Analytical and Numerical Solutions for Natural Convection in a Corner
Laminar natural convection flow in a corner delimited by a vertical heated semi-infinite plate and a second room-temperature plate forming an arbitrary angle is studied both analytically and numerically. Analytically, repeated use of the matched asymptotic expansions technique shows that the boundary layer along the vertical plate is described, to first order, by Polhausen's classical similarity solution; this buoyancy-induced flow drives an outer irrotational flow which, in turn, provides the motive force for a self-similar viscous boundary layer along the second plate. In the numerical approach, a variable-spaci ng, finite difference method with dynamic mesh modification permits a solution of the Navier-Stokes equations to be obtained in the whole field, confirming the validity of the approximate analytical model.