In a compost pile, the biochemical conversion process from waste to compost is accompanied by heat generation. Composting systems need to be designed properly so that the temperature rise due to...

In a compost pile, the biochemical conversion process from waste to compost is accompanied by heat generation. Composting systems need to be designed properly so that the temperature rise due to generated heat does not reach above 65 °C, which is when the beneficial microbes start to die off. Consider a compost pile on the ground (assume a pile to be a horizontal layer of a certain thickness) as a steady-state, one-dimensional system with heat transfer along the vertical direction. For simplicity, consider the top and bottom of the pile to be maintained at the same temperature, 20 °C, making the layer symmetric. The volumetric heat generation is 7W/m3, and the thermal conductivity of the compost material is 0.1 W/m*K.

1. 
   

   Write the final governing equation for this problem, keeping only the relevant terms.

   
   


2. 
   

   Solve the equation for the particular boundary condition to obtain the solution T-Ts = (Q*L2/2k)(1-x2/L2) where the symbols have their usually meanings.

   
   

c. What should be the maximum height of the pile be so that the beneficial microbes do not die off at the warmest location?

Don’t use Heissler charts to answer this question.