Data mining techniques for thermophysical properties of refrigerants

Energy Conversion and Management 50 (2009) 399–412

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Data mining techniques for thermophysical properties of refrigerants Ecir Ug˘ur Küçüksille, Resßat Selbasß, Arzu Sßencan * Department of Mechanical Education, Technical Education Faculty, Süleyman Demirel University, 32260 Isparta, Turkey

a r t i c l e

i n f o

Article history: Received 29 January 2008 Accepted 6 September 2008 Available online 23 October 2008 Keywords: Refrigerant Thermophysical properties Data mining Linear regression Multi layer perception Pace regression Simple linear regression Sequential minimal optimization KStar Additive regression M5 model tree Decision table M5’Rules

a b s t r a c t This study presents ten modeling techniques within data mining process for the prediction of thermophysical properties of refrigerants (R134a, R404a, R407c and R410a). These are linear regression (LR), multi layer perception (MLP), pace regression (PR), simple linear regression (SLR), sequential minimal optimization (SMO), KStar, additive regression (AR), M5 model tree, decision table (DT), M5’Rules models. Relations depending on temperature and pressure were carried out for the determination of thermophysical properties as the specific heat capacity, viscosity, heat conduction coefficient, density of the refrigerants. Obtained model results for every refrigerant were compared and the best model was investigated. Results indicate that use of derived formulations from these techniques will facilitate design and optimize of heat exchangers which is component of especially vapor compression refrigeration system. Ó 2008 Elsevier Ltd. All rights reserved.

1. Introduction Refrigerants are one of the most important parts of refrigeration and heat pump systems. For many years, CFCs and HCFCs have been used successfully as refrigerants, blowing agents, cleaning solvents, and aerosol propellants. CFCs seemed to be an ideal choice due to their unique combination of properties; however, the exceptional stability of these compounds, coupled with their chlorine content, has linked them to the depletion of the earth’s atmosphere protective ozone layer. By international agreement (Montreal Protocol), signed in 1987 and later amended several times, this group of refrigerants, consisting primarily of R11, R-12, R-113, R-114, R-115, R-500 and R-502 were scheduled to be phased out of production by 1 January 1996, in the developed countries and by the year 2000 in the developing countries [1,2]. The objective of this study is to obtain thermophysical properties depending on temperature and pressure values of different new refrigerants used in the vapor compression refrigeration system. The calculations were made for alternative refrigerants R134a, R404a, R407c and R410a, which do not damage to ozone

* Corresponding author. Tel.: +90 246 211 1399; fax: +90 246 2371283. E-mail addresses: [email protected] (E.U. Küçüksille), [email protected] (R. Selbasß). 0196-8904/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2008.09.002

layer. The thermophysical properties of refrigerants were taken from Solkane Software. All data mining analyses were performed using WEKA software and thermophysical property formulations of refrigerants were derived using linear regression (LR), multi layer perception (MLP), pace regression (PR), simple linear regression (SLR), sequential minimal optimization (SMO), KStar, additive regression (AR), M5 model tree, decision table (DT), M5’Rules techniques within data mining. WEKA software contains a suite of advanced knowledge discovery algorithms that extract knowledge from an investigated database and present this knowledge in symbolic rules that can be interpreted by a user. Development of a model requires the user to input a set of dependent and independent variables, either directly or by importing from an existing file (e.g., an excel spreadsheet). The user must simply specify a dependent variable, the independent variables, a time limit for running the algorithm, and a desired standard error. Use of the package seems quite appropriate for many users. Data mining is applied in a wide variety of fields for prediction, customer behavior, and production control. In addition, data mining has also been applied to other types of scientific data such as bioinformatical, astronomical, and medical data [3]. In the literature, available studies on analysis with data mining approach of energy systems are very limited. Sßencan has used data mining process to determine specific volume values of

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Nomenclature MAE P RMSE R2 t c

mean absolute error pressure (bar) root mean squared error correlation coefficient temperature (°C) specific heat capacity (kJ/kg K)

k

q

heat conduction coefficient (mW/mK) density (kg/l, kg/m3)

Subscripts l liquid phase v vapour phase

Greek symbols l dynamic viscosity (mPa s)

methanol/LiBr and methanol/LiCl used in absorption heat pump systems. Mathematical formulations were found to be in good agreement with the experimental data [4]. Tso and Yau have used regression analysis, decision tree and neural networks models in the data mining approach for the prediction of electricity energy consumption [5]. Kusiak et al. was applied data mining approach to analyze relationships among parameters of a circulating fluidized-bed boiler. The efficiency could be predicted to the same degree of accuracy with and without the data describing the fuel composition or boiler demand levels in study. Authors have determined that data mining approach is applicable to different types of burners and fuel types [6]. Figueiredo et al. have presented an electricity consumer characterization framework based on a knowledge discovery in databases procedure, supported by data mining techniques. This framework consists of two main modules: the load profiling module and the classification module. The load profiling module creates a set of consumer classes using a clustering operation and the representative load profiles for each class. The classification module uses this knowledge to build a classification model able to assign different consumers to the existing classes [7]. The electricity price forecast framework, which can predict the normal price as well as the price spikes based on data mining approach by Lu et al. has carried out. The proposed model is based on a mining database including market clearing price, trading hour, electricity demand, electricity supply and reserve. This proposed model is able to generate forecasted price spike, level of spike and associated forecast confidence level [8]. S ß encan et al. have used different methods such as linear regression (LR), pace regression (PR), sequential minimal optimization (SMO), M5 model tree, M5’Rules, decision table and back propagation neural network (BPNN) for modelling the absorption heat transformer [9].

2. Data mining methodologies Data mining comprises numerical and statistical techniques that can be applied in a wide variety of fields for prediction. A functional general definition of data mining is the use of numerical analysis, visualization or statistical techniques to identify non-trivial numerical relationships within a dataset to derive a better understanding of the data and to predict future results [10]. Data mining is a complex process. Typically it involves the following procedures [11]:  Developing an understanding of the application domain.  Creating a target data set. When the database is very large, it may be necessary to analyze a subset of variables or data.  Data pre-processing for noise removal, missing data handing and data dimension reduction.  Selection of data mining techniques and tools.  Interpretation and validation of discovered knowledge.

Predictive modeling tries to find good rules for predicting the values of one or more variables in a data set (outputs) from the values of other variables in the data set (inputs). In this study, ten predictive modeling techniques were applied to obtain thermophysical properties depending on temperature and pressure values of different new refrigerants. The algorithms developed in these modeling techniques arise from methodological research in various disciplines, including statistics, pattern recognition, and machine learning. 2.1. Linear regression (LR) Linear regression is a well-known method of mathematical modeling of the relationship between a dependent variable and one or more independent variables [12]. Regression uses existing (or known) values to forecast the required parameters. In the simplest case, regression employs standard statistical techniques such as linear regression. Unfortunately, many real-world problems are not simply linear projections of previous values. For instance, sales volumes, stock prices, product failure rates and models of engineering systems are all very difficult to predict because they may depend on complex interactions of multiple predictor variables. Therefore, more complex techniques (e.g., logistic regression, decision trees, or neural networks) may be necessary to forecast future values [13–19]. 2.2. Multi layer perception (MLP) Multi-layer perception (MLP). MLP are feed-forward neural networks trained with the standard backpropagation algorithm. They are supervised networks so they require a desired response to be trained. They learn how to transform input data into a desired response, so they are widely used for pattern classification. With one or two hidden layers, they can approximate virtually any input– output map. They have been shown to approximate the performance of optimal statistical classifiers in difficult problems. The most popular static network is the MLP [20]. 2.3. Pace regression (PR) The basic idea of regression analysis is to fit a linear model to a set of data. The classical ordinary least squares estimator is simple, computationally cheap, and has well-established theoretical justification. Nevertheless, the models produced are often not satisfactory. Page regression improves the classical ordinary least squares regression by evaluating the effect of each variable and using a clustering analysis to improve the statistical basis for estimating their contribution to the overall regressions. Under regularity conditions, pace regression is provably optimal when the number of coefficients tends to infinity. It consists of a group of estimators that are either overall optimal or optimal under certain conditions [21,22].

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2.4. Simple linear regression (SLR)

2.10. M5’Rules

The purpose of simple regression analysis is to evaluate the relative impact of a predictor variable on a particular outcome. This is different from a correlation analysis, where the purpose is to examine the strength and direction of the relationship between two random variables [23].

The method for generating rules from model trees, which is called M5’Rules, is straightforward and works as follows; a tree learner (in this case model trees) is applied to the full training dataset and a pruned tree is learned. Next, the best branch (according to some heuristic) is made into a rule and the tree is discarded. All instances covered by the rule are removed from the dataset. The process is applied recursively to the remaining instances and terminates when all instances are covered by one or more rules. This is a basic separate-and-conquer strategy for learning rules; however, instead of building a single rule, as it is usually done, we built a full model tree at each stage, and make its ‘‘best” branch into a rule. This avoids potential for over-pruning called hasty generalization. In contrast to PART (partial decision trees), which employs the same strategy for categorical prediction, M5’Rules builds full trees instead of partially explored trees. Building partial trees leads to a greater computational efficiency, and does not affect the size and accuracy of the resulting rules [13–28].

2.5. Sequential minimal optimization (SMO) Sequential minimal optimization (SMO) is a simple algorithm that can quickly solve the SVM (support vector machine) QP (quadratic programming) problem without any extra matrix storage and without using numerical QP optimization steps at all. SMO decomposes the overall QP problem into QP sub-problems, using Osuna’s theorem to ensure convergence [13–24]. 2.6. KStar KStar is an instance-based classifier, i.e. the class predicted for a test instance is based upon the class of those training instances similar to the test instance, as determined by some similarity function. It differs from other instance-based learners in that it uses an entropy-based distance function [25]. 2.7. Additive regression (AR) AR is a flexible non-parametric regression method. The AR model is a spline regression model that uses a specific class of basis functions as predictors in place of the original data. The AR basis function transform makes it possible to selectively blank out certain regions of a variable by making them zero, allowing AR to focus on specific sub-regions of the data. AR excels at finding optimal variable transformations and interactions, as well as the complex data structure that often hides in high-dimensional data [20]. 2.8. M5 model tree The method used by M5 model tree algorithm is to split the parameter space into areas (subspaces) and build in each of them a local specialized linear regression model. The splitting in M5 model tree follows the idea used in building a decision tree, but instead of the class labels it has linear regression functions at the branches, which can predict continuous numeric attributes. Model trees generalize the concepts of regression trees, which have constant values at their branches. So, they are analogous to piecewise linear functions (and hence are non-linear). Model trees learn more efficiently and can tackle tasks with very high dimensionality – up to hundreds of attributes. The major advantage of model trees over regression trees is that model trees are much smaller than regression trees, the decision strength is clear, and the regression functions do not normally involve many variables [13–26]. 2.9. Decision table (DT) Given a training set of labeled instances, an induction algorithm builds a classifier. Two variants of decision table classifiers were described. The first classifier, called DTMaj (decision table majority) returns the majority of the training set if the decision table cell matching the new instance is empty, i.e., it does not contain any training instances. The second classifier, called DTLoc (decision table local), is a new variant that searches for a decision table entry with fewer matching attributes (larger cells) if the matching cell is empty. This variant therefore returns an answer from the local neighborhood small changes in a relevant attribute do not result in changes to the label [27].

3. Application of data mining for thermophysical properties prediction of refrigerants In this study, different data mining techniques (LR, MLP, PR, SLR, SMO, KStar, AR, M5 model tree, DT, M5’Rules) were used for determining thermophysical properties as the specific heat capacity, viscosity, heat conduction coefficient, density relating to liquid and vapour phase of the refrigerants. Furthermore, comparison of these different modeling techniques was presented. The thermophysical properties of refrigerants used in data mining analysis were taken from Solkane Software. In Table 1, input–output parameter and refrigerants used in analysis is shown. For R134a, a comparison of the results obtained from the various methods is shown in Table 2. The comparison parameters are the correlation coefficient (R2-value), mean absolute error (MAE), root mean squared error (RMSE). These parameters can be written as follows [29–31]:

Pn

R2 ¼ 1  Pnm¼1 m¼1

MAE ¼

ðt m;m  yp;m Þ2 ðt m;m  tm;m Þ2

ð1Þ

n 1X jy  t m;m j n m¼1 p;m

ð2Þ

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn 2 m¼1 ðyp;m  t m;m Þ RMSE ¼ n

ð3Þ

where n is the number of data patterns, yp,m indicates the predicted, tm,m is the measured value of one data point m, and t m;m is the mean value of all measure data points. As can be seen in Table 2, the best results for specific heat capacity relating to liquid and vapour phase of R134a are obtained from SMO method. The equations obtained from SMO method for specific heat capacity relating to liquid and vapour phase are

cl ¼ 0:0005  t þ 0:0201  P þ 1:2791

ð4Þ

Table 1 Input and output parameters Refrigerants

Input parameters

Output parameters

R134a R404a R407c R410a

Temperature (t) Pressure (P)

Specific heat capacity (c) Dynamic viscosity (l) Heat conduction coefficient (k) Density (q)

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Table 2 Comparison of different techniques for thermophysical properties relating to liquid and vapour phase of R134a Thermophysical properties

Method

Phase Liquid phase

Vapour phase

Comparison parameters

Specific heat capacity (c)

Dynamic viscosity (l)

Heat conduction coefficient (k)

Density (q)

LR MLP PR SLR SMO KStar AR M5 model DT M5’Rules LR MLP PR SLR SMO KStar AR M5 model DT M5’Rules LR MLP PR SLR SMO KStar AR M5 model DT M5’Rules LR MLP PR SLR SMO KStar AR M5 model DT M5’Rules

cv ¼ 0:0014  t þ 0:0264  P þ 0:7999

tree

tree

tree

tree

MAE

RMSE

R2

MAE

RMSE

0.9995 0.999 0.9995 0.9986 0.9996 0.9996 0.9843 0.9978 0.9895 0.999 0.9171 0.9994 0.9994 0.9889 0.9987 0.9975 0.9833 0.9988 0.9904 0.9992 1 0.9998 1 1 1 0.9988 0.9637 1 0.9917 1 1 0.9997 1 0.9976 1 0.9991 0.9669 0.9998

0.0027 0.0047 0.0027 0.0043 0.0022 0.0023 0.0147 0.0055 0.0128 0.0052 0.0243 0.0028 0.0021 0.0088 0.0026 0.0031 0.011 0.0027 0.0086 0.0025 0.0023 0.267 0.0024 0.0023 0.0213 0.3366 2.3493 0.0023 1.1676 0.0023 0.0003 0.003 0.0003 0.0055 0.0004 0.0027 0.019 0.0015

0.0032 0.0052 0.0032 0.0052 0.0033 0.0034 0.0176 0.0065 0.0149 0.0067 0.0294 0.0039 0.0028 0.0111 0.0049 0.0065 0.014 0.0039 0.0107 0.0033 0.0029 0.335 0.0029 0.0029 0.0272 0.5996 2.7649 0.0029 1.3499 0.0029 0.0004 0.0035 0.0004 0.0063 0.0004 0.0044 0.0234 0.0019

0.9996 0.9989 0.9996 0.9971 0.9996 0.9995 0.9796 0.9983 0.9885 0.9993 0.9999 0.9993 0.9999 0.9914 0.9999 0.9993 0.9713 0.9992 0.9914 0.9996 1 0.9998 1 0.9993 1 0.9991 0.9697 0.9999 0.9919 0.9999 0.9999 0.9998 0.9999 0.9996 0.9999 0.9998 0.9903 0.9963 0.9926 0.9985

0.0039 0.0076 0.0039 0.009 0.0029 0.0037 0.0246 0.0071 0.0198 0.0052 0.0167 0.0552 0.0167 0.1383 0.0136 0.0349 0.2686 0.0412 0.1451 0.0288 0.0065 0.0475 0.0065 0.0655 0.0063 0.0642 0.4324 0.0197 0.2356 0.022 0.3175 0.3774 0.3175 0.6046 0.2757 0.4487 2.7016 1.5238 2.4507 0.952

0.0045 0.0083 0.0045 0.0111 0.0041 0.0054 0.0324 0.0086 0.0232 0.0071 0.0197 0.0626 0.0197 0.1668 0.0177 0.0548 0.3278 0.0509 0.1686 0.0387 0.0082 0.0582 0.0082 0.0785 0.0072 0.1104 0.5158 0.0252 0.271 0.0275 0.3769 0.4322 0.3769 0.6476 0.4026 0.5788 3.1098 1.8737 2.8196 1.458

ð5Þ

The best result for dynamic viscosity relating to liquid phase of R134a is obtained from PR method. The equation obtained from this method for dynamic viscosity relating to liquid phase is

ll ¼ 0:2502  0:0045  t þ 0:0088  P

ð6Þ

The best result for dynamic viscosity relating to vapour phase of R134a is obtained from SMO method. The equation obtained from this method for dynamic viscosity relating to vapour phase is

lv ¼ 10:3233 þ 0:0252  t þ 0:1571  P

ð7Þ

The best results for heat conduction coefficient relating to liquid phase of R134a are obtained from SLR, M5 model tree and M5’Rules methods. The equation obtained from these methods for heat conduction coefficient relating to liquid phase is

kl ¼ 0:4278  t þ 94:21

ð8Þ

The best result for heat conduction coefficient relating to vapour phase of R134a is obtained from SMO method. The equation obtained from this method for heat conduction coefficient relating to vapour phase is

kv ¼ 0:076  t þ 0:0656  P þ 11:6216

Comparison parameters

R2

ð9Þ

The best results for density relating to liquid phase of R134a are obtained from LR, PR and SMO methods. The equation obtained from these methods for density relating to liquid phase is

ql ¼ 0:0027  t  0:0056  P þ 1:3116

ð10Þ

The best result for density relating to vapour phase of R134a is obtained from SMO method. The equation obtained from this method for density relating to vapour phase is

qv ¼ 0:1054  t þ 5:6313  P  2:4347

ð11Þ

For R404a, a comparison of the results obtained from the various methods is shown in Table 3. The comparison parameters are the coefficient of multiple determinations (R2-value), mean absolute error (MAE), root mean squared error (RMSE). As can be seen in Table 3, the best results for specific heat capacity relating to liquid and vapour phase of R404a are obtained from MLP method. The equations obtained from MLP method for specific heat capacity relating to liquid and vapour phase are

cl ¼ 0:0038  t þ 0:0476  Pl þ 1:0533

ð12Þ

cv ¼ 0:0019  t þ 0:0474  P l þ 0:6762

ð13Þ

The best results for dynamic viscosity relating to liquid and vapour phase of R404a are obtained from MLP method. The equations

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E.U. Küçüksille et al. / Energy Conversion and Management 50 (2009) 399–412 Table 3 Comparison of different techniques for thermophysical properties relating to liquid and vapour phase of R404a Thermophysical properties

Method

Phase Liquid phase

Vapour phase

Comparison parameters

Specific heat capacity (c)

Dynamic viscosity (l)

Heat conduction coefficient (k)

Density (q)

LR MLP PR SLR SMO KStar AR M5 model DT M5’Rules LR MLP PR SLR SMO KStar AR M5 model DT M5’Rules LR MLP PR SLR SMO KStar AR M5 model DT M5’Rules LR MLP PR SLR SMO KStar AR M5 model DT M5’Rules

tree

tree

tree

tree

Comparison parameters

R2

MAE

RMSE

R2

MAE

RMSE

0.997 0.9997 0.9987 0.9877 0.9951 0.9997 0.9816 0.9941 0.9949 0.9989 0.923 1 0.9997 0.9898 0.9994 0.9999 0.9871 0.999 0.9756 0.9995 0 0.868 0 1 0.8146 0.0336 0.8826 0.0437 0 0.2001 0.9999 1 1 0.9948 0.9999 0.9999 0.9885 0.9994 0.9748 0.9999

0.0151 0.0029 0.0093 0.031 0.0192 0.0039 0.0362 0.0208 0.0249 0.0087 0.0246 0.0003 0.0015 0.0087 0.0023 0.0009 0.0112 0.0025 0.0079 0.0029 95.9105 535.4014 72.5495 99.5613 7.7187 89.8271 56.5752 54.8009 95.9105 69.1281 0.0012 0.0004 0.0008 0.0109 0.0012 0.0019 0.016 0.0036 0.0145 0.002

0.0181 0.0063 0.0121 0.0344 0.027 0.0059 0.0474 0.0262 0.0309 0.0109 0.0274 0.0003 0.0018 0.0104 0.0036 0.0012 0.0136 0.0032 0.0164 0.0036 96.6331 569.3077 73.5021 103.1482 8.8174 383.0225 81.4657 77.2336 96.6331 92.2376 0.0014 0.0005 0.001 0.0125 0.0017 0.0025 0.0198 0.0043 0.0281 0.0027

0.9968 0.9999 0.9984 0.9951 0.9949 0.9998 0.978 0.9952 0.9801 0.9991 0.9994 1 0.9997 0.998 0.999 0.9998 0.9803 0.9977 0.9769 0.9994 0.9995 1 0.9997 0.9966 0.9994 0.9998 0.9814 0.9981 0.9762 0.9997 0.9994 1 0.9997 0.9977 0.9991 0.9998 0.9787 0.9951 0.9945 0.9987

0.0195 0.0038 0.0129 0.0214 0.0212 0.0047 0.0472 0.0208 0.034 0.012 0.0616 0.0139 0.0412 0.1098 0.0698 0.0348 0.3157 0.1139 0.2416 0.0622 0.104 0.027 0.072 0.2463 0.1142 0.0612 0.5473 0.1889 0.4333 0.0916 1.1689 0.1983 0.7698 2.3801 1.3751 0.7199 6.1025 3.3863 4.2685 1.7839

0.0226 0.0045 0.016 0.0273 0.034 0.0071 0.0583 0.0282 0.0563 0.0151 0.0719 0.0176 0.0508 0.1293 0.103 0.0477 0.4234 0.1375 0.4393 0.0863 0.119 0.0341 0.0859 0.299 0.1421 0.0848 0.7373 0.2225 0.803 0.1138 1.3652 0.2419 0.9583 2.7039 2.1246 1.0873 8.1316 4.1145 4.995 2.3743

obtained from MLP method for dynamic viscosity relating to liquid and vapour phase are

ll ¼ 0:1105  0:0042  t þ 0:262  Pl  0:2554  Pv

ð14Þ

lv ¼ 10:5658 þ 0:0296  t  7:7204  Pl þ 7:9289  Pv

ð15Þ

The best result for heat conduction coefficient relating to liquid phase of R404a is obtained from AR method. But, as can be seen from comparison parameters (R2, MAE, RMSE), results are not very satisfactory. For this reason, equation obtained from this method for heat conduction coefficient relating to liquid phase was not given. The best result for heat conduction coefficient relating to vapour phase of R404a is obtained from MLP method. The equation obtained from this method for heat conduction coefficient relating to vapour phase is

kv ¼ 11:9118 þ 0:0627  t  12:3181  Pl þ 12:6457  Pv

ð16Þ

The best results for density relating to liquid and vapour phase of R404a are obtained from MLP method. The equations obtained from MLP method for density relating to liquid and vapour phase are

ql ¼ 1:1765  0:0028  t þ 0:1492  Pl  0:1559  Pv

ð17Þ

qv ¼ 3:7436  0:04  t  146:2049  Pl þ 152:9297  Pv

ð18Þ

For R407c, a comparison of the results obtained from the various methods is shown in Table 4. The comparison parameters are the coefficient of multiple determinations (R2-value), mean absolute error (MAE), root mean squared error (RMSE). As can be seen in Table 4, the best results for specific heat capacity relating to liquid and vapour phase of R407c are obtained from MLP method. The equations obtained from MLP method for specific heat capacity relating to liquid and vapour phase are

cl ¼ 1:468 þ 0:0032  t  0:1518  Pl þ 0:1763  Pv

ð19Þ

cv ¼ 1:012 þ 0:0047  t  0:2271  Pl þ 0:2637  Pv

ð20Þ

The best results for dynamic viscosity relating to liquid and vapour phase of R407c are obtained from MLP method. The equations obtained from MLP method for dynamic viscosity relating to liquid and vapour phase are

ll ¼ 0:095  0:0053  t þ 0:085  Pl  0:0806  Pv

ð21Þ

lv ¼ 11:3612 þ 0:0478  t  1:0372  Pl þ 1:2087  Pv

ð22Þ

The best results for heat conduction coefficient relating to liquid phase of R407c are obtained from LR, PR, SLR, M5 model tree and M5’Rules methods. The equation obtained from these methods for heat conduction coefficient relating to liquid phase is

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Table 4 Comparison of different techniques for thermophysical properties relating to liquid and vapour phase of R407c Thermophysical properties

Method

Phase Liquid phase

Vapour phase

Comparison parameters

Specific heat capacity (c)

Dynamic viscosity (l)

Heat conduction coefficient (k)

Density (q)

LR MLP PR SLR SMO KStar AR M5 model DT M5’Rules LR MLP PR SLR SMO KStar AR M5 model DT M5’Rules LR MLP PR SLR SMO KStar AR M5 model DT M5’Rules LR MLP PR SLR SMO KStar AR M5 model DT M5’Rules

tree

tree

tree

tree

kl ¼ 0:4615  t þ 96:1973

MAE

RMSE

R2

MAE

RMSE

0.9996 1 0.9998 0.9996 0.9995 0.9999 0.9728 0.9966 0.9895 0.998 0.9131 1 0.9997 0.9881 0.9988 0.9989 0.9732 0.9985 0.9923 0.9991 1 1 1 1 1 0.9996 0.979 1 0.9935 1 0.9916 0.9919 0.9916 0.9895 0.9918 0.9908 0.9678 0.9918 0.9814 0.9926

0.0033 0.0012 0.0015 0.0033 0.0026 0.0015 0.0234 0.0082 0.0157 0.0063 0.0201 0.0002 0.0008 0.0078 0.002 0.0014 0.0113 0.0026 0.0059 0.0018 0.0015 0.0224 0.0015 0.0015 0.023 0.204 1.9712 0.0015 1.0157 0.0015 0.0031 0.0033 0.0031 0.0086 0.0033 0.0044 0.0186 0.0047 0.011 0.0044

0.0036 0.0018 0.0024 0.0036 0.0047 0.0021 0.0278 0.0098 0.0181 0.0081 0.0235 0.0003 0.0013 0.009 0.003 0.0028 0.0148 0.0032 0.0073 0.0025 0.0019 0.0293 0.0019 0.0019 0.0272 0.3405 2.3924 0.0019 1.2227 0.0019 0.0121 0.0119 0.0121 0.0132 0.012 0.0126 0.0254 0.0118 0.0176 0.0118

0.9995 1 0.9998 0.9994 0.9995 0.9999 0.9725 0.9967 0.9893 0.9993 0.9998 1 0.9999 0.9941 0.9998 0.9998 0.9857 0.9989 0.9942 0.9991 0.9641 0.9624 0.9625 0.9631 0.964 0.9614 0.9495 0.9593 0.9432 0.9634 0.9997 1 0.9999 0.9995 0.9998 0.9999 0.9679 0.9957 0.9909 0.9975

0.0053 0.0011 0.0016 0.0056 0.0047 0.0024 0.0347 0.0121 0.0232 0.0081 0.0256 0.0069 0.0073 0.1311 0.022 0.0226 0.1988 0.0554 0.1247 0.0513 0.1963 0.1809 0.1764 0.3088 0.1935 0.2022 0.4948 0.2987 0.5094 0.2299 0.4938 0.1156 0.1317 0.6445 0.4085 0.2825 4.6412 1.8723 2.7836 1.3033

0.0059 0.002 0.0032 0.0065 0.0067 0.0035 0.0412 0.0143 0.0267 0.0103 0.0281 0.0108 0.0148 0.1539 0.029 0.0345 0.265 0.066 0.1507 0.0642 0.6979 0.713 0.7083 0.7017 0.7006 0.7098 0.8128 0.7343 0.8964 0.708 0.5422 0.186 0.2809 0.75 0.5726 0.4195 5.7384 2.1883 3.2538 1.5985

ð23Þ

The best result for heat conduction coefficient relating to vapour phase of R407c is obtained from LR method. The equation obtained from this method for heat conduction coefficient relating to vapour phase is

kv ¼ 0:0403  t  0:2718  Pl þ 0:6179  Pv þ 11:218

ð24Þ

The best results for density relating to liquid phase of R407c are obtained from M5’Rules method. The equation obtained from this method for density relating to liquid phase is

ql ¼ 1:2639  0:0027  t  0:005  Pl

ð25Þ

The best result for density relating to vapour phase of R407c is obtained from MLP method. The equation obtained from this method for density relating to vapour phase is

qv ¼ 14:1778 þ 0:223  t  17:8089  Pl þ 23:1397  Pv

Comparison parameters

R2

ð26Þ

For R410a, a comparison of the results obtained from the various methods is shown in Table 5. The comparison parameters are the coefficient of multiple determinations (R2-value), mean absolute error (MAE), root mean squared error (RMSE). As can be seen in Table 5, the best results for specific heat capacity relating to liquid and vapour phase of R410a are obtained

from MLP method. The equations obtained from MLP method for specific heat capacity relating to liquid and vapour phase are

cl ¼ 1:1416  0:0049  t  4:9495  Pl þ 5:0098  Pv

ð27Þ

cv ¼ 0:6584  0:0019  t  3:2372  Pl þ 3:2966  Pv

ð28Þ

The best results for dynamic viscosity relating to liquid and vapour phase of R410a are obtained from MLP method. The equations obtained from MLP method for dynamic viscosity relating to liquid and vapour phase are

ll ¼ 0:142  0:003  t þ 0:1286  Pl  0:1258  Pv

ð29Þ

lv ¼ 10:3112 þ 0:0222  t  7:8706  Pl þ 8:0729  Pv

ð30Þ

The best results for heat conduction coefficient relating to liquid phase of R410a are obtained from PR, SLR, M5 model tree and M5’Rules methods. The equation obtained from these methods for heat conduction coefficient relating to liquid phase is

kl ¼ 0:51  t þ 99:94

ð31Þ

The best result for heat conduction coefficient relating to vapour phase of R410a is obtained from MLP method. The equation obtained from this method for heat conduction coefficient relating to vapour phase is

405

E.U. Küçüksille et al. / Energy Conversion and Management 50 (2009) 399–412 Table 5 Comparison of different techniques for thermophysical properties relating to liquid and vapour phase of R410a Thermophysical properties

Method

Phase Liquid phase

Vapour phase

Comparison parameters

Specific heat capacity (c)

Dynamic viscosity (l)

Heat conduction coefficient (k)

Density (q)

LR MLP PR SLR SMO KStar AR M5 model DT M5’Rules LR MLP PR SLR SMO KStar AR M5 model DT M5’Rules LR MLP PR SLR SMO KStar AR M5 model DT M5’Rules LR MLP PR SLR SMO KStar AR M5 model DT M5’Rules

tree

tree

tree

tree

Comparison parameters

R2

MAE

RMSE

R2

MAE

RMSE

0.8941 0.9999 0.9829 0.9618 0.9698 0.9977 0.982 0.9842 0.9929 0.996 0.9994 1 0.9995 0.9957 0.9998 0.9999 0.9632 0.9996 0.9942 0.9996 1 1 1 1 1 0.9998 0.9792 1 0.9946 1 0.9999 1 0.9999 0.9953 0.9998 0.9996 0.9836 0.9993 0.9937 0.9999

0.1161 0.0035 0.0466 0.0657 0.0624 0.0136 0.0526 0.0447 0.0287 0.0202 0.0017 0.0004 0.0015 0.0067 0.0011 0.0009 0.0114 0.0018 0.0052 0.0021 0.0175 0.0577 0.0151 0.0151 0.0308 0.2609 2.408 0.0151 1.3159 0.0151 0.0016 0.0008 0.0014 0.0119 0.0017 0.0026 0.019 0.0039 0.0122 0.0017

0.1733 0.0046 0.0636 0.0978 0.1238 0.0343 0.0664 0.0785 0.0416 0.029 0.002 0.0005 0.0018 0.0077 0.0013 0.0013 0.0139 0.0022 0.0061 0.0026 0.0206 0.0738 0.0178 0.0178 0.0354 0.3981 3.0223 0.0178 1.471 0.0178 0.0019 0.0011 0.0018 0.0156 0.0025 0.0048 0.0242 0.0058 0.0137 0.0022

0.9946 1 0.9957 0.9923 0.992 0.9987 0.9864 0.9924 0.9953 0.9992 0.9989 1 0.9991 0.9989 0.9984 0.9993 0.9836 0.9971 0.9922 0.9993 0.9998 0.9999 0.9998 0.9999 0.9998 0.9996 0.9897 0.998 0.997 0.9996 0.9991 1 0.9993 0.9977 0.9988 0.9992 0.9921 0.996 0.9964 0.9997

0.0352 0.0033 0.0314 0.0397 0.0418 0.0139 0.0596 0.0433 0.0384 0.0158 0.0897 0.0143 0.0781 0.1389 0.0998 0.0596 0.3324 0.1461 0.2357 0.0861 0.0693 0.0509 0.0594 0.0677 0.0672 0.0851 0.4837 0.2689 0.2712 0.0685 1.4723 0.2554 1.2794 2.3187 1.7931 1.1643 4.7431 3.7298 3.3655 0.8719

0.0459 0.0043 0.0422 0.0567 0.0809 0.0321 0.0721 0.0703 0.0478 0.0208 0.1113 0.0222 0.1025 0.1567 0.1747 0.1227 0.4284 0.2226 0.2835 0.1047 0.0801 0.0706 0.0737 0.08 0.0891 0.1704 0.6592 0.3605 0.3277 0.1168 1.8186 0.4146 1.673 3.2531 3.2252 2.5486 5.8596 5.6148 4.115 1.1242

kv ¼ 0:39  P v þ 10:06

ð32Þ

The best results for density relating to liquid and vapour phase of R410a are obtained from MLP method. The equations obtained from this method for density relating to liquid and vapour phase are

ql ¼ 1:2117  0:0027  t þ 0:1482  Pl  0:1538  Pv

ð33Þ

qv ¼ 10:425  0:2295  t  126:9336  Pl þ 132:4188  Pv

ð34Þ

4. Results and discussion In this work, data mining methods were used for determining thermophysical properties as the specific heat capacity, viscosity, heat conduction coefficient, density of R134a, R404a, R407c and R410a refrigerants which do not cause ozone depletion for vapor compression refrigeration systems. The best approaches which have minimum errors were obtained. Therefore, equations of thermophysical properties were derived. In Table 6, a comparison is given between the Solkane Software results and obtained results with the equations derived from this study for specific heat capacity relating to liquid and vapor phase of R134a refrigerant. In Table 7, a comparison is given between the Solkane Software results and obtained results with the equations derived from this

study for viscosity relating to liquid and vapor phase of R134a refrigerant. In Table 8, a comparison is given between the Solkane Software results and obtained results with the equations derived from this study for heat conduction coefficient relating to liquid and vapor phase of R134a refrigerant. In Table 9, a comparison is given between the Solkane Software results and obtained results with the equations derived from this study for density relating to liquid and vapor phase of R134a refrigerant. In Table 10, a comparison is given between the Solkane Software results and obtained results with the equations derived from this study for specific heat capacity relating to liquid and vapor phase of R404a refrigerant. In Table 11, a comparison is given between the Solkane Software results and obtained results with the equations derived from this study for viscosity relating to liquid and vapor phase of R404a refrigerant. In Table 12, a comparison is given between the Solkane Software results and obtained results with the equations derived from this study for heat conduction coefficient relating to liquid and vapor phase of R404a refrigerant. In Table 13, a comparison is given between the Solkane Software results and obtained results with the equations derived from

406

E.U. Küçüksille et al. / Energy Conversion and Management 50 (2009) 399–412

Table 6 Comparison of obtained results for specific heat capacity relating to liquid and vapor phase of R134a refrigerant Temperature

Pressure

Liquid phase specific heat capacity

Vapor phase specific heat capacity

t (°C)

P (bar)

Actual values (cl, kJ/kg K

Estimated values (cl, kJ/kg K)

Error

Actual values (cv, kJ/kg K)

Estimated values (cv, kJ/kg K)

Error

25 20 15 10 5 0 5 10 15 20 25 30 35 40 45 50 55 60

1.06 1.33 1.64 2.01 2.43 2.93 3.5 4.15 4.88 5.72 6.65 7.7 8.87 10.17 11.6 13.18 14.92 16.82

1.2821 1.2925 1.3035 1.3152 1.3277 1.341 1.3553 1.3707 1.3874 1.4056 1.4255 1.4475 1.4719 1.4994 1.5307 1.5668 1.6093 1.6601

1.287906 1.295833 1.304564 1.314501 1.325443 1.337993 1.35195 1.367515 1.384688 1.404072 1.425265 1.44887 1.474887 1.503517 1.53476 1.569018 1.606492 1.647182

0.00581 0.00333 0.00106 0.000699 0.002257 0.003007 0.00335 0.003185 0.002712 0.001528 0.000235 0.00137 0.00299 0.00412 0.00406 0.00222 0.002808 0.012918

0.7857 0.803 0.8212 0.8403 0.8604 0.8816 0.9041 0.928 0.9535 0.981 1.0106 1.0429 1.0784 1.118 1.1626 1.2139 1.2741 1.3463

0.79288 0.80701 0.8222 0.83896 0.85705 0.87725 0.8993 0.92346 0.94973 0.97891 1.01046 1.04518 1.08307 1.12439 1.16914 1.21785 1.27079 1.32795

0.00718 0.00401 0.001 0.001336 0.003348 0.004348 0.0048 0.00454 0.003768 0.002092 0.00014 0.00228 0.00467 0.00639 0.00654 0.00395 0.003312 0.018352

Table 7 Comparison of obtained results for viscosity relating to liquid and vapor phase of R134a refrigerant Temperature

Pressure

Liquid phase viscosity

t (°C)

P (bar)

Actual values (ll, mPa s)

Estimated values (ll, mPa s)

Error

Actual values (lv, mPa s)

Vapor phase viscosity Estimated values (lv, mPa s)

Error

25 20 15 10 5 0 5 10 15 20 25 30 35 40 45 50 55 60

1.06 1.33 1.64 2.01 2.43 2.93 3.5 4.15 4.88 5.72 6.65 7.7 8.87 10.17 11.6 13.18 14.92 16.82

0.3792 0.3545 0.3317 0.3106 0.291 0.2728 0.2557 0.2398 0.2248 0.2107 0.1974 0.1849 0.1731 0.1619 0.1512 0.1411 0.1316 0.1225

0.372028 0.351904 0.332132 0.312888 0.294084 0.275984 0.2585 0.24172 0.225644 0.210536 0.19622 0.18296 0.170756 0.159696 0.14978 0.141184 0.133996 0.128216

0.007172 0.002596 0.00043 0.00229 0.00308 0.00318 0.0028 0.00192 0.00084 0.000164 0.00118 0.00194 0.002344 0.002204 0.00142 8.4E-05 0.0024 0.00572

9.8266 10.0098 10.1985 10.3932 10.5945 10.803 11.0197 11.2457 11.4824 11.7314 11.9947 12.2748 12.5746 12.898 13.2496 13.6356 14.0637 14.5447

9.859826 10.02824 10.20294 10.38707 10.57905 10.7836 10.99915 11.22727 11.46795 11.72591 11.99802 12.28897 12.59878 12.92901 13.27966 13.65388 14.05323 14.47772

0.03323 0.01844 0.00444 0.006129 0.015447 0.019397 0.02055 0.018435 0.014452 0.005488 0.00332 0.01417 0.02418 0.03101 0.03006 0.01828 0.010468 0.066978

Table 8 Comparison of obtained results for heat conduction coefficient relating to liquid and vapor phase of R134a refrigerant Temperature

Pressure

Liquid phase heat conduction coefficient

t (°C)

P (bar)

Actual values (kl, mW/mK)

Estimated values (kl, mW/mK)

Error

Actual values (kv, mW/mK)

Vapor phase heat conduction coefficient Estimated values (kv, mW/mK)

Error

25 20 15 10 5 0 5 10 15 20 25 30 35 40 45 50 55 60

1.06 1.33 1.64 2.01 2.43 2.93 3.5 4.15 4.88 5.72 6.65 7.7 8.87 10.17 11.6 13.18 14.92 16.82

104.91 102.77 100.63 98.49 96.35 94.21 92.07 89.93 87.79 85.65 83.51 81.37 79.24 77.1 74.96 72.82 70.68 68.54

104.905 102.766 100.627 98.488 96.349 94.21 92.071 89.932 87.793 85.654 83.515 81.376 79.237 77.098 74.959 72.82 70.681 68.542

0.005 0.004 0.003 0.002 0.001 0 0.001 0.002 0.003 0.004 0.005 0.006 0.003 0.002 0.001 0 0.001 0.002

9.81 10.2 10.59 10.99 11.39 11.8 12.22 12.65 13.08 13.52 13.96 14.42 14.87 15.34 15.81 16.29 16.78 17.27

9.79114 10.1888 10.5892 10.9935 11.401 11.8138 12.2312 12.6538 13.0817 13.5168 13.9578 14.4067 14.8635 15.3288 15.8026 16.2862 16.7804 17.285

0.018864 0.011152 0.000816 0.00346 0.01101 0.01381 0.0112 0.00384 0.00173 0.003168 0.00216 0.01328 0.006528 0.011248 0.00744 0.003792 0.00035 0.01499

407

E.U. Küçüksille et al. / Energy Conversion and Management 50 (2009) 399–412 Table 9 Comparison of obtained results for density relating to liquid and vapor phase of R134a refrigerant Temperature

Pressure

Liquid phase density

Vapor phase density

t (°C)

P (bar)

Actual values (ql, kg/l)

Estimated values (ql, kg/l)

Error

Actual values (qv, kg/m3)

Estimated values (qv, kg/m3)

Error

25 20 15 10 5 0 5 10 15 20 25 30 35 40 45 50 55 60

1.06 1.33 1.64 2.01 2.43 2.93 3.5 4.15 4.88 5.72 6.65 7.7 8.87 10.17 11.6 13.18 14.92 16.82

1.374 1.359 1.343 1.327 1.311 1.295 1.278 1.261 1.243 1.225 1.206 1.187 1.167 1.146 1.125 1.102 1.078 1.053

1.37316 1.35815 1.34292 1.32734 1.31149 1.29519 1.2785 1.26136 1.24377 1.22557 1.20686 1.18748 1.16743 1.14665 1.12514 1.10279 1.07955 1.05541

0.000836 0.000848 8.4E-05 0.00034 0.00049 0.00019 0.0005 0.00036 0.00077 0.00057 0.00086 0.00048 0.00043 0.00065 0.00014 0.00079 0.00155 0.00241

5.51 6.79 8.29 10.05 12.08 14.43 17.14 20.23 23.76 27.78 32.35 37.53 43.4 50.06 57.62 66.21 76.03 87.28

6.16948 7.16293 8.38163 9.93821 11.7764 14.065 16.7479 19.8812 23.465 27.6683 32.3784 37.7643 43.8259 50.6196 58.1454 66.5158 75.7873 85.9598

0.65948 0.37293 0.09163 0.111787 0.303641 0.364991 0.39215 0.348805 0.294956 0.111664 0.02845 0.23431 0.42593 0.55962 0.52538 0.30583 0.242704 1.320234

Table 10 Comparison of obtained results for specific heat capacity relating to liquid and vapor phase of R404a refrigerant Temperature

Liquid phase pressure

Vapor phase pressure

Liquid phase specific heat capacity

t (°C)

Pl (bar)

Pv (bar)

Actual values (cpl, kJ/kg K)

Estimated values (cpl, kJ/kg K)

Error

Actual values (cpv, kJ/kg K)

Vapor phase specific heat capacity Estimated values (cpv, kJ/kg K)

Error

45 40 35 30 25 20 15 10 5 0 5 10 15 20 25 30 35 40 45 50

1.07 1.35 1.68 2.08 2.54 3.07 3.69 4.39 5.19 6.1 7.13 8.27 9.55 10.97 12.55 14.28 16.19 18.29 20.59 23.11

1.04 1.31 1.64 2.02 2.47 3 3.61 4.31 5.1 6 7.02 8.16 9.43 10.84 12.41 14.14 16.05 18.15 20.44 22.96

1.2429 1.2508 1.2595 1.269 1.2797 1.2916 1.3051 1.3204 1.338 1.3583 1.3819 1.4098 1.4428 1.4824 1.5306 1.59 1.6644 1.7598 1.8873 2.0181

1.275232 1.26956 1.266268 1.266308 1.269204 1.275432 1.285944 1.300264 1.319344 1.34366 1.373688 1.408952 1.45088 1.499472 1.55568 1.619028 1.690944 1.771904 1.862384 1.963336

0.03233 0.01876 0.00677 0.002692 0.010496 0.016168 0.019156 0.020136 0.018656 0.01464 0.008212 0.000848 0.00808 0.01707 0.02508 0.02903 0.02654 0.0121 0.024916 0.054764

0.7765 0.7952 0.8144 0.8343 0.8552 0.8773 0.9009 0.9262 0.9536 0.9835 1.0165 1.0532 1.0946 1.1419 1.1968 1.2619 1.3412 1.441 1.5728 1.7582

0.81242 0.81619 0.82233 0.83179 0.8441 0.85972 0.87961 0.90329 0.93171 0.96534 1.00466 1.0492 1.10037 1.15818 1.22357 1.29607 1.37711 1.46715 1.56667 1.67661

0.03592 0.02099 0.00793 0.002508 0.011104 0.017582 0.021294 0.022914 0.021894 0.01816 0.011838 0.004002 0.00577 0.01628 0.02677 0.03417 0.03591 0.02615 0.006134 0.081586

Table 11 Comparison of obtained results for viscosity relating to liquid and vapor phase of R404a refrigerant Temperature

Liquid phase pressure

Vapor phase pressure

Liquid phase viscosity

t (°C)

Pl (bar)

Pv (bar)

Actual values (ll, mPa s)

Estimated values (ll, mPa s)

Error

Actual values (lv, mPa s)

Vapor phase viscosity Estimated values (lv, mPa s)

Error

45 40 35 30 25 20 15 10 5 0 5 10 15 20 25 30 35 40 45 50

1.07 1.35 1.68 2.08 2.54 3.07 3.69 4.39 5.19 6.1 7.13 8.27 9.55 10.97 12.55 14.28 16.19 18.29 20.59 23.11

1.04 1.31 1.64 2.02 2.47 3 3.61 4.31 5.1 6 7.02 8.16 9.43 10.84 12.41 14.14 16.05 18.15 20.44 22.96

0.3231 0.3017 0.2818 0.2632 0.246 0.2299 0.2149 0.2009 0.1878 0.1755 0.164 0.1532 0.143 0.1335 0.1245 0.116 0.1081 0.1006 0.0935 0.0869

0.31422 0.29763 0.2788 0.26555 0.25014 0.23264 0.21829 0.20191 0.18874 0.1763 0.16465 0.15118 0.14118 0.1321 0.12409 0.1145 0.10611 0.09897 0.0957 0.09134

0.008876 0.004074 0.002996 0.00235 0.00414 0.00274 0.00339 0.00101 0.00094 0.0008 0.00065 0.002024 0.001822 0.001396 0.000414 0.001496 0.00199 0.00163 0.0022 0.00444

9.0878 9.2763 9.4717 9.6743 9.8849 10.1043 10.3336 10.5743 10.828 11.0969 11.3836 11.6915 12.0247 12.3887 12.7904 13.2391 13.7478 14.3343 15.0254 15.8625

9.21903 9.34612 9.56292 9.63575 9.80037 10.0589 10.2569 10.5508 10.7863 11.0448 11.3282 11.7139 12.0495 12.4143 12.8124 13.3211 13.8674 14.4532 15.0015 15.6749

0.13123 0.06982 0.09122 0.038554 0.084533 0.045428 0.076747 0.023497 0.041686 0.05214 0.055374 0.02242 0.02481 0.02559 0.02203 0.08203 0.11957 0.11892 0.02392 0.1876

408

E.U. Küçüksille et al. / Energy Conversion and Management 50 (2009) 399–412

Table 12 Comparison of obtained results for heat conduction coefficient relating to vapor phase of R404a refrigerant Temperature

Liquid phase pressure

Vapor phase pressure

Vapor phase heat conduction coefficient

t (°C)

Pl (bar)

Pv (bar)

Actual values (kv, mW/mK)

Estimated values (kv, mW/mK)

Error

45 40 35 30 25 20 15 10 5 0 5 10 15 20 25 30 35 40 45 50

1.07 1.35 1.68 2.08 2.54 3.07 3.69 4.39 5.19 6.1 7.13 8.27 9.55 10.97 12.55 14.28 16.19 18.29 20.59 23.11

1.04 1.31 1.64 2.02 2.47 3 3.61 4.31 5.1 6 7.02 8.16 9.43 10.84 12.41 14.14 16.05 18.15 20.44 22.96

8.76 9.2 9.62 10.05 10.47 10.9 11.33 11.77 12.23 12.71 13.22 13.78 14.38 15.04 15.77 16.58 17.49 18.51 19.65 20.93

9.06146 9.34023 9.76184 9.95347 10.2912 10.7783 11.1685 11.7113 12.1604 12.6456 13.1701 13.857 14.4634 15.1156 15.8203 16.7005 17.6397 18.6412 19.5817 20.7208

0.30146 0.14023 0.14184 0.096534 0.178795 0.121667 0.161512 0.058692 0.069569 0.06441 0.049939 0.07703 0.0834 0.07563 0.05028 0.12053 0.14975 0.13121 0.068271 0.209219

Table 13 Comparison of obtained results for density relating to liquid and vapor phase of R404a refrigerant Temperature

Liquid phase pressure

Vapor phase pressure

Liquid phase density

t (°C)

Pl (bar)

Pv (bar)

Actual values (ql, kg/l)

Estimated values (ql, kg/l)

Error

Actual values (qv, kg/m3)

Vapor phase density Estimated values (qv, kg/m3)

Error

45 40 35 30 25 20 15 10 5 0 5 10 15 20 25 30 35 40 45 50

1.07 1.35 1.68 2.08 2.54 3.07 3.69 4.39 5.19 6.1 7.13 8.27 9.55 10.97 12.55 14.28 16.19 18.29 20.59 23.11

1.04 1.31 1.64 2.02 2.47 3 3.61 4.31 5.1 6 7.02 8.16 9.43 10.84 12.41 14.14 16.05 18.15 20.44 22.96

1.303 1.287 1.272 1.255 1.239 1.222 1.205 1.187 1.169 1.15 1.13 1.11 1.089 1.067 1.044 1.019 0.993 0.965 0.934 0.899

1.30001 1.28569 1.26948 1.25592 1.2404 1.22284 1.20625 1.18756 1.16976 1.15122 1.13188 1.11024 1.08922 1.06727 1.04424 1.01865 0.99185 0.96378 0.93593 0.90505

0.002992 0.001309 0.00252 0.00092 0.0014 0.00084 0.00125 0.00056 0.00076 0.00122 0.00188 0.00024 0.00022 0.00027 0.00024 0.00035 0.001147 0.001217 0.00193 0.00605

5.59 6.98 8.61 10.54 12.79 15.4 18.43 21.91 25.9 30.47 35.7 41.68 48.5 56.31 65.27 75.58 87.52 101.45 117.92 137.7

8.15124 8.30489 10.3241 9.7554 11.1195 14.4837 16.9237 21.4311 25.0816 29.4719 34.6692 42.1354 49.0139 56.8338 65.7297 77.1636 89.808 103.73 117.468 134.214

2.56124 1.32489 1.71408 0.784598 1.670487 0.916343 1.506264 0.478904 0.818361 0.99809 1.030843 0.45543 0.51388 0.52379 0.45968 1.58359 2.28795 2.28003 0.452223 3.485727

Table 14 Comparison of obtained results for specific heat capacity relating to liquid and vapor phase of R407c refrigerant Temperature

Liquid phase pressure

Vapor phase pressure

Liquid phase specific heat capacity

t (°C)

Pl (bar)

Pv (bar)

Actual values (cpl, kJ/kg K)

Estimated values (cpl, kJ/kg K)

Error

Actual values (cpv, kJ/kg K)

Vapor phase specific heat capacity Estimated values (cpl, kJ/kgK)

Error

35 30 25 20 15 10 5 0 5 10 15 20 25 30 35 40 45 50

1.51 1.87 2.3 2.8 3.38 4.05 4.81 5.68 6.66 7.76 9 10.38 11.9 13.59 15.45 17.49 19.72 22.16

1.1 1.39 1.73 2.15 2.63 3.2 3.85 4.61 5.47 6.45 7.56 8.8 10.2 11.76 13.49 15.41 17.54 19.88

1.3227 1.3322 1.3431 1.3552 1.3688 1.3838 1.4004 1.4186 1.4385 1.4604 1.4845 1.5111 1.5408 1.5743 1.6126 1.6574 1.7113 1.7787

1.320712 1.333191 1.343859 1.358005 1.370585 1.38537 1.400597 1.418519 1.437373 1.459167 1.482628 1.507756 1.53984 1.574326 1.612977 1.657801 1.710806 1.768956

0.001988 0.00099 0.00076 0.0028 0.00178 0.00157 0.0002 8.1E-05 0.001127 0.001233 0.001872 0.003344 0.00096 2.6E-05 0.00038 0.0004 0.000494 0.009744

0.795 0.8109 0.828 0.8465 0.8665 0.8883 0.912 0.938 0.9666 0.9983 1.0335 1.073 1.1174 1.1678 1.2255 1.2925 1.3714 1.4663

0.79465 0.81287 0.82837 0.84908 0.86743 0.88909 0.91139 0.93773 0.96545 0.99757 1.03217 1.06926 1.11675 1.16782 1.22512 1.29164 1.37039 1.45682

0.000351 0.00197 0.00037 0.00257 0.00093 0.00079 0.000606 0.000271 0.001147 0.000731 0.001328 0.003738 0.00065 2.3E-05 0.000382 0.000862 0.001014 0.00948

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E.U. Küçüksille et al. / Energy Conversion and Management 50 (2009) 399–412 Table 15 Comparison of obtained results for viscosity relating to liquid and vapor phase of R407c refrigerant Temperature t (°C)

Liquid phase pressure Pl (bar)

Vapor phase pressure Pv (bar)

35 30 25 20 15 10 5 0 5 10 15 20 25 30 35 40 45 50

1.51 1.87 2.3 2.8 3.38 4.05 4.81 5.68 6.66 7.76 9 10.38 11.9 13.59 15.45 17.49 19.72 22.16

1.1 1.39 1.73 2.15 2.63 3.2 3.85 4.61 5.47 6.45 7.56 8.8 10.2 11.76 13.49 15.41 17.54 19.88

Liquid phase viscosity

Vapor phase viscosity

Actual values (ll, mPa s)

Estimated values (ll, mPa s)

Error

Actual values (lv, mPa s)

Estimated values (lv, mPa s)

Error

0.323 0.3025 0.2835 0.2659 0.2495 0.2342 0.22 0.2067 0.1943 0.1826 0.1716 0.1613 0.1516 0.1424 0.1338 0.1256 0.1179 0.1106

0.32019 0.30092 0.28356 0.26571 0.24982 0.23433 0.22004 0.20623 0.19372 0.18173 0.17116 0.16202 0.15188 0.14329 0.13546 0.1276 0.11898 0.11127

0.00281 0.001584 6.2E-05 0.00019 0.00032 0.00013 4E-05 0.000466 0.000582 0.00087 0.000436 0.00072 0.00028 0.00089 0.00166 0.002 0.00108 0.00067

9.4568 9.6616 9.8724 10.0898 10.3144 10.5472 10.7892 11.0417 11.3066 11.5857 11.8816 12.1973 12.5367 12.9047 13.3074 13.7529 14.2522 14.82

9.4516 9.66773 9.87169 10.0997 10.3173 10.5504 10.7868 11.042 11.304 11.5866 11.8812 12.1876 12.5423 12.914 13.3148 13.7586 14.2592 14.7958

0.005202 0.00613 0.000709 0.00995 0.00295 0.00318 0.002437 0.00031 0.002563 0.00094 0.000428 0.009676 0.00556 0.00926 0.00742 0.00574 0.00701 0.024196

Table 16 Comparison of obtained results for heat conduction coefficient relating to vapor phase of R407c refrigerant Temperature

Liquid phase pressure

Vapor phase pressure

Liquid phase heat conduction coefficient

t (°C)

Pl (bar)

Pv (bar)

Actual values (kl, mW/mK)

Estimated values (kl, mW/mK)

Error

Actual values (kv, mW/mK)

Vapor phase heat conduction coefficient Estimated values (kv, mW/mK)

Error

35 30 25 20 15 10 5 0 5 10 15 20 25 30 35 40 45 50

1.51 1.87 2.3 2.8 3.38 4.05 4.81 5.68 6.66 7.76 9 10.38 11.9 13.59 15.45 17.49 19.72 22.16

1.1 1.39 1.73 2.15 2.63 3.2 3.85 4.61 5.47 6.45 7.56 8.8 10.2 11.76 13.49 15.41 17.54 19.88

112.35 110.04 107.73 105.43 103.12 100.81 98.5 96.2 93.89 91.58 89.27 86.97 84.66 82.35 80.04 77.74 75.43 73.12

112.35 110.042 107.735 105.427 103.12 100.812 98.5048 96.1973 93.8898 91.5823 89.2748 86.9673 84.6598 82.3523 80.0448 77.7373 75.4298 73.1223

0.0002 0.0023 0.0048 0.0027 0.0002 0.0023 0.0048 0.0027 0.0002 0.0023 0.0048 0.0027 0.0002 0.0023 0.0048 0.0027 0.0002 0.0023

10.13 10.37 10.64 10.95 11.28 11.65 12.06 12.51 13.01 13.54 14.12 14.74 15.41 16.13 16.89 17.69 18.55 19.45

10.0768 10.3596 10.6543 10.9794 11.3199 11.6915 12.0881 12.5227 12.9892 13.4973 14.0476 14.6402 15.2937 15.9997 16.7647 17.5981 18.5096 19.4938

0.053228 0.010385 0.01433 0.02945 0.03989 0.04149 0.02806 0.0127 0.020775 0.042713 0.072376 0.099764 0.11634 0.130258 0.125339 0.091943 0.04043 0.04376

Table 17 Comparison of obtained results for density relating to liquid and vapor phase of R407c refrigerant Temperature

Liquid phase pressure

Vapor phase pressure

Liquid phase density

t (°C)

Pl (bar)

Pv (bar)

Actual values (ql, kg/l)

Estimated values (ql, kg/l)

Error

Actual values (qv, kg/m3)

Vapor phase density Estimated values (qv, kg/m3)

Error

35 30 25 20 15 10 5 0 5 10 15 20 25 30 35 40 45 50

1.51 1.87 2.3 2.8 3.38 4.05 4.81 5.68 6.66 7.76 9 10.38 11.9 13.59 15.45 17.49 19.72 22.16

1.1 1.39 1.73 2.15 2.63 3.2 3.85 4.61 5.47 6.45 7.56 8.8 10.2 11.76 13.49 15.41 17.54 19.88

1.354 1.338 1.322 1.306 1.289 1.272 1.254 1.236 1.218 1.199 1.179 1.159 1.137 1.115 1.092 1.068 1.042 1.014

1.35085 1.33555 1.3199 1.3039 1.2875 1.27065 1.25335 1.2355 1.2171 1.1981 1.1784 1.158 1.1369 1.11495 1.09215 1.06845 1.0438 1.0181

0.00315 0.00245 0.0021 0.0021 0.0015 0.00135 0.00065 0.0005 0.0009 0.0009 0.0006 0.001 1E-04 5E-05 0.00015 0.00045 0.0018 0.0041

4.99 6.22 7.69 9.42 11.45 13.81 16.54 19.68 23.3 27.44 32.18 37.58 43.76 50.81 58.87 68.12 78.78 91.12

4.93503 6.34934 7.67401 9.60324 11.4961 13.8688 16.4898 19.6973 23.2597 27.4618 32.1788 37.4108 43.8518 50.9677 58.9898 68.2029 78.8916 90.6998

0.054969 0.12934 0.015989 0.18323 0.04613 0.0588 0.050164 0.01727 0.040315 0.0218 0.001168 0.169222 0.09183 0.15772 0.11985 0.08292 0.11163 0.420188

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this study for density relating to liquid and vapor phase of R404a refrigerant. In Table 14, a comparison is given between the Solkane Software results and obtained results with the equations derived from this study for specific heat capacity relating to liquid and vapor phase of R407c refrigerant. In Table 15, a comparison is given between the Solkane Software results and obtained results with the equations derived from this study for viscosity relating to liquid and vapor phase of R407c refrigerant. In Table 16, a comparison is given between the Solkane Software results and obtained results with the equations derived from this study for heat conduction coefficient relating to liquid and vapor phase of R407c refrigerant. In Table 17, a comparison is given between the Solkane Software results and obtained results with the equations derived from

this study for density relating to liquid and vapor phase of R407c refrigerant. In Table 18, a comparison is given between the Solkane Software results and obtained results with the equations derived from this study for specific heat capacity relating to liquid and vapor phase of R410a refrigerant. In Table 19, a comparison is given between the Solkane Software results and obtained results with the equations derived from this study for viscosity relating to liquid and vapor phase of R410a refrigerant. In Table 20, a comparison is given between the Solkane Software results and obtained results with the equations derived from this study for heat conduction coefficient relating to liquid and vapor phase of R410a refrigerant. In Table 21, a comparison is given between the Solkane Software results and obtained results with the equations derived from

Table 18 Comparison of obtained results for specific heat capacity relating to liquid and vapor phase of R410a refrigerant Temperature

Liquid phase pressure

Vapor phase pressure

Liquid phase specific heat capacity

Vapor phase specific heat capacity

t (°C)

Pl (bar)

Pv (bar)

Actual values (cpl, kJ/kg K)

Estimated values (cpl, kJ/kg K)

Error

Actual values (cpv, kJ/kg K)

Estimated values (cpl, kJ/kg K)

Error

50 45 40 35 30 25 20 15 10 5 0 5 10 15 20 25 30 35 40 45 50

1.09 1.39 1.75 2.19 2.7 3.3 4.01 4.82 5.75 6.81 8.01 9.36 10.88 12.58 14.48 16.57 18.89 21.45 24.26 27.34 30.71

1.09 1.39 1.75 2.18 2.69 3.29 3.99 4.8 5.73 6.78 7.98 9.33 10.85 12.54 14.43 16.52 18.83 21.38 24.19 27.26 30.63

1.3743 1.3832 1.3932 1.4041 1.416 1.429 1.4431 1.4585 1.4754 1.494 1.5149 1.5387 1.5665 1.5998 1.6409 1.6937 1.7641 1.8617 2.0035 2.2199 2.571

1.45233 1.44592 1.44313 1.39506 1.40131 1.41299 1.38121 1.40555 1.43713 1.42645 1.47431 1.53121 1.59837 1.62628 1.66625 1.76778 1.83308 1.91285 2.05779 2.16892 2.34763

0.07803 0.06272 0.04993 0.009041 0.014688 0.016008 0.061893 0.05295 0.038271 0.067551 0.040591 0.007486 0.03187 0.02648 0.02535 0.07408 0.06898 0.05115 0.05429 0.050982 0.223371

0.7611 0.7812 0.803 0.8266 0.8522 0.88 0.9102 0.943 0.9788 1.0181 1.0615 1.1097 1.1638 1.2252 1.296 1.3792 1.4789 1.6019 1.7589 1.9686 2.2662

0.81815 0.82647 0.83835 0.82202 0.84281 0.86895 0.86866 0.90728 0.95302 0.97352 1.0353 1.10599 1.18677 1.24529 1.31568 1.43033 1.52567 1.63527 1.79268 1.93317 2.12385

0.05705 0.04527 0.03535 0.00458 0.009386 0.011046 0.041538 0.035724 0.025782 0.044584 0.026204 0.003714 0.02297 0.02009 0.01968 0.05113 0.04677 0.03337 0.03378 0.035432 0.142354

Table 19 Comparison of obtained results for viscosity relating to liquid and vapor phase of R410a refrigerant Temperature

Liquid phase pressure

Vapor phase pressure

Liquid phase viscosity

t (°C)

Pl (bar)

Pv (bar)

Actual values (ll, mPa s)

Estimated values (ll, mPa s)

Error

Actual values (lv, mPa s)

Vapor phase viscosity Estimated values (lv, mPa s)

Error

50 45 40 35 30 25 20 15 10 5 0 5 10 15 20 25 30 35 40 45 50

1.09 1.39 1.75 2.19 2.7 3.3 4.01 4.82 5.75 6.81 8.01 9.36 10.88 12.58 14.48 16.57 18.89 21.45 24.26 27.34 30.71

1.09 1.39 1.75 2.18 2.69 3.29 3.99 4.8 5.73 6.78 7.98 9.33 10.85 12.54 14.43 16.52 18.83 21.38 24.19 27.26 30.63

0.2995 0.2824 0.2665 0.2516 0.2376 0.2243 0.2118 0.1999 0.1885 0.1777 0.1674 0.1575 0.148 0.1389 0.1301 0.1217 0.1136 0.1058 0.0983 0.0911 0.0843

0.29505 0.28089 0.2669 0.25439 0.24082 0.2275 0.21574 0.20301 0.19062 0.17984 0.1682 0.15698 0.14624 0.13726 0.12883 0.11969 0.11244 0.10587 0.09873 0.09362 0.08805

0.004448 0.001508 0.0004 0.00279 0.00322 0.0032 0.00394 0.00311 0.00212 0.00214 0.0008 0.000518 0.001762 0.001644 0.001266 0.002014 0.00116 6.6E-05 0.00043 0.00252 0.00375

9.2686 9.4777 9.6933 9.9157 10.1456 10.3839 10.6318 10.8906 11.1621 11.4484 11.7521 12.0766 12.4258 12.8049 13.2205 13.6814 14.1993 14.7903 15.4773 16.2947 17.2966

9.42171 9.5934 9.77723 9.89651 10.1107 10.3431 10.517 10.7918 11.091 11.3357 11.6894 12.0735 12.492 12.8662 13.2809 13.8147 14.3143 14.8624 15.5419 16.1953 16.988

0.15311 0.1157 0.08392 0.019192 0.034919 0.040839 0.114835 0.098772 0.071133 0.112724 0.062664 0.003059 0.06624 0.06132 0.06036 0.13327 0.11497 0.07213 0.0646 0.09945 0.308599

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E.U. Küçüksille et al. / Energy Conversion and Management 50 (2009) 399–412 Table 20 Comparison of obtained results for heat conduction coefficient relating to vapor phase of R410a refrigerant Temperature

Liquid phase pressure

Vapor phase pressure

t (°C)

Pl (bar)

Pv (bar)

Liquid phase heat conduction coefficient Actual values (kl, mW/mK)

Estimated values (kl, mW/mK)

Error

Actual values (kv, mW/mK)

Vapor phase heat conduction coefficient Estimated values (kv, mW/mK)

Error

50 45 40 35 30 25 20 15 10 5 0 5 10 15 20 25 30 35 40 45 50

1.09 1.39 1.75 2.19 2.7 3.3 4.01 4.82 5.75 6.81 8.01 9.36 10.88 12.58 14.48 16.57 18.89 21.45 24.26 27.34 30.71

1.09 1.39 1.75 2.18 2.69 3.29 3.99 4.8 5.73 6.78 7.98 9.33 10.85 12.54 14.43 16.52 18.83 21.38 24.19 27.26 30.63

125.28 122.75 120.21 117.67 115.14 112.6 110.07 107.53 105 102.46 99.93 97.39 94.86 92.32 90.78 87.25 84.71 82.18 79.64 77.11 74.57

125.44 122.89 120.34 117.79 115.24 112.69 110.14 107.59 105.04 102.49 99.94 97.39 94.84 92.29 89.74 87.19 84.64 82.09 79.54 76.99 74.44

0.16 0.14 0.13 0.12 0.1 0.09 0.07 0.06 0.04 0.03 0.01 0 0.02 0.03 1.04 0.06 0.07 0.09 0.1 0.12 0.13

10.78 10.81 10.87 10.96 11.1 11.29 11.52 11.82 12.17 12.58 13.06 13.61 14.23 14.92 15.69 16.53 17.45 18.45 19.52 20.67 21.89

10.4851 10.6021 10.7425 10.9102 11.1091 11.3431 11.6161 11.932 12.2947 12.7042 13.1722 13.6987 14.2915 14.9506 15.6877 16.5028 17.4037 18.3982 19.4941 20.6914 22.0057

0.2949 0.2079 0.1275 0.0498 0.0091 0.0531 0.0961 0.112 0.1247 0.1242 0.1122 0.0887 0.0615 0.0306 0.0023 0.0272 0.0463 0.0518 0.0259 0.0214 0.1157

Table 21 Comparison of obtained results for density relating to liquid and vapor phase of R410a refrigerant Temperature

Liquid phase pressure

Vapor phase pressure

Liquid phase density

t (°C)

Pl (bar)

Pv (bar)

Actual values (ql, kg/l)

Estimated values (ql, kg/l)

Error

Actual values (qv, kg/m3)

Estimated values (qv, kg/m3)

Error

50 45 40 35 30 25 20 15 10 5 0 5 10 15 20 25 30 35 40 45 50

1.09 1.39 1.75 2.19 2.7 3.3 4.01 4.82 5.75 6.81 8.01 9.36 10.88 12.58 14.48 16.57 18.89 21.45 24.26 27.34 30.71

1.09 1.39 1.75 2.18 2.69 3.29 3.99 4.8 5.73 6.78 7.98 9.33 10.85 12.54 14.43 16.52 18.83 21.38 24.19 27.26 30.63

1.345 1.329 1.313 1.296 1.28 1.262 1.245 1.227 1.208 1.189 1.17 1.149 1.128 1.106 1.083 1.059 1.034 1.006 0.976 0.944 0.907

1.3406 1.32542 1.3099 1.29547 1.27912 1.26226 1.24632 1.22828 1.20958 1.19168 1.17146 1.1504 1.12839 1.1069 1.0843 1.0591 1.03414 1.00785 0.97861 0.9494 0.91703

0.004404 0.003584 0.0031 0.000526 0.000882 0.00026 0.00132 0.00128 0.00158 0.00268 0.00146 0.0014 0.00039 0.0009 0.0013 9.8E-05 0.00014 0.00185 0.00261 0.0054 0.01003

4.45 5.6 6.97 8.61 10.53 12.78 15.39 18.42 21.92 25.94 30.55 35.84 41.89 48.84 56.78 65.93 76.49 88.77 103.17 120.27 140.94

7.02887 7.52693 8.3541 8.2959 9.94585 12.0895 13.5123 16.8078 20.7615 24.1041 29.5389 35.7964 42.9864 49.8396 57.7898 68.1063 78.3603 89.9307 104.197 118.619 135.957

2.57887 1.92693 1.3841 0.3141 0.584148 0.690528 1.877724 1.612212 1.158476 1.835852 1.011112 0.043592 1.09641 0.99956 1.00976 2.17632 1.8703 1.16072 1.02664 1.650636 4.983012

this study for density relating to liquid and vapor phase of R410a refrigerant. 5. Conclusions In this work, data mining techniques was used for determining the thermophysical properties of R134a, R404a, R407c and R410a refrigerator which do not cause ozone depletion for vapor compression refrigeration systems. Used data mining techniques are LR, MLP, PR, SLR, SMO, KStar, AR, M5 model tree, DT, M5’Rules models. The best approach for specific heat capacity relating to liquid and vapour phase of R134a is SMO model. The best approach for viscosity relating to liquid phase of R134a is PR model. The best approach for viscosity relating to vapour phase of R134a is SMO

Vapor phase density

model. The best approaches for heat conduction coefficient relating to liquid phase of R134a are LR, SLR, M5 model tree and M5’Rules model. The best approach for heat conduction coefficient relating to vapour phase of R134a is SMO model. The best approaches for density relating to liquid phase of R134a are LR, PR and SMO model. The best approach for density relating to vapour phase of R134a is SMO model. The best approach for specific heat capacity relating to liquid and vapour phase of R404a is MLP model. The best approach for viscosity relating to liquid and vapour phase of R404a is MLP model. Obtained results from data mining techniques for heat conduction coefficient relating to liquid phase of R404a is not satisfactory. Therefore, equation for this property was not derived. The best approach for heat conduction coefficient relating to vapour phase of

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R404a is MLP model. The best approach for density relating to liquid and vapour phase of R404a is MLP model. The best approach for specific heat capacity relating to liquid and vapour phase of R407c is MLP model. The best approach for viscosity relating to liquid and vapour phase of R407c is MLP model. The best approaches for heat conduction coefficient relating to liquid phase of R407c are LR, PR, SLR, M5 model tree and M5’Rules model. The best approach for heat conduction coefficient relating to vapour phase of R407c is LR model. The best approach for density relating to liquid phase of R407c is M5’Rules model. The best approach for density relating to vapour phase of R407c is MLP model. The best approach for specific heat capacity relating to liquid and vapour phase of R410a is MLP model. The best approach for viscosity relating to liquid and vapour phase of R410a is MLP model. The best approaches for heat conduction coefficient relating to liquid phase of R410a are PR, SLR, M5 model tree and M5’Rules model. The best approach for heat conduction coefficient relating to vapour phase of R410a is MLP model. The best approach for density relating to liquid and vapour phase of R410a is MLP model. Mathematical equations from different data mining techniques for thermophysical properties of every refrigerant were derived. The values calculated from obtained formulations were found to be in good agreement with actual values. The new equations can provide simplicity in the thermodynamic analysis and design of vapor compression refrigeration systems. References [1] Dupont. DuPont de Nemours and Company Inc.; 2004. . [2] S ß encan A, Selbasß R, Kızılkan Ö, Kalogirou SA. Thermodynamic analysis of subcooling and superheating effects of alternative refrigerants for vapor compression refrigeration cycles. Int J Energy Res 2006;30:323–47. [3] Li ST, Shue LY. Data mining to aid policy making in air pollution management. Expert Syst Appl 2004;27:331–40. [4] S ß encan A. Modeling of thermodynamic properties of refrigerant/absorbent couples using data mining process. Energy Convers Manage 2007;48:470–80. [5] Tso GKF, Yau KKW. Predicting electricity energy consumption: a comparison of regression analysis, decision tree and neural Networks. Energy 2007;32:1761–8. [6] Kusiak A, Burns A, Milster F. Optimizing combustion efficiency of a circulating fluidized boiler: a data mining approach. Int J Knowl Based Intell Eng Syst 2005;9:263–74. [7] Figueiredo V, Rodrigues F, Gouveia JG. An electric energy consumer characterization framework based on data mining techniques. IEEE Trans Power Syst 2005;20:596–602.

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