Question

In one of the manufacturing processes of silicon wafers, thin silicon sheets are pulled out of molten silicon. The speed of this process is slow, and the thin sheets solidify as they are being pulled out, because they cool through convection to the ambient. The melting temperature of the silicon is 1685 K. Assume a temperature of T∞= 700 K in the ambient surrounding the sheets with a convective heat transfer coefficient of h= 10 W/m²·K. Assume that the width and the thickness of the sheets are8.5 cm and 0.150 mm, respectively. What is the maximum velocity with which the sheet can be pulled out of the molten silicon? Assume all the energy released by solidification is dissipated by convection from the two sides of the sheet. Take the latent heat of fusion for silicon as hsf= 1.8 × 10⁶ J/kg.

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