FINITE ANALYTIC METHOD BASED ON POWER SERIES EXPANSION FOR UNSTEADY HEAT CONDUCTION PROBLEMS

Abstract

A new finite analytic method based on power series expansion is proposed in this article. It has a simpler form compared with other methods based on analytical techniques. It is applied to an unsteady heat conduction problem, and its solution is compared with those of other methods. The comparison shows that the new method's solutions are more accurate than those obtained from the explicit, Crank-Nicolson, and fully implicit methods for a wide range of mesh Fourier number f . It gives the most accurate solutions of all finite-difference methods for f  > 6.0.