Consider the cylindrical bales of hay in Problem 3.82. It is proposed to utilize the microbial energy generation associated with wet hay to heat water. Consider a 30-mm diameter, thin-walled tube inserted lengthwise through the middle of a cylindrical bale. The tube carries water at T_∞,i = 20°C with h_i = 200 W/m² · K. 

(a) Determine the steady-state heat transfer to the water per unit length of tube.
(b) Plot the radial temperature distribution in the hay, T(r).
(c) Plot the heat transfer to the water per unit length of tube for bale diameters of 0.2 m ≤ D ≤ 2 m.

Data From Problem 3.82

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 = 1W/m³), moist hay (q = 10 W/m³), and wet hay (q = 100 W/m³). Ambient  conditions are T_∞ = 0°C and h = 25 W/m² · K.