Large, cylindrical bales of hay used to feed livestock in the winter months are
ID: 2324509 • Letter: L
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. The thermal conductivity of baled hay is k = 0.04 W/m middot K and the ambient conditions are T_infinity = 0 degree C and h = 25 W/m^2 middot K. Determine the surface temperature and the centerline temperature for dry hay (e_gen = 1 W/m^3) and for too-wet hay (e_gen = 100 W/m^3).Explanation / Answer
Type of problem- cylinders with generation of thermal energy
From the problem-
Diameter-Do=2 m, ro=1m
K=0.004 w/m k
T ambient = 0 o C =273 K , h= 25 W/m2
Heat generation, qg =1 w/ m3 for dry hay
Heat generation, qg =100 w/ m3 for too wet hay
Solving the problem on 1m lenth basis
We know Q at surface= r2L qg
=3.14 x12x1x1=3.14 W/m for dry hay
=3.14 x12x1x100=314 W/m for wet hay
We know Qat surface=h A ( Tsurface- T ambient )=25 x DL ( Tsurface- T ambient )
3.14=25x3.14x2x1 (Tsurface- 273)
Tsurface =273.02 K for dry hay
Similarly Tsurface =279.28 K for wet hay
Centre temperature To = Tsurface + (qg ro2 ) /(4k)
=335.52 K for dry hay
Similarly Centre temperature To for wet hay=6529.28 K
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