Scaling in laminar natural convection in laterally heated cavities: Is turbulence essential in the classical scaling of heat transfer?

We analyze heat transfer and flow properties in laminar natural convection driven by a horizontal temperature gradient in a closed cavity and propose that for the classical scaling of heat transfer turbulence does not play a decisive role. Direct numerical simulations were performed with the Rayleigh number (Ra) from 1 to 10⁸ and the Prandtl number Pr=0.71. In the laminar steady flow regime with the Ra approximately from 10³ to 10⁷, power-law scalings of heat transfer and maximum velocity with Ra have exponents of 0.31 and 0.54, respectively. The scalings agree well with results obtained in turbulent Rayleigh-Bernard convection, turbulent convection in laterally heated cavities and laminar convection in inclined enclosures, etc., which, with some simple physical arguments and reviews of the literature, leads us to propose that turbulence is not essential for the classical near 1∕3 power-law scaling of Nu.