Integral modelling of an unsteady natural convection boundary layer

Abstract

The study concerns an unsteady natural convection boundary layer (NCBL) over a geometrically unbounded vertical isothermal wall with Prandtl number of Pr = 0.71. A threedimensional direct numerical simulation (DNS) is carried out to investigate the NCBL. In the present study we identify the plume-like region of the NCBL by a wall-normal distance δ i at which point the molecular diffusion matches the magnitude of the turbulent heat flux. Based on the DNS data, we have found that the plume-like region of the turbulent NCBL can be well described by the integral model supplied by proper boundary conditions at δ i . The profile coefficients obtained from the integral model appears independent of the growth of the boundary layer thickness, indicating the outer part plume-like region is self-similar.