At time = 285hours

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Figure 6 .9: Comparison of measured and predicted temperature profiles at time=285 hours.

The observations at this time are similar to those indicated at the previous time.

Numerical and Experimental Study of Transient Heat Trans~r Through Concrete

6 -9

Chapter 6 -Discussion of Results

6.3 General Comments

The comparison between the measured and the predicted temperature profiles for both the temperature versus time and temperature versus distance curves have been discussed. At distances where the boundary conditions have been imposed the predicted and measured temperature curves agree very well.

Similar agreements are observed at the other positions at greater times. The great concern is the error that is experienced at distances positions 100, 250, 500 and 750 mm for smaller times. Further analysis have been carried out to determine whether cause of the errors is not linked to the Green element method or the choice of the heat of hydration curve, which is the Heat rate versus Nurse-Saul equivalence hours.

Three analysis were carried out. The first involved selection of the Heat rate versus normal time curve as an input describing the heat of hydration. The results obtained showed that the error increased by 1 .2% for times less than approximately 60 hours, at times greater than 60 hours the results were unchanged. The Heat rate versus Arrhenius equivalence hours was selected for the second analysis and the results showed a negligible increase in error as compared to the results from the Heat rate versus Nurse-Saul equivalence hours input. These comparisons are given in figure 6.10 below for position, x= 750mm.

The third analysis involved using the green element method approach of improving the results obtained from the Heat rate versus Nurse-Saul equivalence hours input. This approach is known as degridding. The degridding approach was achieved by increasing the number of nodes at d istances where the errors are experienced .

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- Measured

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Figure 6.10: Comparison of measured and predicted temperature profiles at x=750mm using

various heat rate curves.

Chapter 6 -Discussion of Results

The results showed a decrease in error of 2% only for times less than approximately 184.667 hours.

Similarly, for times greater than 184.667 hours the results were unchanged. The curves for other position are found in appendix B.

The results confirm that the error may be associated mainly with the thermal conductivity and the value of the initial temperature as discussed earlier.

Numerical and Experimental Study of Transient Heat Transfer Through Concrete

6-11

Chapter 7 - Conclusion

CHAPTER 7 - CONCLUSION

The study on heat transfer and numerical prediction of temperature development in hardening concrete gives a indication that it is possible to predict with reasonable accuracy the temperature development in hardening concrete in the field. The work presented in this thesis can be of great use for estimation of temperature gradients caused by the hydration heat in developing concrete , which consequently results into crack formation. The avoidance of such cracks is developed mainly for concrete structures such as, large concrete dams, massive hydraulic structures, concrete walls subjected to fires and concrete nuclear power station.

High accuracy performance is required for temperature predictions in hardening concrete and can only be achieved by both non-complicated and reliable test for determining hydration heat and numerical technique. It is more significant when the numerical model and hydration curve determination methods are used as a basis for numerical analysis of thermal cracking and for fire safety assessments in nuclear reactors and tall buildings. The adiabatic calorimeter used in this research demonstrates the ability to measure heat of hydration of a concrete with respect to time. In addition, it was manufactured from equipment that is of a low cost and easy to assemble. G . Y . Gibbon and Y Ballim

⁸

describe improvements made to the adiabatic calorimeter to enable the determination heat of hydration and thermal conductivity with respect to time.

The Green element method has the ability to solve most engineering problems that are more practically based and complex in nature without being combined with another numerical method. These engineering problems exhibit properties such as, non-linearity, transient nature and heterogeneity. Transformation of a Green element method solution procedure into computer based Fortran program, doubles the advantages that the method usually posses when the solution is obtained by hand.

Combination of the adiabatic calorimeter and the computerized Green element method has been used in

this thesis to predict the measured temperature profiles with acceptable practical accuracy. According to

Wang and Dingler9, 20 - 30% of error is considered excellent accuracy in practical problems. The main

source or error is from the input data variable.

Chapter 7 - Conclusion

It can thus be concluded that high levels of accuracy that is required for prediction of temperature distribution can be achieved by using a combination of the adiabatic calorimeter and the computerized Green element method incorporating carefully selected input data. Apart from fire safety assessments and nuclear power station temperature predictions and crack prevention, the results may also be used to help in construction planning. This refers to the design of curing measures that are required to prevent concrete from freezing in cold weather, or to achieve the desired strength at an early age and to maintain the specified temperature differential limits in a structure.

Numerical and Experimental Study of Transient Heat Transfer Through Concrete

7-2

Chapter 8 - Recommendations

CHAPTER 8 - RECOMMENDATIONS

The main source of error encountered in prediction of measured temperature distribution is undoubtedly the input data variables. Some of these variables have been mentioned in chapter 6. Many key parameters, such as the thermal conductivities of concrete and formworklinsulation materials, specific heat capacity, convection heat transfer coefficient, ambient air temperature, initial temperature etc, vary in wide ranges.

Most researchers have brought the attention that thermal conductivity of concrete depends on numerous variables such as moisture content, aggregate type and content, porosity, density, temperature and time.

To date, limited work has been done in developing an expression that relates the thermal conductivity with all these parameters.

It must be appreciated that the thermal conductivity is one of the main input variables that are incorporated during the element by element analysis performed by most numerical technique, if not all. So an incorrect thermal conductivity can result in large errors in the output. To ensure that a reasonable thermal conductivity is used, the researcher is required to research on the thermal conductivity that take into consideration, the variables that have a greater effect on it, namely, the moisture content, type and content of aggregate and temperature.

Also it is very important to note that special attention should be paid in the selection of the initial temperature. Heat is generated immediately when water reacts with cement, the temperature of the mix will also vary, hence it will be incorrect to wait until the beam or any sample is cast before the initial temperature is recorded. The initial temperature should be measured as soon as the mixing of the concrete constituents has been completed.

Limited research has shown that the specific heat capacity is dependent on degree of hydration. It then becomes essential to incorporate such effect when selecting of the specific heat capacity is done.

It is recommended that for future temperature prediction using the Green Element Method and Adiabatic

Calorimeter or any other appropriate methods, the effects on the input variables mention above should be

taken into consideration.

Chapter 8 - Recommendations

It is recommended that future research should consider case of a two and three-dimensional heat flow problem incorporating the effects of time on thermal conductivity of concrete using the Green Element Method and Adiabatic Calorimeter. The three-dimensional heat research describes a more realistic situation and will bear a great impact in the field of heat transfer.

Numerical and Experimental Study of Transient Heat Transfer Through Concrete

8-2

Chapter 9 - References