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 liquid-solid interface, resulting in 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 a cover plate evacuated space absorber plate water tw insulation l t q"rad nanowire that may be grown for conditions characterized by h 105 w/m2 k and t 8000 k. assume properties of the nanowire are the same as for bulk silicon carbide.