One method that is used to grow nanowires (nanotubes with solid cores) is to initially deposit a small droplet of liquid catalyst onto a flat surface. The surface and catalyst are heated and simultaneously exposed to a higher-temperature, low-pressure gas that contains a mixture of chemical species from which the nanowire is to be formed. The catalytic liquid slowly absorbs the species from the gas through its top surface and converts these to a solid material that is deposited onto the underlying liquid-solid interface, resulting in the construction of the nanowire. The liquid catalyst remains suspended at the tip of the nanowire. Consider the growth of a 15-nm-diameter silicon carbide nanowire onto a silicon carbide surface. The surface is maintained at a temperature of Ts = 2400 K, and the particular liquid catalyst that is used must be maintained in the range 2400 K < Tc < 3000 K to perform its function. Determine the maximum length of nanowire that may be grown for conditions characterized
by h = 10(5)W/m(2) *K and Too=8000k. Assume properties of the nanowire are the same as for bulk silicon carbide.