Aim\ The finite element method is applied to analyze transient heat conduction problem of the barrel. Method\ According to axisymmetric unsteady heat conduction equation of orthogonal aniso tropic material and boundary conditions

the equilibrium equation of a system of finite elements is deduced with triangular element of high accuracy

and programs are designed. Results Examples are presented to demonstrate the validity of the theory and method

and the transient heat conduction problem of the barrel is calculated. Conclusion\ The theory and the method will be universally available to axisymmetric unsteady heat conduction problems.