Problem 4.13: A steel rod of diameter D = 2 cm, length L = 5 cm, and thermal conductivity is exposed to ambient air at with a heat transfer coefficient If the left end of the rod is maintained at temperature determine the temperatures at distances 25 mm and 50 mm from the left end, and the heat at the left end. The governing equation of the problem is
where is the temperature, and The boundary conditions are
Use (a) two linear elements and (b) one quadratic element to solve the problem by the finite element method. Compare the finite element nodal temperatures against the exact values.