Scales of natural convection on a convectively heated vertical wall

Natural convection on a convectively heated vertical wall, one of the fundamental issues of heat and mass transfer in many engineering applications, is investigated in this work. The configuration is governed by the Rayleigh number (RaL or Ra), the Prandtl number (Pr), and the non-dimensional convective heat transfer coefficient (CiL or Ci). A scaling analysis for the dynamics of the boundary layer flow and heat transfer is carried out. The scales of the velocity/thickness of the boundary layer flow and the temperature/thickness of the thermal boundary layer related to the non-dimensional governing parameters are obtained. The scales are validated using the numerical results by large eddy simulation. The results show that the non-dimensional velocity of the boundary layer flow is proportional to CiL2/5RaL2/5; the thickness from the wall to the layer of the maximal velocity is inversely proportional CiL1/5RaL1/5; the non-dimensional thickness of the thermal boundary layer is inversely proportional CiL1/5RaL1/5; the non-dimensional temperature in the thermal boundary layer is proportional to CiL4/5RaL−1/5. The reduction factor describing the thermal resistance of the thermal boundary layer is further discussed, which is proportional to Ci4/5Ra−1/5.