2. (25 pts) Grain stored in a silo can self-heat due to fermentation, causing temperature runaway and spontaneous combustion (https://extension.psu.edu/silo-fires)! Consider a tall cylindrical silo (diameter D = 6 m) filled

with dry corn (bulk thermal conductivity k = 0.5 W m¹¹ K-¹). The fermentation process causes volumetric heating with q"" = 50 W m³. Assume ambient air blows over the outside of the silo (h= 10 W m² K¹, T = 20°C). a. (7 pts) Sketch the grain silo, indicating the main heat generation and heat transfer processes in the system. List appropriate simplifying assumptions for this problem. b. (7 pts) Simplify the governing heat conduction equation for this silo (hint - use the cylindrical coordinate form). Specify the boundary conditions. c. (6 pts) Solve the governing equation for the steady temperature profile in the silo. Make a plot of the temperature profile (T(r)) and indicate the peak temperature.