Natural convection boundary-layer adjacent to an inclined flat plate subject to sudden and ramp heating

The natural convection thermal boundary-layer adjacent to an inclined flat plate subject to sudden heating and a temperature boundary condition which follows a ramp function up until a specified time and then remains constant is investigated. The development of the flow from start-up to a steady state has been described based on scaling analyses and verified by numerical simulations. Different flow regimes based on the Rayleigh number are discussed with numerical results for both boundary conditions. For ramp heating, the boundary-layer flow depends on the comparison of the time at which the ramp heating is completed and the time at which the boundary layer completes its growth. If the ramp time is long compared with the steady-state time, the layer reaches a quasi-steady mode in which the growth of the layer is governed solely by the thermal balance between convection and conduction. On the other hand, if the ramp is completed before the layer becomes steady; the subsequent growth is governed by the balance between buoyancy and inertia, as for the case of instantaneous heating.