  The effect of rotation on the boundary layers (BLs) in a Rayleigh-Benard (RB)
system at a relatively low Rayleigh number, i.e. $Ra = 4\times10^7$, is studied
for different Pr by direct numerical simulations and the results are compared
with laminar BL theory. In this regime we find a smooth onset of the heat
transfer enhancement as function of increasing rotation rate. We study this
regime in detail and introduce a model based on the Grossmann-Lohse theory to
describe the heat transfer enhancement as function of the rotation rate for
this relatively low Ra number regime and weak background rotation $Ro\gtrsim
1$. The smooth onset of heat transfer enhancement observed here is in contrast
to the sharp onset observed at larger $Ra \gtrsim 10^8$ by Stevens {\it{et
al.}} [Phys. Rev. Lett. {\bf{103}}, 024503, 2009], although only a small shift
in the Ra-Ro-Pr phase space is involved.
