Natural convection due to a heat source on a vertical plate

In this work, the flow over a discrete heat source flush mounted on a vertical adiabatic surface is studied. The two- and three-dimensional formulations were adopted in order to compare with the results presented in the literature. The flow was assumed incompressible and laminar with constant fluid properties under Boussinesq assumption. The finite volume control method was used for the discretization of the elliptic governing equations. The numerical results presented confirm in part the theoretical behavior and show the existence of a transition between the two- and three-dimensional plume. Additionally, similarity scales for the thermal boundary layer were proposed for the xy and zy planes. The presence of this region of transition emphasizes the complexity of this kind of flow, where two- or three-dimensional effects must not be studied separately, mainly on electronic packaging where heat sources are in that transition region.