Consider a nuclear fuel element (k = 57 W/m · K) that can be modeled as a plane wall with thickness of 4 cm. The fuel element generates 3 × 10⁷ W/m³ of heat uniformly. Both side surfaces of the fuel element are cooled by liquid with temperature of 80°C and convection heat transfer coefficient of 8000 W/m² · K. Using a uniform nodal spacing of 8 mm,

(a) Obtain the finite difference equations,

(b) Determine the nodal temperatures by solving those equations,

(c) Compare the surface temperatures of both sides of the fuel element with analytical solution.

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h, To Nuclear fuel element ė 4 cm h, T