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

• Published in: Journal of fluid mechanics Vol. 401; pp. 365 - 377
• Main Author: McBAIN, G. D.
• Format: Journal Article
• Language: English
• Published: Cambridge Cambridge University Press 25.12.1999
• Subjects: Convection and heat transfer; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Laminar flows; Laminar flows in cavities; Physics; Turbulent flows, convection, and heat transfer; Elliptical section; Boussinesq equations; Laminar flow; Rectangular cross section; Natural convection; Modelling; Velocity distribution; Cavity flow; Heat transfer
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/S0022112099006783

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 profile 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 verified that the flow in the plane of spanwise symmetry is practically independent of the span if this exceeds 1.7 times the breadth.