We consider the laminar convective heat transfer near a corner formed by two quarter-infinite flat plates. The corner layer equations and their appropriate boundary conditions are formulated based on the method of matched asymptotic expansions. Suitable transformations are used for the corner layer variables, to impose the asymptotic boundary conditions at true infinity and increase the resolution near the corner where large gradients are expected. The flow and temperature profiles have been determined from the numerical solutions by the finite difference method.
Firstly, we analyze the forced convection in streamwise corner of an arbitrary angle on the basis of the boundary-layer approximations. Two different constant wall temperature conditions are considered: 1) Both wall are heated and 2) one wall heated and the other cooled. Numerical results for temperature distribution and rate of heat transfer are presented for corners with vertex angles ranging from 45˚ to 315˚ and the several Pandtl numbers.
Secondly, the laminar natural convection near a rectangular corner formed by the intersection of two vertical quarter-infinite flat plates is considered. For large Grashof number, the "boundary-layer" equations in the corner layer are derived and appropriate boundary conditions are determined using the method of matched asymptotic expansions. Solutions of the corner layer equations are numerically obtained for velocity and temperature distributions for Prandtl numbers 0.72 and 7.0. The cross-flow pattern is quite different from the high-Reynolds number flow along the corner; the simple inflow toward the corner appears, and the swirling motion in the corner is not found.
Thirdly, the laminar natural convective heat transfer near a corner of an arbitrary angle is presented. The analysis is general to any corner angle except the limiting angles 0˚ and 360˚. The velocity and temperature distributions for corner angles of 90˚, 135˚, 225˚, and 270˚ with the Prandtl numbers 0.72 and 7.0 are obtained numerically by the alternating direction implicit scheme. The cross-flow patterns are shown to exhibit a simple antisymmetric behavior for angles equidistant from 180˚.
