Before being injected into a furnace, pulverized coal is preheated by passing it through a cylindrical tube whose surface is maintained at Tsur = 1000 C. The coal pellets are suspended in an air flow and are known to move with a speed of 3 m/s. If the pellets may be approximated as spheres of 1-mm diameter and it may be assumed that they are heated by radiation transfer from the tube surface, how long must the tube be to heat coal entering at 25 C to a temperature of 600 C? Is the use of the lumped capacitance method justified?