Solutions to transient conduction problems with convection boundary conditions involve infinite series that usually converge rapidly. Evaluation of these series requires the computation of eigenvalues from equations that can only be solved by trial and error. Because this process is rather tedious, several approximate methods have been developed. These methods are less tedious to apply than the exact solution, but they must be used with care. This article makes a comparison of the exact solution to transient heat conduction in a sphere to three approximate methods: satisfies the eigenvalue equation capacity method, the Heisler chart method, and the Heat Balance Integral method. Mathcad software was used with each of these methods.
