We consider fully developed steady laminar flow through a uniformly heated horizontal pipe is simplified by assuming infinite Prandtl number. The solution is expanded in powers of a single combined similarity parameter which is the product of the Prandtl, Rayleigh, and Reynolds numbers 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 exactness is almost the same order of the radius of convergence but Pade approximation lead our result to be good even for much higher value of the similarity parameter.

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