Fully developed laminar buoyant flow in vertical cavities and ducts of bounded section

The fully developed flow in a vertical cavity or duct subject to horizontal heating is considered. Solutions of the Boussinesq equations are obtained for rectangular and elliptic sections, in terms of Fourier series and polynomials, respectively. Both generalize the familiar odd-symmetric cubic prole of the plane cavity. Uniqueness is demonstrated under the restriction that the flow is independent of height. For cavities with rectangular sections, it is predicted and veried that the flow in the plane of spanwise symmetry is practically independent of the span if this exceeds 1.7 times the breadth. 1