4) (60pts) A new Composter Design - the fabulous Skip-o-Poster! Many of the new "compostable" food containers made from biodegradable plastics (such as PLA) require high temperatures and high moisture content

to properly decompose. I have designed a new composter, the Skip-o-Poster that is a plastic (HDPE) drum with a four impeller shaft down the center for easy and rapid mixing of the compost. The HDPE drum is 1.0 m tall with a 0.5 m diameter. It is completely insulated on the outside of the barrel, except for the cover, which is a 2.5 cm thick HDPE sheet. I need to do a heat transfer calculation so that I can claim that the average temperature of the compost in the Skip-o-Poster is at least 70°C. That is the approximate temperature needed for composting biodegradable plastics such as PLA. a) Sketch and clearly label the problem. Clearly state all given information and assumptions. b) What is the average compost temperature at steady state when the Skip-o-Poster is filled with compost? Can I make my claim of an average temperature of 70°C? Hint: The average temperature in the compost can be taken as the average of the temperature at the top and bottom of the compost (and NOT the container walls) (Top+Thou)/2. c) If the compost bed were FULL (instead of % full), would the average temperature go up, down, or not change. Explain with reference to the calculations made in the problem (use equations). A simple statement of up, down, no change will get no points. Show all work and units, and clearly state All ASSUMPTIONS. Useful Information (start here!): - heat transfer related to the mixing shaft may be neglected - calculations should be made for winter conditions Tout = 5°C and ho = 5.0 W/m²-K - compost decomposition gives a constant net heat generation=85 W/m³ of compost. - when the compost bed is not full, assume the air layer above it is stagnant and moist. - thermal conductivities (k): Compost-1.0 W/m-K; Air (moist)-0.38 W/m-K; HDPE=0.5 W/m-K