(60pts) OSU Dairy Farm Biological Digester - Operating Conditions The OSU Dairy farm has a herd of cattle and they generate a lot of biowaste (cow poop). The dairy runs a biological digester to turn the biowaste, grass clippings, straw, etc. into manure, which is then sprayed out on the fields. If you ever bike out by the covered bridge in the Spring you can both see and smell the result of their efforts! The digester is a HDPE tank with D=3m and L=3m(L/D=1.0). It is completely insulated on the outside (q(r)=0), except for the top, where a 2.5cm thick Styrofoam lid has been added. The digester biowaste generates heat (10W/m3). The optimum temperature for digestion is T (average) >80C(353K). Some additional important information is given below. a) Sketch and clearly label the problem. Clearly state all given information and assumptions. b) What is the average biowaste temperature at steady state when the digester is 3/4 filled with biowaste? Does this meet the optimum requirements for digestion, which is T (average) >80C(353K). Hint: The average temperature in the biowaste can be taken as the average of the temperature at the top and bottom of the biowaste (Ttop+Tbot)/2. c) If the digester was FULL (instead of 3/4 full), calculate the average temperature in the biowaste. Does this meet the optimum requirements for digestion, which is T (average) >8C(353K). Show all work and units, and clearly state All ASSUMPTIONS. Useful Information (start here!): - Assume that the digester is well-mixed and that an average temperature can be achieved. - The digester is outside and calculations should be made for winter conditions Tout=5C and h0=20W/m2K - waste decomposition leads to a constant net heat generation =10W/m3 of biowaste. - when the digester is not full, assume the air layer above it is stagnant and moist. - thermal conductivities (k) : biowaste =1.0W/mK, Air ( moist )=0.38W/mK; Styrofoam =0.035W/mK