Temperature-Time Profiles

5.12) This function will be used in the program when the time equals or greater than 12.6669 hours and

CHAPTER 6 DISCUSSION OF RESULTS 6.1 Introduction

6.2 Comparison of Experimental and Numerical Results

6.2.1 Temperature-Time Profiles

The results for the predicted temperature profiles and the measured temperature profiles are presented at all six positions are presented below with the discussions.

Numerical and Experimental Study of Transient Heat Transfer Through Concrete

6-1

Chapter 6 -Discussion of Results

.:. Distance x=Omm(boundary condition)

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Figure 6.1: Comparison of measured and predicted temperature profiles at distance x=Omm.

The predicted curve at this distance compares very well with the measured temperature curve as was expected of a position where the boundary condition have been imposed. This clearly indicates that the approximation of the analytical expression for the boundary condition curve and the numerical analysis were successful.

An important aspect to note is that peak temperature at this boundary condition position is reached when temperature is approximately equal to 36.274°C at time of 43hours. Both temperature curves show a steep gradient at early ages and this is associated with the heat of hydration effects. The time and the value of the peak temperature will later be compared with the temperature peaks at other positions.

After the peak, both curves show a gradual decrease in temperature values and this occurs as a

result of two things, the decrease in the rate of heat of hydration curve and the fact that since this

position is at the exposed surface, some of the concrete heat is lost to the environment.

Chapter 6 • Discussion of Results

.:. Distance x=100mm

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Figure 6.2: Comparison of measured and predicted temperature profiles at distance x=100mm.

The two curves compare well except that the predicted temperature curve is lower than the measured temperature curve between 1 0 and 60 hours. The difference in values between the two curves increases in value from time=10 h our s and reaches its maximum at approximately 15 hours. As the time increases, the differ ence gradually decreases until it reaches 0 at time = 60 hours. The maximum error of the predicted curve values is 9.9331%. This error may be associated with various reasons mainly coming fr om the input parameters.

The one parameter that may be the cause of the error is the initial temperature. It must be recalled that, during the laboratory testing, the measurement for temperature was taken almost 2 hours after concrete mixing. This indicates that the initial temperature value should have been taken immediately after the concrete was m ixed .

The value used in this analysis was obtained by taking the average of the first temperature reading at all positions, this may not have been the correct value. The correct value could have been higher than the value used as a result of the heat of hydration generated immediately when water combines with cement, immediately after mixing.

Numerical and Experimental Study of Transient Heat Transfer Through Concrete

6-3

Chapter 6 -Discussion of Results

The other input parameter may have been the fact that the assumed value of thermal conductivity does not take account of other effects such as time and type of the cement and moisture content of the concrete. It was based on the aggregate type alone. The thermal conductivity could have been the main source of error as it also influences the thermal diffusivity of concrete.

Another observation to make is that the peak temperature of the measured temperature curve occurs at 38 hours, which is earlier than that of the predicted temperature occurring at 66.667 hours. The peak temperature has a value of 37.34°e that is higher than the value of 36.58 °e, for the predicted temperature curve .

. :. Distance x=250mm

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Figure 6.3: Comparison of measured and predicted temperature profiles at distance x=250mm.

Similar to the previous case, the two curves compare well except that the predicted temperature curve is lower than the measured temperature curve between 5 and 90 hours. The difference increases from time equals 5 hours and reaches its maximum at approximately 15 hours before it gradually decreases to ooe at the time of 60 hours. The maximum error computed is 21.5105%.

This error may be associated with various reasons mainly coming form the input parameters as

described in the previous case.

Chapter 6 -Discussion of Results

The maximum error experienced at this position is greater than the error experienced before at Omm. Also the length of the time at which the difference between the predicted and the measured temperature curves has increased from10-60 hours at position 100mm to 5-90 hours at position 250mm. This is associated with the thermal conductivity error.

The explanation to these observations is that the effects of thermal conductivity exhibit a vital role as we move away from the boundary conditions positions, hence the increase in error as well as the length of time at which the difference is experienced.

The peak temperature of the measured temperature curve occurs at 42 hours, which is earlier than that of the predicted temperature occurring at 78.667hours. The peak temperature of the measured temperature curve has a value of 37 . 34°C that is higher than the value of 36.58 °C for the predicted temperature curve .

. :. Distance x=500mm.

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Figure 6.4: Comparison of measured and predicted temperature profiles at distance x=500mm.

Similarly to the previous cases, the two curves compare well except for the fact that predicted temperature curve is lower than the measured temperature curve between 5 and 132. 6667 hours.

The difference increases from at time of 5 hours and reaches its maximum at approximately 19 hours before it gradually decreases to almost nothing at the time of 132.6667 hours. The maximum error computed is 27.7377% .

Numerical and Experimental Study of Transient Heat Transfer Through Concrete

6-5

Chapter 6 -Discussion of Results

A maximum error experienced at this position is greater than the error experienced in the latter cases. Also the length of the time at which the difference between the predicted and the measured temperature curves observed is between 5 and 132.667 hours at this position. The explanation to these observations is similar to the previous case.

The peak temperature of the measured temperature curve occurs at 50.6667 hours, which is earlier than that of the predicted temperature occurring at 84.667hours. The peak temperature of the measured temperature curve has a value of 45.9081DC that is higher than the value of 41 .2431 DC for the predicted temperature curve .

. :. Distance x=750mm

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Figure 6.5: Comparison of measured and predicted temperature profiles at distance x=750mm

The two curves compare well except that the predicted temperature curve is lower than the

measured temperature curve between 0 and 154.6667 hours. The difference increases from a time

of 0 hours and reaches its maximum at approximately 154.6667 hours before it gradually

decreases to almost nothing at the time of 154.6667 hours. The maximum error computed is

19.8466%. It is observed that the maximum error is less than the error observed at distances 250

and 500mm. This confirms the expectations that the maximum error should be experienced at

distance 500mm, which is the position that is furthest from the boundary conditions.

Chapter 6 - Discussion of Results

The peak temperature of the measured temperature curve occurs at 54.6667 hours, which is earlier than that of the predicted temperature occurring at 76.667hours. The peak temperature of the measured has a value of 48.149°C that is higher than the value of 44.3114°C for the predicted temperature curve .

. :. Distance x=1000mm(boundary condition)