Effective boundary conditions for buoyancy-driven flows and heat transfer in fully open-ended two-dimensional enclosures

The present work achieves an accurate representation of the effective boundary conditions at the aperture plane of a two-dimensional open-ended structure for wide range of pertinent parameters. The presented effective boundary conditions are correlated in terms of Rayleigh number, Prandtl number, and the aspect ratio of the open-ended geometry. The numerical procedure used in this work is based on the Galerkin weighted residual method of finite-element formulation. Comprehensive comparisons between the present investigation using the effective boundary conditions for the anticipated closed-ended model and the results for the fully extended computational domain confirm successful implementation of the proposed model. Implementation of this representation reduces the main difficulties associated with specifying the open-ended boundary conditions and results in very substantial savings in CPU and memory usage. The present work plays an important role on modeling a basic and generic set of effective boundary conditions at the aperture plane for several applications of practical interest.