Find the temperature distribution in a rod (Fig. P31.11) with internal heat generation using the finite-element method. Derive the element nodal equations using Fourier heat conduction
and heat conservation relationships
where
Develop the nodal equations that must be solved for the temperatures and temperature gradients at each of the six nodes. Assemble the equations, insert the boundary conditions, and solve the resulting set for the unknowns.
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Numerical Methods for Engineers
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