Longitudinal vortices in a laminar natural convection boundary layer flow on an inclined flat plate and their influence on heat transfer

The linear and nonlinear growth of longitudinal vortices in a laminar boundary layer and the development of secondary instabilities are investigated theoretically and by experiment. As a prototype problem the natural convection flow along a constant-heat-flux inclined flat plate in water is chosen. Based upon the smallness of the plate's angle of inclination from the vertical, the largeness of the Grashof number, and the smallness of the vortex strength, a perturbation method is used to derive and solve a consistent set of governing equations for the linear, weakly nonlinear and the strongly nonlinear regimes which is asymptotically correct to first order. Liquid-crystal thermography based on wide-band liquid crystals is used to provide full-field, highly accurate wall temperature measurements and visualizations. The spanwise periodic thickening and thinning of the boundary layer through a nonlinear, but steady, vortex growth is seen to be responsible for practically all of the increase of mean heat transfer values during the laminar–turbulent transition. Secondary instabilties in the form of sinuous and varicose unsteady wave modes and the steady merging of vortices are visualized but are seen to have only a minor additional influence on mean heat transfer.