Consider the compost bed shown in the right-hand figure. The dimensions of the bed are 1 m by 2 m. A 10-cm (0.10-m) thick layer of organic compost lines the bottom as shown. Slow bacterial decomposition of the organic material in the compost generates heat at a constant rate of 600 W per m³of compost. An inert granular mineral layer 2-cm thick is placed over the compost layer. The sides and bottom of the compost bed are perfectly insulated. Air flows over the bed to provide a convective heat-transfer coefficient of 5 W/m²· K. The ambient air temperature is constant at 15°C. Thermophysical properties are provided below. There are no other direct energy inputs to the compost bed.

a. What is the steady-state heat-transfer rate from the compost bed to the surrounding air?
b. What is the temperature at top of the organic compost layer€”i.e., T_c?
c. What is the temperature, T_L, at the base of the compost bed?
d. If the thickness of the compost layer is increased, then which will occur?
1. T_c and T_s will both increase
2. T_c will increase but T_s will stay the same
3. T_c and Ts will not change

Cross section of compost bed.

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Thermophysical properties Material Thermal Heat Bulk Conductivity Capacity J/kg-K Density kg/m³ W/m-K Organic compost Inert granular mineral layer 1500 0.1 300 0.4 1700 1600 Too = 15°C 00 Ts air boundary layer, h =5.0 W/m2-K To inert granular mineral layer (2.0 cm) compost layer (10.0 cm thick) 600 W / m3 TL well-insulated boundary (base & sides)