A chemical fertilizer undergoes a slow chemical reaction, which results in a vol

Question

A chemical fertilizer undergoes a slow chemical reaction, which results in a volumetric heat generation rate of q''' = 5 W/m3. This material is stored in tall cylindrical silos with sheet metal walls, and the outside surface of the silo is exposed to air at 30 degrees C; the associated convection coefficient is 25 W/m2 middot K. The thermal conductivity of the fertilizer is 0.2 W/m middot K. A significant safety concern is that the fertilizer can undergo a chain detonation when its temperature exceeds 150 degrees C. Given this, calculate the maximum safe diameter of the silo.

Explanation / Answer

let d be the diameter of the tower and l the length

at steady state

then rate of heat generated must be equal to rate of heat transfer out to the surrounding

q'''*V = UAdelT

h'''*pi*(d^2)h/4 = U*pi*d*h*(150-30)

d = U*4*120/(h''')

d = 25*4*120/5 = 2400 m

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