The vertical plate in laminar free convection: effects of leading and trailing edges and discontinuous temperature

Abstract

For laminar free-convection flow past a heated vertical plate of finite length, the local asymptotic flow structure is studied in regions where the boundary-layer equations do not provide a correct approximation at large Grashof numbers. The leading-edge region is shown to contribute a secondorder term to the integrated heat transfer. An integral form of the energy equation permits calculation of this correction in terms of the second-order boundary-layer solution away from the edge, without knowledge of the flow details near the edge, which can be obtained only by solution of the full Navier-Stokes equations. Near the trailing edge and near a jump in the prescribed plate temperature the longitudinal pressure gradient is found to be important in a thin sublayer adjacent to the plate, and the transverse pressure gradient is important in the remainder of the boundary layer, each for a distance along the plate which is slightly larger in order of magnitude than the boundary-layer thickness. At the trailing edge the sublayer problem is nonlinear and cannot be solved analytically, but it can be shown that the local correction to the total heat transfer is of slightly larger order of magnitude than the leading-edge correction. It is pointed out that the trailing-edge flow is identical in form to the flow near the edge of a rotating disc in a stationary fluid. The temperature-jump problem is linear and a solution is given which shows how the singularity in streamline slope predicted by the boundary-layer solution is removed.