Free convection past a uniform flux surface inclined at a small angle to the horizontal

Abstract

Free convection boundary layer over a semi-infinite flat plate with a uniform surface heat flux which is inclined at a small angle to the horizontal is discussed. When the plate is inclined at a positive angle, series solutions, one valid near the leading edge and the other at large distances from it, are obtained. Very accurate numerical results are determined by using an implicit finite-difference scheme known as keller box method in the region where neither series is adequate. For negatively inclined plate, a series solution valid near the leading edge is again obtained and the same numerical method is employed to solve the full boundary layer equations to extend the solution downstream, past the point at which the boundary layer separates from the plate. Eigenvalues and their corresponding eigenfunctions which are associated with large distances from the leading edge have been sought and it has been found that their contribution up to third-order correction is identically zero. Numerical results have been determined for a wide range of values of the Prandtl number Pr but the results are only presented for Pr=0.72 (air).