The cooling of concrete slabs using water pipe networks
Problem raised by Cement and Concrete Institute, Midrand, Gauteng, South Africa
Dr. Sarah Mitchell
(MACSI, Department of Mathematics and Statistics, University of Limerick, Ireland)
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:
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.