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) < Delta t, Delta x(E), and Delta x(W), a < 10(5), and 10(-5) < beta < 10(5). Comparison of its solutions with those by the fully implicit and Stefanovic-Stephan methods showed that this method yielded more accurate and robust solutions. (C) 2005 Wiley Periodicals, Inc.