Before being injected into a furnace, pulverized coal

Chapter 5, Problem 5.32

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Before being injected into a furnace, pulverized coal ispreheated by passing it through a cylindrical tubewhose surface is maintained at Tsur = 1000C. The coal pellets are suspended in an airflow 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 maybe assumed that they are heated by radiation transfer from the tube surface, how long must the tube be to heat coal entering at 25C to a temperature of 600C? Is the use of the lumped capacitance method justified?

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