The cooling of concrete slabs using water pipe networks

Problem raised by Cement
and Concrete Institute, Midrand, Gauteng, South Africa

Coordinator:

Dr. Sarah Mitchell

(MACSI, Department of Mathematics and Statistics, University of Limerick,
Ireland)

Assistant:

Nadia Smith (Facultad
de Matemáticas, UCM)

**Exposition of the problem:**

The proposed problem concerns a simplified model to describe the removal
of hydration heat from concrete dams during construction using piped water.

As part of the construction of dams, large concrete slabs are poured
(usually of the order of 10x10x3m). The chemical process taking place within
the concrete can cause extreme temperature rises which often leads to internal
cracking and therefore weakening of the dam structure. One way of preventing
these high temperatures is to embed an array of pipe networks into the concrete
blocks. Then cold water is pumped through the pipes and at a later time these
are filled in with concrete.

The aim of this study is to estimate the temperature within the concrete
slab and to analyse the effect of pumping water through it. Ultimately, the
engineer is concerned with reducing the maximum temperature in the concrete to
an acceptable level whilst using a minimal (i.e. least expensive) pipe network.
It is clear that the efficiency of heat removal from the slab will decrease as
the water temperature increases. Of course, a good pumping system should be
able to perform close to this design limit but these are likely to be expensive
and so there needs to be an appropriate balance between thermal efficiency and
cost. It is hoped that this study will provide a measure for the efficiency of
practical water network designs and to estimate the optimal spacing of pipes
and pipe length.

** **

**Scheme of the work to be done:**

1) Begin by setting up a simple cylindrical model where a single pipe
cools in an insulated concrete cylinder. This will determine a system
describing the temperatures in both the concrete and pipe.

2)
Perform a dimensional analysis and use this information to obtain a simplified
model. Use appropriate mathematical techniques to solve the resulting equations
to analyse the thermal variation in the concrete/water
system.

3) Examine the effect of including the neglected higher order terms (by
performing a perturbation analysis and solving the resulting system
numerically).

4) Extension to a more realistic model which has an array of pipes in
order to allow for the fact that the geometry is in practice not cylindrical: a
periodic array of pipes would be far more realistic. Another extension would be
to analyse the fact that the pipes tend to loop back and forth throughout the
slabs meaning that the flow in adjacent pipes is usually in opposite
directions.