Scaling transient natural convection from a non-uniformly heated cylinder

We explored the laminar boundary-layer dynamics of natural convection from a horizontal cylinder with a linearly varying wall temperature using scaling analysis and direct numerical simulations. The parameter space covers Rayleigh numbers 10 Superscript 6 Baseline less than or equals upper R a less than or equals 10 Superscript 8 10 6 ≤ R a ≤ 10 8 $10^{6}\leq Ra\leq 10^{8}$ , Prandtl numbers 2 less than or equals upper P r less than or equals 100 2 ≤ P r ≤ 100 $2\leq Pr\leq 100$ and wall-temperature-gradient parameters 0 less than or equals s less than or equals 2 0 ≤ s ≤ 2 $0\leq s\leq 2$ . The imposed temperature gradient couples with the geometric buoyancy projection, producing distinct initial and steady-state regimes. Initially, the thermal response is controlled by radial diffusion, giving delta Subscript upper T Baseline tilde upper F o Superscript 1 divided by 2 δ T ∼ F o 1 / 2 $\delta _T\sim Fo^{1/2}$ and italic Nu tilde upper F o Superscript negative 1 divided by 2 Nu ∼ F o − 1 / 2 $ \textit{Nu}\sim Fo^{-1/2}$ , where upper N u N u $Nu$ is the Nusselt number and italic Fo