Natural convection near 4 °C in a horizontal water layer heated from below

A numerical study of two-dimensional natural convection in a horizontal water layer heated from below is reported. The density maximum associated with water at 3.98 °C and atmospheric pressure occurs inside the layer, as the top surface is maintained at 0 °C while the bottom surface temperature varies in the range 4 °C–10 °C. Three separate series of numerical simulations document the effect of Rayleigh number, bottom wall temperature and layer horizontal length on the flow pattern and on the net heat transfer rate vertically through the layer. These effects are documented numerically and graphically in the domain104<Ra<3×105, 1/6<H/L<1, where Ra is the Rayleigh number for a fluid with density maximum, and H/L is the (height/length) ratio of the water system selected for analysis. It is found that steady-state convection is present at Rayleigh numbers as low as 2.3×104 when TH =8 °C and H/L=0.5, and as low as 105 when TH =6.3 °C and H/L=0.5. These Rayleigh numbers agree very well with the corresponding critical values recommended by linear stability analysis.