Heat transfer is important in many applications. For instance, due to the decrease in size of electronics, it
becomes more necessary to have efficient and smaller cooling systems. In order to increase the effect of the
cooling liquids used, it might be interesting to add extra solid particles with a high conductivity, to possibly
increase the effective heat transfer fromthe wall to the liquid. These particles can be separated in 2 categories:
point particles, with a very small size compared to the flow phenomena, and finite sized particles, which due
to their larger size are able to significantly influence the fluid flow. In this thesis, the finite sized particles
and their effect on the effective conductivity have been analyzed by using a CFD code. The main focus has
been on the effect of the mechanical and thermal Stokes numbers, which give an indication about the time
required for the particles to react to changes in surrounding flow and temperature compared to the relevant
flow time scale.
To investigate the effect of large particles on the effective conductivity of a fluid a numerical method to
solve heat transfer inside a fluid and between fluid and particles has been implemented. This method, based
on an immersed boundary method combined with DNS, is able to solve both isolated particles and extremely
high conductivity particles. To solve the heat transfer for finite conductivities, a volume of fluid method has
also been implemented. These methods have been verified by comparing the simulation results to known
results for single sphere heat transfer and conservation of energy.
With this code, the influence of the thermal and mechanical Stokes numbers have been analyzed for
laminar Couette flow. In order to gain a better understanding of the underlying heat transfer mechanics, it
has been assumed that the natural convection is negligible and the density ratio between the particle and the
fluid is taken to be equal to one (no effects of gravity). From this it appeared that the effective conductivity
of a suspension can be split in 3 components: the non-moving conductivity, an enhancement due to fluid
convection induced by the particles and an increase in heat transfer due to particle convective heat transfer.
The non-moving conductivity is only dependent on the conductivity of the particles and the fluid, and
on the particle concentration. It stays close to constant independent of Stokes numbers. In contrast, the
fluid convection appeared to scale significantly with the mechanical Stokes number and with the particle
concentration. This appeared to be due to the increase in particle inertia resulting in more movement in
wall normal direction and as a result moving more fluid in wall normal direction. The particle convection
appeared to not only scale with the thermal Stokes number and the particle concentration, but also with the
mechanical Stokes number. This increase was caused by the particles being able to absorb and release more
thermal energy for higher thermal Stokes numbers, and thus transport more heat from the hot wall to the
cold wall.
Finally, the resulting effective conductivity and effective viscosity of the suspension were compared and
it was shown that it is possible to enhance the heat transfer more than the viscosity, but only by either introducing
a small amount of highly conductive particles, or by introducing well-conducting particles with very
low mechanical Stokes numbers. It appeared to not be possible to increase the heat conductivity more than
the viscosity for particles with equal or lower conductivity compared to the fluid.