  In a recent paper (El Omari and Le Guer, IJHMT, 53, 2010) we have
investigated mixing and heat transfer enhancement in a mixer composed of two
circular rods maintained vertically in a cylindrical tank. The rods and tank
can rotate around their revolution axes while their surfaces were maintained at
a constant temperature. In the present study we investigate the differences in
the thermal mixing process arising from the utilization of a constant heat flux
as a boundary condition. The study concerns a highly viscous fluid with a high
Prandtl number $Pr = 10,000$ for which this chaotic mixer is suitable. Chaotic
flows are obtained by imposing temporal modulations of the rotational
velocities of the walls. By solving numerically the flow and energy equations,
we studied the effects of different stirring protocols and flow configurations
on the efficiency of mixing and heat transfer. For this purpose, we used
different statistical indicators as tools to characterize the evolution of the
fluid temperature and its homogenization. Fundamental differences have been
reported between these two modes of heating or cooling: while the mixing with
an imposed temperature results in a homogeneous temperature field, with a fixed
heat flux we observe a constant difference between the maximal and minimal
temperatures that establish in the fluid; the extent of this difference is
governed by the efficiency of the mixing protocol.
