HIGH-ACCURACY SERIES SOLUTION FOR TWO-DIMENSIONAL CONVECTION IN A HORIZONTAL CONCENTRIC CYLINDER

High order series solutions of two-dimensional buoyancy-induced flow in the horizontal annulus between concentric cylinders are computed. A new efficient algorithm based on computation sequences and a detailed analysis of the shape of the solution is used to compute the solutions up to 30th order. The quotient-difference (QD) algorithm is applied to locate the singularities of the series solution, which gives accurate estimation of the radius of convergence. The condition number and the stability of the solution are also studied. All these resources obtained from the series solution make it a good reference to justify the results from more commonly used purely numerical methods, particularly for delicate solutions.