Chapter 3, Problem 3.82P

Large, cylindrical bales of hay used to feed livestock in the winter months are $D=2\text{m}$ 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 $k=0.04\text{W/m}\cdot \text{K,}$ determine the maximum steady-state hay temperature for dry hay $\left(\stackrel{.}{q}=1{\text{W/m}}^{\text{3}}\right),$ moist hay $\left(\stackrel{.}{q}=10{\text{W/m}}^{\text{3}}\right),$ and wet hay $\left(\stackrel{.}{q}=100{\text{W/m}}^{\text{3}}\right).$ Ambient conditions are $T_{\infty }=0°\text{C}$ and $h=25{\text{W/m}}^{\text{2}}\cdot \text{K}\text{.}$