A cylindrical stainless steel (k = 25 W/m K) ingot, 10 cm in diameter and 25 cm long, passes through a heat treatment furnace which is 5 meter in length. The initial ingot temperature is 90 degree Celsius, the furnace gas is at 1260 degree Celsius and the combined radiant and convective surface coefficient is 100 W/m² K. Determine the maximum speed with which the ingot moves through the furnace if it must attain 830 degree Celsius temperature. Take thermal diffusivity as 0.45 * 10¯⁵ m²/s