Large, cylindrical bales of hay used to feed livestock in the winter months are

Question

Large, cylindrical bales of hay used to feed livestock in the winter months are D = 2 m in diameter and are stored end-to-end in long rows. Microbial energy generation occurs in the hay and can be excessive if the farmer bales the hay in a too-wet condition. Assuming the thermal conductivity of baled hay to be k = 0.04 W/m*K, determine the maximum steady-state hay temperature for dry hay (q,dot = 1W/m3), moist hay (q,dot = 10 W/m3), and wet hay (q,dot = 100 W/m3). Ambient conditions are T,infinity = 0 degrees C and h = 25 W/m2*K.

Explanation / Answer

There's convection outside the cylinder, and conduction inside the cylinder. The heat flux due to conduction has to match the heat flux due to conduction at the boundary of the cylinder. T0-qr2b4k=Tb -k(dTdr)r=rb=qrb2=h(T0-qr2b4k)

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