Heat is generated uniformly in the fuel rod of a nuclear reactor. The rod has a long, hollow cylindrical shape with its inner and outer surfaces at temperatures of Ti and To, respectively. Derive an expression for the temperature distribution.
GIVEN
• A long, hollow cylinder with uniform internal generation
• Inner surface temperature = Ti
• Outer surface temperature = To FIND
• The temperature distribution
ASSUMPTIONS
• Conduction occurs only in the radial direction
• Steady state prevails
SKETCH
The one dimensional, steady state conduction equation in cylindrical coordinates is given
With boundary conditions
Integrating the conduction equation once
Integrating again
Applying the first boundary condition
Applying the second boundary condition
Substituting the constants into the temperature distribution
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