Heat flux enhancement by regular surface protrusions in turbulent thermal convection*

We performed two-dimensional numerical simulations in a square Rayleigh-B\'{e}nard (RB) convection enclosure with equally spaced protrusions in the top and bottom conduction plates for the range of Rayleigh number $10^6$ to $10^8$ and at a fixed Prandtl number of $1$. The protrusions are in the form of a parallelepiped base and triangular top with vertex angle $90^o$. We have varied the protrusion height from $10\%$ to $25\%$ of enclosure height and found an increase in heat flux approximately up to $1.38$ times of classical square RB. The enhancement in heat transport up to a certain protrusion height and the heat transport decreases with a further increase in protrusion height. As protrusion height increases, the large-scale circulation can not thoroughly wash out the cavity between two consecutive protrusions.