A nuclear reactor fuel rod is a circular cylinder 6 cm in diameter. The rod is to be tested by cooling it with a flow of sodium at 205°C and a velocity of 5 cm/s perpendicular to its axis. If the rod surface is not to exceed 300°C, estimate the maximum allowable power dissipation in the rod.
GIVEN
• Cylinder in a cross flow of liquid sodium
• Cylinder diameter (D) = 6 cm = 0.06 m
• Sodium temperature (T?) = 205°C
• Sodium velocity (U?) = 5 cm/s = 0.05 m/s
• Maximum rod surface temperature (Ts) = 300°C FIND
• The maximum allowable power dissipation Gq
ASSUMPTIONS
• Steady state
• Turbulence in the sodium flow approaching the rod is low
• Heat generation per unit volume in the rod is uniform
SKETCH
The Reynolds number is
Therefore, may be applied
The rate of heat transfer at the maximum surface temperature is
The maximum rate of heat generation per unit volume of the rod is
COMMENTS
If the rate of heat generation exceeds the value calculated, the surface temperature will rise to dissipate
the energy. Also, non-uniform heat generation can lead to hot spots as will variations in the local value
of the heat transfer coefficient around the circumference
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