Natural Convection in a Right-Angle Corner: Higher-Order Analysis
Ingham, D.B. Pop, I.
Natural Convection in a Right-Angle Corner: Higher-Order Analysis - 2167-2177 p.
Higher-order boundary-layer effects for natural convection flow in a right-angle corner formed by a semi-infinite vertical plate, which is prescribed with a uniform heat flux, and a semi-infinite horizontal plate, which is thermally insulated, is presented. Using the method of asymptotic matched expansions the solution is obtained up to the fourth-order expansion. For the first time the interplay between the two boundary-layer flows, which takes place through the outer inviscid region, has been investigated. Eigen-values and their corresponding eigenfunctions which are associated with the inner expansions have been sought and it has been found that their contribution up to fourth-order correction is identically zero. Numerical results have been obtained for Prandtl numbers of 0.72 (air), 1 and 6.7 (water) and the flow in the outer region and the velocity and temperature profiles in the boundary layers are presented. Also the variation of the local Nusselt number and skin friction coefficients on the plates are presented as functions of the local Grashof numbers. It is found that the presence of the horizontal plate has quite a substantial effect on the higher-order approximations in the vertical boundary layer and the outer region.
0017-9310
Natural Convection
Right-Angle Corner
Higher-Order Analysis
Semi-Infinite Vertical Plate
Natural Convection in a Right-Angle Corner: Higher-Order Analysis - 2167-2177 p.
Higher-order boundary-layer effects for natural convection flow in a right-angle corner formed by a semi-infinite vertical plate, which is prescribed with a uniform heat flux, and a semi-infinite horizontal plate, which is thermally insulated, is presented. Using the method of asymptotic matched expansions the solution is obtained up to the fourth-order expansion. For the first time the interplay between the two boundary-layer flows, which takes place through the outer inviscid region, has been investigated. Eigen-values and their corresponding eigenfunctions which are associated with the inner expansions have been sought and it has been found that their contribution up to fourth-order correction is identically zero. Numerical results have been obtained for Prandtl numbers of 0.72 (air), 1 and 6.7 (water) and the flow in the outer region and the velocity and temperature profiles in the boundary layers are presented. Also the variation of the local Nusselt number and skin friction coefficients on the plates are presented as functions of the local Grashof numbers. It is found that the presence of the horizontal plate has quite a substantial effect on the higher-order approximations in the vertical boundary layer and the outer region.
0017-9310
Natural Convection
Right-Angle Corner
Higher-Order Analysis
Semi-Infinite Vertical Plate