Chapter 13, Problem 13.138P

A novel infrared recycler has been proposed for reclaiming the millions of kilograms of waste plastics produced by the dismantling and shredding of auto motive vehicles following their retirement. To address the problem of sorting mixed plastics into components such as polypropylene and polycarbonate, a washed stream of the mixed plastics is routed to an infrared heating system, where it is dried and subsequently heated to a temperature for which one of the components begins to soften, while the others remain rigid. The mixed stream is then routed through steel rollers, to which the softened plastic sticks and is removed from the stream. Heating of the stream is then continued to facilitate removal of a second component, and the heating/removal process is repeated until all of the components are separated.

Consider the initial drying stage for a system comprised of a cylindrical heater aligned coaxially with a rotating drum of diameter $D_d=1\text{m}$ . Shortly after entering the drum, wet plastic pellets may be assumed to fully cover the bottom semicylindrical section and to remain at a temperature of $T_p=325\text{K}$ during the drying process. The surface area of the pellets may be assumed to correspond to that of the semicylinder and to have an emissivity of ${\epsilon }_p=0.95$ .
(a) If the flow of dry air through the drum maintains a convection mass transfer coefficient of
0.024 m/s on the surface of the pellets, what is the evaporation rate per unit length of the drum?
(b) Neglecting convection heal transfer, determine the temperature T_hthat must be maintained by a heater of diameter $D_h=0.10\text{m}$ and emissivity ${\epsilon }_h=0.8$ to sustain the foregoing evaporation rate. What is the corresponding value of the temperature T_dfor the top surface of the drum? The outer surface of the drum is well insulated, and its length-to-diameter ratio is large. As applied to the top (d) or bottom (p) surface of the drum, the view factor of an infinitely long semicylinder to itself, in the presence of a concentric, coaxial cylinder, may be expressed as
$F_{ii}=1-\frac{2}{\pi }\left\{\left[1-{\left(D_h/D_d\right)}^2\right]1/2+\left(D_h/D_d\right){\sin }^{-1}\left(D_h/D_d\right)\right\}$