Transient thermo-solutal convection of water near 4 °C with opposing gradients in a square cavity

A numerical study of two-dimensional thermo-solutal convection of water in a square cavity heated from below and salted from above for various value of Lewis number is conducted. The maximum density associated with water around 4 °C occurs inside the cavity, as the top wall is maintained at 0 °C while the bottom wall temperature varies in the range 8–12 °C. The maximum density region acts as an obstacle to prohibit convectional heat, mass, and momentum transfer. These effects are investigated numerically in the domain −5 × 10² < Ra_T < 2 × 10⁴, 1 × 10⁵ < Ra_S < 8 × 10⁶ and L = 0.015 m length of square cavity where Ra is the Rayleigh number of the fluid. The effect of Lewis number on the heat, mass, and momentum transfer is also systematically studied. For certain range of parameters, it is interesting to find that the flow pattern may change inversely from rolling (fluid particles raise along both vertical side walls and fall along the vertical center line) to plume motion (fluid particles raise along the vertical center line and fall along both side walls) as the bottom wall temperature and top wall concentration increase. Further increase in the value of Rayleigh number results in oscillating two cell flow structure in the cavity. It is found that there is a temporal maximum absolute value of average Nusselt and Sherwood number followed by a temporal minimum absolute value of average Nusselt and Sherwood number in a small time interval (0 < t < 300 s) and the steady state is reached after a certain time interval at the bottom wall. These time intervals are reduced with increasing Lewis number. Also, critical Grashof number which accounts for oscillatory heat and mass transfer with Lewis number is studied and it reveals that an increase in Lewis number results in slowing down oscillation and oscillation cycle becomes shorter with increasing species Grashof number.