outside of the hay bale (where the hay is touching the air) ? b. Now for the same hay bale properties, find the maximum temperature if the hay is damp and volumetric heat generation from bacteria is q_dot=15W/m3. Also, what is the temperature on the outside of the damp hay bale (where the hay is touching the air)? c. Finally, for the same hay bale properties, find the maximum temperature if the hay is wet and volumetric heat generation from bacteria is q_dot=80W/m3

Let's assume that hay bales can be approximated as cylinders with a diameter of D=2m. They are kept in long rows (you can neglect heat transfer from their ends and only need to account for radial conduction along the diameter of the hay as if they were a very long cylinder) and are in steady-state conditions. Air outside is at T∞=0∘C (in the winter) with ℎ=30W/(m2 ⋅K) for convection on the outside of the hay bales. If the thermal conductivity of the tightly packed hay is k=0.03W/(m⋅K) a. First find the maximum temperature in the bales for dry hay, which has a uniform volumetric heat generation of q_dot=2W/m3 from bacterial growth. After finding the maximum temperature of the bales, what is the temperature on the outside of the hay bale (where the hay is touching the air) ? b. Now for the same hay bale properties, find the maximum temperature if the hay is damp and volumetric heat generation from bacteria is q_dot=15W/m3. Also, what is the temperature on the outside of the damp hay bale (where the hay is touching the air)? c. Finally, for the same hay bale properties, find the maximum temperature if the hay is wet and volumetric heat generation from bacteria is q_dot=80W/m3

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