p2.5-2 - 2.5-2 Figure P2.5-2 illustrates a composite...

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2.5-2 Figure P2.5-2 illustrates a composite material that is being machined on a lathe. H =3cm W =12cm 20 C chuck T depends on 20 C hR S T composite th ins =100 μ m k ins =1.5W/m-K th m =200 μ m k m =35W/m-K l q ′′ ± x y Figure P2.5-2: Composite material being machined on a lathe. The composite is composed of alternating layers of insulating material and metal. The insulating layers have thickness th ins = 100 μ m and conductivity k ins = 1.5 W/m-K. The metal layers have thickness th m = 200 μ m and conductivity k m = 35 W/m-K. The workpiece is actually cylindrical and rotating. However, because the radius is large relative to it thickness and there are no circumferential variations we can model the workpiece as a 2-D problem in Cartesian coordinates, x and y , as shown in Figure 2.5-2. The width of the workpiece is W = 12 cm and the thickness is H = 3 cm. The left surface of the workpiece at x = 0 is attached to the chuck and therefore maintained at T chuck = 20°C. The inner surface at y = 0 is insulated. The outer surface (at y = H
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p2.5-2 - 2.5-2 Figure P2.5-2 illustrates a composite...

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