A model of confined thermal convection driven by non-uniform heating from below

摘要: A model is presented of the two-dimensional boundary-layer and interior flow in a rectangular box resulting from application quadratic temperature variation on its lower surface. The other walls are insulating. It shown that similarity form exists for narrow, thermocline-like layer near surface, this can satisfy all known consistency conditions with interior, together either laminar or turbulent side-wall regions. Nusselt number to be insensitive Prandtl number, primarily functions horizontal Rayleigh Ra L . Specifically, temperature, relative coldest applied value, 60% total range. predicted vary as $0.26 Ra^{\frac{1}{5}}_L$ unit aspect ratio. dynamics region, details imposed appear unimportant determining overall buoyancy exchange. solutions compared numerical observational results, generally good agreement found.