A warm water flow (density of 1000 [Kg/m3], viscosity of 5∙10-4 [Pa s], thermal conductivity 0.6 [W/m°C] and specific heat 4186 [J/Kg°C]) with a given velocity enters into a sort of heat exchanger where some hot circles are present.

We would like to compute the outlet fluid temperature imaging that the
flow is sufficiently low to allow a pure Galerkin approach.

We decided to consider only the upper part of this heat exchanger in view of the symmetry with respect to the x-axis. The mesh contains 10673 nodes, leading to 22587 velocities and pressures nodal unknowns and 10302 nodal temperatures unknowns.
The symmetry conditions are simply given by imposing homogeneous vertical velocity and thermal flux on the boundaries lying on the symmetry axis. The horizontal inlet velocity follows a parabolic law which goes to zero on the boundary and assume a maximum value of 1∙10-3 [m/s] on the symmetry axis. The inlet temperature is 20 [°C] and the temperature of the circle surfaces has been set to 50 [°C]. The outlet pressure has been set to zero in order to get a unique solution. The velocity and pressure fields can be computed first and then the energy equation can be tackled in a second phase to compute the temperature in each point.

Geometry and Meshing

The symmetry axis is highlighted in blue and some dimensioning (in [cm]) is reported.

Velocity magnitude

Temperature field

It can be seen that the inlet temperature is 20 [°C], the circles temperature is 50 [°C], while the outlet temperature vary from a minimum of 32.60 [°C] up to a maximum of 44.58 [°C].

Sources:

http://wiki.scilab.org/Tutorials?action=AttachFile&do=get&target=ns_Margonari_enginsoft-fix.pdf