Abstracts - KTH Mechanics

106
Turbulent thermal convection over grooved surfaces: effect of
the finite thermal conductivity of the plates.
G.Stringano ∗ , G.Pascazio ∗ and R.Verzicco ∗
The effects of the finite thermal conductivity of the plates in turbulent thermal
convection over grooved surfaces are investigated by direct numerical simulations of
the Navier-Stokes equations with the Boussinesq approximation. The simulations are
performed in a cylindrical cell of aspect ratio, diameter over cell height, Γ = 1/2 at
Prandtl number Pr =0.7. The cell is heated from below and cooled from above
with an adiabatic sidewall. The plate geometry presents five axisymmetric V shaped
grooves with the height of the tip over height of the cell, H/h =0.025 and vertex
angle equal to 90 o . The presence of grooves forces the formation of plumes over
the tips, with a dynamics very similar to the ’wedge effect’ in electrical problems 1
2 . This effect, combined with a finite thermal conductivity of the plates, leads to a
non isothermal fluid–plate interface and therefore to weaker wall normal temperature
gradients thus reducing the overall heat flux. A comparison with ideal plates with
infinite thermal conductivity, shows a decrease of the heat transfer, when the ratio
between plates and fluid thermal resistance is smaller than a threshold value. This
behaviour can be explained in terms of thermal energy balance: if the plates thermal
conductivity is too low, the supplied heat flux can not balance the heat taken away
by thermal plumes and the plate cools down below a developing plume. The different
balance between the heat needed by an ascending plume and that supplied by the
plate can alter the plume dynamics and consequently modify the heat transfer. Since
regardless of the particular shape every non flat surface will have cusps and throats
the main conclusion is that the tips of the rough elements represent a critical region
for heat transfer. A detailed analysis of the plume dynamics and their role in the heat
transfer will be presented at the conference.
∗DIMeG & CEMEC Politecnico di Bari, Via Redavid 200, 70125 Bari, Italy.
1G.Stringano, G.Pascazio and R.Verzicco, Turbulent thermal convection over grooved plates, J.
Fluid Mech. 2005 in press.
2Y.-B.Du and P.Tong, Turbulent thermal convection in a cell with ordered rough boundaries, J.
Fluid Mech. 2000, vol. 407, pp 57-84.
Figure 1: Temperature field at Ra =2· 10 10 and Pr =0.7 (closeup of the hot plate).