Plate glass is made by the float process. A molten glass slab rides on a pool of liquid metal. The other side of the glass is exposed to the air. To produce a striated, textured plate glass, the molten glass is sheared between two plates as shown in Figure P4.8. Derive an expression for the temperature and velocity profiles within the glass. Determine the force necessary to shear the glass as a function of the temperature difference between the upper and lower plates. Assume the plates are infinitely long and that the thermal conductivity of the glass is constant.

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FIGURE P4.8 y=0 y = L k T=T melt u = u,exp[aT] V =0 T=T low