For the design of novel type of nuclear power plant, it is necessary to determine the temperature distribution in a large slab-type nuclear fuel element. Volumetric heat is generated uniformly in the fuel element at the rate of 2*107 W/m3 . This slab fuel is insulated on one side, while on other side it is covered by a stainless steel cladding of 0.3 cm thickness. Heat is removed from the fuel slab by a liquid at 2000C that flows on the other side of the steel cladding with the convective heat transfer coefficient of 10,000 W/(m2 K). Determine the maximum temperature in the fuel element and sketch the temperature distribution.
GIVEN
FIND
Maximum temperature in fuel element
Sketch temperature distribution.
ASSUMPTIONS
• 1 Dimensional steady state heat transfer
• Constant properties.
• Uniform heat generation.
• Negligible contact resistance between surfaces.
SKETCH
Heat transfer equation in 1 dimension with steady state and uniform heat generation is given by
Integrating twice we get
Applying boundary conditions
2. Using energy conservation equation
Substituting C1 and C2 in the integrated differential equation we get
Applying this condition in differential equation above we get
Substituting values to get Tmax we get
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