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The chemical process taking place within the concrete can cause extreme f[[R[[R[7.yd[[yR[[$R[$y[7[R[RRy.[R$[[y[$[R[yv$.[$[y.[[yR[[R7[.[yR[[yR[[R[y[R.7[[.6&'2 X&6temperature rises which often leads to internal cracking and therefore weakening of the .[[[7[.[7[N7$R[RMv[$R[M[..[[M$[[[RM.[M$[.[7[[$MR7[RR$[[M[[[M.[[7[.[7[Mv[[R[[$[[M[.M.[[M2 &6dam [[.6&'2 _&6structure. One way of preventing these high temperatures is to embed an array of pipe networks R.7[R.[7[.6[[6v[R6[.6[7[R[[.$[[6.[[R[6[$[[6.[[[7[.[7[R6$R6.[6[[[[6[[6[77[R6[.5[$[[5[[.v[7RR.6&'2 ~ `&6into the concrete blocks. Then cold water is pumped through the pipes and at a later time these $[.[9.[[9R[[R7[.[9[$[RRR.9d[[[9R[$[9v[.[79$R9[[[[[9.[7[[[[9.[[9[$[[R9[[[9[.9[8$[.[78.$[8.[[R[.6&'52 c!&6are filled in with concrete.[7[..$$$[[.$[.v$.[.R[[R7[.[. 2 c! &6 0X6&';2 I" &6The aim of this study is to estid[[;[$;[.;.[$R;R.[[R;$R;.[:[R.$m2 I"VA&6mate the temperature within the concrete slab and to analyse the [.[:.[[:.[[[7[.[7[:v$.[$[:.[[:R[[R7[.[:R$[[:[[[:.[:[[[$RR[:.[[.6&'2 .#\&6effect of pumping water through it. Ultimately, the engineer is concerned with reducing the [..[R.[[.[[[[$[[[v[.[7[.[7[[[[[$..Zv$.$[.[$R.Z.[[Z[[[$[[[7Z$RZR[[R[7[[[Zv$.[Z7[[[R$[[Z.[[.6&'2 $^&6maximum temperature in the concrete to an acceptable level whilst using a minimal (i.e. least [R$[G.[[[7[.[7[G$[G.[[GR[[R7[.[G.[F[[F[RR[[.[[$[F$[R[$Fv[$$R.F[R$[[F[F$[$[$F7$.[.F$[[R..6&'2 $&6expen[R[[[2 $H`&6sive) pipe network. It is clear that the efficiency of heat removal from the slab will decrease R$R[74[$[[4[[.v[7R.4..4$R3R$[[73.[[.3.[[3[..$R$[[RR3[.3[[[.37[[R[$3.7[3.[[3R$[[3v$$$3[[R7[[R[.6&'2 %W&6as the water temperature increases. Of course, a good pumping system should be able to [RX.[[Xv[.[7X.[[[7[.[7[X$[R7[[R[R.X.XR[[7R[.X[X[[[[X[[[$[[XRRR.[WR[[[$[W[[W[[$[W.[.6&'y2 &I&6perform close to this design limit but these are likely to be expensive a[[7.[71R$[R[1.[1.[$R1[[R$[[1$$$.1[[.1.[[R[1[7[1$$R[$R1.[0[[0[R[[[R$R[0[42 &&6nd so there needs to be an .[[0R[0.[[7[0[[[[R0.[0[[0[[.6&'2 'd&6appropriate balance between thermal efficiency and cost. It is hoped that this study will provide a [[[7[[7$[.[4[[$[[R[4[[.v[[[4.[[7[$4[..$R$[[RR4[[[4R[R..4..4$R4[[[[[4.[[.4.[$R3R.[[R3v$$$3[7[R$[[3[.6&'2 (b&6measure for the efficiency of practical water network designs and to estimate the optimal spacing [[R[7[3.[73.[[3[..$R$[[RR3[.3[7[R.$R[$3v[.[73[[.v[7R3[[R$[[R3[[[3.[2[R.$[.[2.[[2[[.$[$2R[[R$[[.6&'12 u)&6of pipes and pipe length.:[..[$[[R.[[[.[$[[.$[[[.[. 2 u) &6 0X6&'- 2 W*&6 02 +&6Schett22 +~&6me of the work to be done:tD|LD\tD|\D\|DxtD|tD 2 +n&6 0-2 -\&61) Begin by setting up a simple cylindrical model where a single pipe cools in an insulated [7Tm[[$[T[RTR[..$[[T[[T[TR$[$[TRR$$[[7$R[$T[[[$Tv[[7[T[SR$[[$[S[$[[SR[[$RS$[S[[S$[R[$[.[[.6&'2 .a&6concrete cylinder. This will determine a system describing the temperatures in both the concrete R[[R7[.[9RR$$[[[7.8d[$R8v$$$8[[.[7$[[8[8RRR.[8[[RR7$[$[[8.[[8.[[[7[.[7[R8$[8[[.[8.[[8R[[R7[.[.6&'2 . &6and pipe.:[[[.[$[[. 2 .,&6 0X6&' 2 /&6 0X6&'-66&&66&&66&&66&&66&&66&&66&&66&&66&& 6 6& &  6 6& &  6 6& &  6 6& &  6 6& & 66&&66&&66&&66&&66&&66&&66&&66&&66&&66&&66&&66&&66&&66&&66&&66&&66&&66&& 6 6& & !!6!6&!&!!""6"6&"&""##6#6&#&##$$6$6&$&$$%%6%6&%&%%