Using the Galerkin Weighted Residual method, obtain the finite element formulation for an axisymmetric thermal problem...

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Using the Galerkin Weighted Residual method, obtain the finite element formulation for an axisymmetric thermal problem for which the temperature field depends only on the radius r and is described by the equation d²T 1 dT Q(r) + + dr² r dr K = 0, for a ≤r≤b where K denotes the (constant) thermal conductivity, Q the distributed heat source and a the radius of the circular domain on which the problem is solved. The boundary conditions involve imposed temperatures at both ends (r=a and r=b). Hint: When integrating over the domain (a ≤ r≤ b), don't forget that the "elemental surface element" is 2 Ar dr. Obtain the expression of the local stiffness matrix and local load vector for the generic 2-node "radial thermal" element of length h shown below. 1 r=ri 2 r=ri+h Using the Galerkin Weighted Residual method, obtain the finite element formulation for an axisymmetric thermal problem for which the temperature field depends only on the radius r and is described by the equation d²T 1 dT Q(r) + + dr² r dr K = 0, for a ≤r≤b where K denotes the (constant) thermal conductivity, Q the distributed heat source and a the radius of the circular domain on which the problem is solved. The boundary conditions involve imposed temperatures at both ends (r=a and r=b). Hint: When integrating over the domain (a ≤ r≤ b), don't forget that the "elemental surface element" is 2 Ar dr. Obtain the expression of the local stiffness matrix and local load vector for the generic 2-node "radial thermal" element of length h shown below. 1 r=ri 2 r=ri+h

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