Stability and accuracy of power‐series method for one‐dimensional heat conduction with non‐uniform grid systems

The power‐series method, a finite analytic approach to heat transfer and fluid flow problems that is based on power‐series expansion, was applied to a one‐dimensional heat‐conduction problem to evaluate its stability and accuracy. Application to a specific heat‐conduction problem with non‐uniform grid systems showed that it had stability within the ranges 10^?5<Δt,Δx_E, and Δx_W,a<10⁵, and 10^?5<β<10⁵. Comparison of its solutions with those by the fully implicit and Stefanovic–Stephan methods showed that this method yielded more accurate and robust solutions. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(7): 470–480, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20085