One method that is used to grow nanowires (nanotubes with solid cores) is to initially deposit a small droplet of a 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 liquidsolid interface, resulting in construction of the nanowire. The liquid catalyst remains suspended at the tip of the nanowire. Consider the growth of a 14-nm-diameter silicon carbide nanowire onto a silicon carbide surface. The surface is maintained at a temperature of Ts=2400K, and the particular liquid catalyst that is used must be maintained in the range 2400KTc 3000K to perform its function. Determine the maximum length, in nm, of a nanowire that may be grown for conditions characterized by h=105W/m2K and T=8000K. Assume properties of the nanowire are the same as for bulk silicon carbide. Lmax=nm