Using stokes expansion for natural convection inside a two-dimensional cavity

Abstract

We consider the two-dimensional problem of steady natural convection in a circular cavity filled with viscous fluid and subjected to a cosine temperature variation on the boundary. The solution is expanded for low Grashof number and extended to 35 terms by computer. Analysis shows that convergence is limited by a square root singularity on the negative real axis of the Grashof number. An Euler transformation and extraction of the leading, secondary and tertiary singularities at infinity render the series accurate for all values of the Grashof number. The major conclusion of this investigation is that, while in previous works using the method of series extension-for example the slowly rotating pipe studied by Mansour (1985, J. Fluid Mech., 150, 1–24)- the limiting values of the quantities of interest for high values of the similarity parameters disagreed with other techniques, in the present work partial agreement with other investigations has been achieved.