ANALYSIS OF CONVECTIVE HEAT TRANSFER IN A HORIZONTAL CYLINDER WITH COMPUTER-EXTENDED PERTURBATION SERIES
The method of extended perturbation series and its improvement are applied to the problem of convective heat transfer in a horizontal porous cylinder with internal heat sources. The objective is to obtain an expansion of the Nusselt number Nu in a power series of the Rayleigh number Ra. Such an expansion was usually terminated at the second order term and, consequently, only has a very limited utility. In this study, we extend the series, with the aid of a computer, up to the fiftieth order. This results in a 26-term power series of Ra2 for the Nusselt number. The domain and the rate of convergence of this series are further increased by various techniques of asymptotic analysis to obtain a new series valid for all Rayleigh numbers. In particular, for Ra > 5000, we obtain the compact relation Nu = (Ra/4)1/3.