  Observations suggest that the large-scale convective velocities obtained by
solar convection simulations might be over-estimated (convective conundrum).
One plausible solution to this could be the small-scale dynamo which cannot be
fully resolved by global simulations. The small-scale Lorentz force suppresses
the convective motions and also the turbulent mixing of entropy between upflows
and downflows, leading to a large effective Prandtl number ($\Pr$). We explore
this idea in three-dimensional global rotating convection simulations at
different thermal conductivity ($\kappa$), i.e., at different $\Pr$. In
agreement with previous non-rotating simulations, the convective velocity is
reduced with the increase of $\Pr$ as long as the thermal conductive flux is
negligible. A subadiabatic layer is formed near the base of the convection zone
due to continuous deposition of low entropy plumes in low-$\kappa$ simulations.
The most interesting result of our low-$\kappa$ simulations is that the
convective motions are accompanied by a change in the convection structure that
is increasingly influenced by small-scale plumes. These plumes tend to
transport angular momentum radially inward and thus establish an anti-solar
differential rotation, in striking contrast to the solar rotation profile. If
such low diffusive plumes, driven by the radiative-surface cooling, are present
in the Sun, then our results cast doubt on the idea that a high effective $\Pr$
may be a viable solution to the solar convective conundrum. Our study also
emphasizes that any resolution of the conundrum that relies on the downward
plumes must take into account angular momentum transport as well as heat
transport.
