Using Symbolic Calculation for Solving Natural Convection in a Narrow Horizontal Cylindrical Annulus

We consider the two-dimensional problem of steady natural convection in a narrow Horizontal Cylindrical annulus filled with viscous fluid due to a sine temperature variation on the outer and adiabatic conditions at the inner boundaries. The solution is expanded in powers of a single combined similarity parameter introduced by [1], which is the product of the Gap ratio to the power of four, and Rayleigh number and the series extended by means of symbolic calculation up to 16 terms. Analysis of these expansions allows the exact computation for arbitrarily accuracy up to 50000 figures. Although the range of the radius of convergence is almost zero but Pade approximation lead our result to be good even for much higher value of the similarity parameter.