Formation and evolution of laminar thermal structures: correlation to the thermal boundary layer and effects of heating time

We report an experimental study of the formation and evolution of laminar thermal structures generated by a small heat source, with a focus on their correlation to the thermal boundary layer and effects of heating time theat. The experiments are performed over the flux Rayleigh number (Raf ) range 2.1 × 10⁶ ≤ Raf ≤ 3.6 × 10⁷ and the Prandtl number (Pr) range 28.6 ≤ Pr ≤ 904.7. The corresponding Rayleigh number (Ra = theat Raf/τ0 Pr) range is 900 ≤ Ra ≤ 4 × 10⁴, where τ0 is a diffusion time scale. For thermal structures generated by continuous heating (i.e. starting plumes), their formation process exists three characteristic times that are well reflected by changes in the thermal boundary layer thickness. These characteristic times, denoted as temit, trecover and tstatic, correspond to the moments when the plume emission begins and completes, and when the thermal boundary layer becomes quasi-static, respectively. Their Raf –Pr dependencies are found to be temit/τ0 ∼ Ra⁻f^0.41 Pr^0.41, trecover/τ0 ∼ Ra⁻f^0.48 Pr^0.48 and tstatic/τ0 ∼ Ra⁻f^0.49 Pr^0.33, respectively. Thermal structures generated by finite theat exhibit similar evolution dynamics once theat ≥ temit, with the accelerating stage behaving like starting plumes and the decay stage like thermals (i.e. a finite amount of buoyant fluids). It is further found that their maximum rising velocity experiences a transition in the Ra-dependence from Ra to (Ra ln Ra)^0.5 at Ra ≃ 6000; and their maximum acceleration reaches the value of starting plumes at theat ≃ trecover, and remains unchanged for larger theat. In particular, the maximum rising velocity for the cases with theat = trecover follows a scaling relation Ra⁰f³⁷ Pr^−0.37, in contrast to the relation Ra⁰f⁴⁸ Pr^−0.48 for starting plumes. This study provides a more comprehensive understanding of laminar thermal structures, which are relevant to a range of processes in nature and laboratory systems such as Rayleigh–Bénard convection.