Solar adsorption refrigeration (SAR) system modeling

Transcription

1 Energy Efficiency (2011) 4: DOI /s Solar adsorption refrigeration (SAR) system modeling Ghassan M. Tashtoush & Mohannad Al-Ata & Atif Al-Khazali Received: 8 September 2009 / Accepted: 29 July 2010 / Published online: 15 August 2010 # Springer Science+Business Media B.V Abstract The solar adsorption refrigeration (SAR) system has economical and environmental aspects that motivate many researches to investigate its capability in cooling system design. In this study, multi-dimensional mathematical models have been generated to predict the coefficient of performance (COP) value of the SAR system as function of the evaporator, condenser, and generator temperatures. Fuzzy logic and regression analysis approaches were implemented to construct a mathematical model for this purpose from one-dimensional collected data that relates COP value separately to condensation, evaporation, and generation temperatures, respectively. The results of COP calculation from the two models were agreed quite well with the measured values. However, the fuzzy logic technique showed excellent accuracy than the regression model when compared to the calculated COP value, as its steps have the optimum nature in constructing the required model. Keywords Adsorption refrigeration. Solar. Fuzzy modeling. Regression analysis G. M. Tashtoush (*) : M. Al-Ata : A. Al-Khazali Mechanical Engineering Department, Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110, Jordan gtash@just.edu.jo Nomenclature A Area (m 2 ) G Total Gibbs function (kj/kg) ΔG Change in total entropy (kj/kg) h,h Specific and total enthalpy (kj/kg, kj) ΔH Change in total enthalpy (J) H Height (m) I p The instantaneous solar irradiation power (Watt) L Back insulation thickness (m) M Mass (kg) P Pressure (N/m 2 ) Q Total heat transfer (J) s, S Specific and total entropy (kj/kg K, kj/k) ΔS Change in total entropy (J/K) T Temperature (K) U The overall heat loss coefficient (W/(m 2 K)) W Total work (J) k Insulation conductivity (W/(m K)) t Time (s) r a Cluster radius in data space x o Limiting adsorption capacity Δx Variation of adsorbate concentration Subscript list amb Ambient g Generator c Condenser e Evaporator reg Regenerator

2 248 Energy Efficiency (2011) 4: p H L gen Absorber plate High-temperature body Low-temperature body Generation per kilogram of adsorbent Greek letters w Volume adsorption μ The overall mean effect w i The amount of output at the quantization level I μ i Firing strength of the rule η c Collector efficiency ε Reject ratio Introduction In the early years of the last century, sorption refrigeration was frequently used. Later, and with the development in power station efficiency and the introduction of chlorofluorocarbons in the 1930s, sorption refrigeration became a key technology (Enrique Vladimir 1995). Adsorption has been shown to be achieved by refrigeration for a long time (Zigler 1999; Zhang and Wang 2002), while the development of solar refrigeration systems using basic solid adsorption cycle did not emerge until the late 1970s after the pioneering work of Tchernev (1974). The interest for adsorption refrigeration or heat pumping since 1970s is mainly due to the fact that such systems are environmentally friendly and that they can produce cooling by using low waste heat source (such as industrial waste energy) or solar energy as a driving force. Adsorption refrigeration systems are promising techniques for utilizing different energy resources, such as solar energy, despite its lower coefficient of performance (COP) as compared with the vapor compression cycle. Solar adsorption refrigeration systems are considered a promising technology of developing cooling systems that can be used for industrial as well as domestic purposes. Determination of suitable adsorbent adsorbate pairs for various applications was performed through various studies that also quantified the COP with respect to the operating temperatures (Meunier 1978; Guilleminot and Meunier 1981; Fan et al. 2007; Grenier and Pons 1983; Kima and Infante Ferreira 2008; Pons and Guilleminot 1986; Boubakri et al. 1985; Miller 1929; Boubakri et al. 1992). These also pinpointed several limitations; the most important of these was the low heat transfer coefficient in the adsorbent bed, which has a real influence on the thermodynamic efficiency of the system. In the field of adsorptive systems, different types of solid gas pairs were studied to build adapted cooling solar systems. At LIMSI, the zeolite water pair was chosen (Guilleminot and Meunier 1981) for refrigeration, and the active carbon methanol pair for ice production (Boubakri et al. 1985). The active carbon ammoniac pair is also usable for ice production. In the refrigerator type, a fluid, generally water, is frozen by the system in the water tank (located in an enclosure and expected to be kept at low temperature). The frozen fluid must be preserved at its most. As a preservative system, and by the means of a valve placed between the collector and the evaporator, heat release in the evaporator is prevented. Heat-driven sorption refrigeration cycles have exited in patent literature since at least 1909, and refrigeration was commercially available in the 1920s. In 1929, Miller described several systems, which utilized silica gel and sulfur dioxide as an adsorbent/adsorbate pair (Miller 1929). In the icemaker type, ice produced in the water tank is removed every morning to be used in another place. No valve is needed, and it does not matter if condensation occurs in the evaporator or anywhere else on condition that all the condensed liquid return to the evaporator before the evaporation phase starts. That is the reason why a new conception of adsorptive solar-powered icemaker equipped with a single heat exchanger playing alternatively the role of condenser and evaporator was suggested. This conception is based on the theoretical and experimental results obtained from tests carried out on the three commercial adsorptive solar-powered icemakers using activated carbon/methanol pair (Boubakri et al. 1992, 2000; Anyanwu and Ezekwe 2003). The classical physical mathematical analysis of solar adsorption system is based on determining the COP at any instant by solving complex nonlinear set of equations (Yeung and Sumathy 2003; Li and Wang 2002). These equations are depending on constant and variables factors. The latter ones are the condensing, evaporating, and generating temperatures, which are usually called the input variables of the system. The great-consumed effort for finding COP from analytical approach forced the researchers to inquire nonclassical techniques to minimize the execution time for COP calculation. Many researches had performed

3 Energy Efficiency (2011) 4: so much work, theoretically and experimentally, to find COP due to the change of one of these three temperatures (Yeung and Sumathy 2003; Li and Wang 2002; Li et al. 2002; Anyanwu 2000). This research aims to build a general and simple multi-dimensional mathematical model from these collected data, which is based on performing curvefitting techniques. The fuzzy logic and regression analysis-based methods are chosen to find two multidimensional models that can estimate COP as the three input temperature variables changes. Fuzzy logic modeling Fuzzy logic modeling techniques can be classified into three categories, namely, the linguistic (Mamdani type), the relational equation, and the Takagi, Sugeno, and Kang (TSK). In linguistic models, both the antecedent and the consequence are fuzzy sets, while in the TSK model, the antecedent consists of fuzzy sets, but the consequence is made up of linear equations. Fuzzy relational equation models aim at building the fuzzy relation matrices according to the input output process data. Based on the TSK model, an adaptive networkbased fuzzy inference system (ANFIS) has been introduced by Jang (1993). This model is mostly suited to the modeling of nonlinear systems. Fuzzy logic is the extension of the Boolean logic that has been proposed to handle the concept of partial truth truth values between completely true and completely false. Dr. Lotfi Zadeh introduced it in the 1960s (Zadeh 1965). He said that rather than regarding fuzzy theory as a single theory, we should regard the process of fuzzification as a methodology to generalize any specific theory from a crisp (discrete) to a continuous fuzzy form (Zadeh 1965). In other words, the fuzzy logic is the extension of classical two-valued logic by using the truth set {0, 1}. Basics of fuzzy logic Fuzzy set In conventional set theory, an element either belongs to the set or not. Fuzzy logic is a generalization of the conventional logic. In fuzzy set theory, the element can belong to the set partially with a certain degree. Let X be a finite set={x1, x2,...,xn}, and let A be a fuzzy set in X, then the grade of membership of element x in fuzzy set A is m A : X! ½0; 1Š. Linguistic variables The main advantage of fuzzy logic is that words or sentences can be used as expressions instead of numeric values. The associative expressions are called linguistic variables. They are common in our daily life. Let us consider the fuzzy variable temperature. It can be, for example, divided into three linguistic values: low, medium, and high, which are fuzzy sets. Each linguistic value is represented by membership function in the universe of discourse. The membership function can vary between zero and unity, and they can have many shapes such as Z, trapezoidal, bell, triangular, and singleton. The singleton type of membership function (fuzzy unit set) is usually employed only for the output variables of the fuzzy reasoning. Fuzzy reasoning In fuzzy reasoning, the most important fuzzy implication inference rule is the generalized modus ponens (GMP) which uses an IF THEN rule that implicitly represents a fuzzy relation. The use of fuzzy rules is important when the causal link between domains is not known. Usually, partial knowledge about the relation between these domains exists in the form of fuzzy rules. In this case, fuzzy reasoning is done by using GMP. The fuzzy rules define the connection between input and output fuzzy (linguistic) variables. The rule consists of two parts: an antecedent and a consequence part. According to the form of the consequent of the fuzzy control rules, we can usually distinguish two main different types of fuzzy logic controls (FLCs; Mamdani FLCs (Mamdani and Assilian 1975) and Takagi Sugeno Kang FLCs (Sugeno and Kang 1988; Takagi and Sugeno 1985)): 1. Mamdani type: rules are composed of input and output linguistic variables taking values on a linguistic term set with a real-world meaning: R i :IFX 1 is A i1 :::and X n is A in ; THEN Y is B i where X n and Y are the input and output linguistic variables, respectively, and A in and B i are linguistic labels with fuzzy sets associated specifying their meaning.

4 250 Energy Efficiency (2011) 4: Takagi Sugeno Kang type: rules are based on the division of the input space into several fuzzy subspaces in which each rule defines a linear input output relationship by means of the realvalued coefficients p in : R i :IFX 1 is A i1 :::and X n is A in ; THEN Y ¼ p i1 :X 1 þ ::: þ p in X n þ p i0 where X n and Y are the input and output linguistic variables, respectively, and A in is the linguistic label with fuzzy sets associated specifying their meaning. In other words, the method of Mamdani inference is to expect all output membership functions to be fuzzy sets. It is intuitive, has widespread acceptance, and is better suited to human input. Its limitation is that the computation for the defuzzification process lasts longer (Ross 1995; Furinwata and Langari 2000). On the other hand, the Sugeno style inference has a computational efficiency, works well with linear techniques, works well with optimization and adaptive techniques, guaranties continuity of the output surface, and it is better suited to mathematical analysis. Also, Mamdani type and Takagi Sugeno (TS, for short) type mainly differ in the fuzzy rule consequent: a Mamdani fuzzy controller utilizes fuzzy sets as the consequent, whereas a TS fuzzy controller employs linear functions of input variables (Hao Ying 2000). We need an operation that converts the fuzzy set obtained from the inference into a crisp value (single value). This process is called defuzzification. The most defuzzification method is the center of gravity. Taking into consideration the effect parameters of Solar Adsorption Refrigeration (SAR) System Modeling Data Set Index Fig. 2 Sub-clustering fuzzy system for theoretical data solar adsorbent refrigeration system, a Takagi and Sugeno inference fuzzy model will be constructed to simulate the COP of the refrigeration system. Theoretical collected data from reference (Yeung and Sumathy 2003) were put through these procedures to calculate COP under different conditions. The COP value for different input variables is calculated by the ANFIS. The results are compared with classical theoretical data of COP under the same conditions. The comparison indicates very good agreement. Furthermore, data collected from experimental setup of given solar adsorption system (Li and Wang 2002; Li et al. 2002; Anyanwu 2000) were used as an input for the statistical and fuzzy logic procedures. The predicated COP at intermediate values between the chosen points, due to the variance of one variable and keeping the other two variables constant, is compared with these values for experimental results. The comparison shows excellent agreement to predict the COP calculated by the proposed two mathematical procedures. This is because the fuzzy logic approach develops an optimum model that fit the given data. The comparison of these two models give us the trust to use both of them to determine COP due to the Data Set Index Fig. 1 Ideal adsorptive cycle in the Clapeyron diagram Fig. 3 Sub-clustering fuzzy system for experimental data

5 Energy Efficiency (2011) 4: Input variable in1 Fig. 4 Membership functions of the evaporator temperature for COP/theoretical data change of one, two, and three input temperatures accurately. Coefficient of performance calculation The index of performance of a refrigerator or heat pump is expressed in terms of the (COP) ratio of desired result to input. This measure of performance may be larger than one, and we want the COP to be as large as possible. For the refrigerator, the desired result is the heat supplied at low temperature, and the input is the net work into the device to make the cycle operate. COP ¼ Q L W net;in ð1þ By applying the first law to the cyclic refrigerator, the COP becomes Q L COP ¼ ð2þ Q H Q L The ideal cycle for an adsorption cooling system corresponds to a hypothetical quadric-thermal machine. This device consists of two coupled machines Fig. 6 Membership functions of the condensation temperature for COP/experimental data operating at two temperature levels without mechanical energy conversion. For solar cooling systems shown in Fig. 1, the coefficient of solar performance (COP s ) is usually calculated from the machine's coefficient of thermal performance (COP t ) times the solar collector efficiency η c. Thus, COP s for an intermittent cycle without heat recovery, at a given T reg,is COP s ¼ h c½m 1 ΔxLðT e Þ Q 1 Š ð3þ m 1 Δxq st T reg þ Q2 þ Q 3 where m 1 is the adsorbent mass, Q 1 is the adsorbate heat transferred from C to D (Fig. 1), Q 2 is the energy supplied to heat the reactor/collector from A to C, and Q 3 is the energy increase to heat the adsorbed mass from A to C. The collector efficiency η c is defined as the ratio between the useful heat gains over some specified period to the incident solar energy over the same period; it can be expressed as h c ¼ 1 U T p T R amb Ip dt ð4þ Fig. 5 Membership functions of the generation temperature for COP/theoretical data Fig. 7 Membership functions of the generation temperature for COP/experimental data

6 252 Energy Efficiency (2011) 4: Fig. 8 The fuzzy system for each input output theoretical data The global heat loss coefficient at the collector top U t was evaluated by an empirical equation given in Duffie and Beckman (1991) 2 3 U t ¼ 6 4 c T p 1 T p T amb 1þf e þ h v 1 s T p þ T 2 amb Tp þ Tamb 2 þ 1 1þf þ0:133" " p þ 0:0059Ih v þ p " g 1 and the collector bottom heat loss is given as ð5þ U b ¼ k ð6þ L In addition, the collector edge heat loss is given as k perimeter U e ¼ ð7þ edge insulated thickness A c According to Eq. 2, the maximum COP for the refrigerator may be calculated as Q L COP R ¼ ¼ Q c ¼ T gðt amb T e Þ ð8þ Q H Q L Q g T e T g T c Actually, the COP for such systems ranges from 0.3 to 0.8theoreticallyandrangesfrom0.11to0.19experimentally. Of course, this depends on the adsorption pair in use and on the solar collector specification. Here, it is slightly less than the specified one. The desorbed refrigerant is condensed in the condenser and flows into evaporator. When the adsorbent bed pressure is lower than the evaporation pressure, the refrigerant liquid in the evaporator will evaporate which causes the refrigeration effect (Anyanwu 2000). Fuzzy modeling discussion The output of the modeling processes is the rule for the COP for both collected theoretical and experimental data. The number of rules associated with each output COP reached 23 for the theoretical and 8 for the experimental data. The Sugeno reasoning method is illustrated by the following simple example with three inputs variables and one output: R 1 :IFT e is low and T c is low and T g is low; THEN COP ¼ 4:75T e 0:49T c þ 0:12T g þ 1:13 Fig. 9 The fuzzy system for each input output experimental data

7 Energy Efficiency (2011) 4: Error R 2 :IFT e is high and T c is high and T g is high; THEN COP ¼ 0:91T e þ 2:81T c 0:83T g 0:83 Take T e as 2 C, T c as 38 C, and T g as 108 C, consequent COP, each membership function has the following values: m low ðt e Þ ¼ m low ð 2Þ ¼ 0:2 m low T c ¼ mlow ð38þ ¼ 0:25 Epochs Fig. 10 Hybrid epoch error for COP after 40 epochs/theoretical data m low T g ¼ mlow ð108þ ¼ 0:94 Epochs Fig. 12 Hybrid epoch error for COP after 420 epochs/ theoretical data Moreover, the corresponding firing strengths for each rule are as follows: w 1 ¼ min m low ðt e Þ; m low T c mlow T g ¼ minf0:2; 0:25; 0:94g ¼ 0:2 n o w 2 ¼ min m high ðt e Þ; m high T c ; mhigh T g ¼ minf0:5; 0:5; 0:94g ¼ 0:5 The individual rule outputs are computed as 1 ¼ 4:75T e 0:49T c þ 0:12T g þ 1:13 ¼ 1:403 m high ðt e Þ ¼ m high ð 2Þ ¼ 0:5 m high T c ¼ mhigh ð38þ ¼ 0:5 m high T g ¼ mhigh ð108þ ¼ 0:98 2 ¼ 0:91T e þ 2:81T c 0:83T g þ 0:07 ¼ 1:539 Therefore, the crisp control action is COP ¼ ð 1:403 0:2 þ 1:539 0:5Þ ¼ 0:4889 Figures 2 and 3 show the fuzzy clustering method where each data point may partially belong to more Error Epochs Fig. 11 Hybrid epoch error for COP after 220 epochs/ theoretical data Fig. 13 Hybrid epoch error for COP after 40 epochs/ experimental data

8 254 Energy Efficiency (2011) 4: Epochs Fig. 14 Hybrid epoch error for COP after 80 epochs/ experimental data Data Set Index Fig. 16 Testing theoretical data for COP after 420 epochs training error than one cluster with degree specified by a membership function which starts with an initial guess for the cluster center location. Subtractive clustering method was used that automatically determines the number of sub-cluster in each temporary cluster. Temporary cluster was acquired by projecting each cluster onto input variable. Figures 4, 5, 6, and 7 show the distribution of the membership functions of the three inputs (T e, T c, and T g ) and two inputs (T c and T g )to one output COP for both collected theoretical and experimental data for COP. It is clearly seen that for every input variable, there is a number of membership functions depending on the number of data. The type of membership functions shows the weight of influence of each value noticing that the highest degree of influence will be on given inputs values in the fuzzy system. For evaporator temperature, there are three membership functions act (T e = 5 C, T e =0 C, and T e =5 C), and at these inputs, the highest degree ofinfluenceoncopcanbeseen,asshowninfig.4. However, for generator temperature (T g ), there are 23 membership functions, which means there are 23 data values as shown in Fig. 6. Data points whose membership grades are among the highest are chosen. The mid-point of these data points is assigned the grade of 1, which is the vertex of the membership function. Then, a membership grade (0<G<1) is assigned to the points at the edges of the cluster. The membership functions of experimental data are less than the membership of theoretical data, as shown in Figs. 6 and 7. Numbers of rules depend on the number of maximum membership functions. From this membership, we will get the interaction between the different input variables, and rules will generate. For collected theoretical and experimental data, numbers of rules are 23 and 8, as shown in Figs. 8 and 9; the optimum value of COP=0.616 at T e =0 C, T c =35 C, and T g =107 C for theoretical data and the optimum value of COP=0.133 at T c =35 C and T g = 89 C for experimental data, respectively. To train the FIS, we used one of two ways: 1. Hybrid optimization method, where the functional signals go forward until the consequent parameters are identified by the least squares estimation (LSE) Error Epochs Fig. 15 Hybrid epoch error for COP after 120 epochs/ experimental data Data Set Index Fig. 17 Testing experimental data for COP after 280 epochs training error/experimental data

9 Energy Efficiency (2011) 4: Back propagation optimization method, where the error rates propagate backward, and the premise parameters are updated by the gradient descent method. The epoch error for hybrid is less than back propagation. Figures 10, 11, and 12 show the hybrid epoch error for COP. Figure 10 shows hybrid epoch error for COP after 40 epochs, and it equals to then starts decreasing until fixed after 420 epochs, and it equals to , as shown in Fig. 12. However, the experimental data shows hybrid epoch error for COP after 40 epochs, and it equals to then starts decreasing until fixed after 120 epochs, and it equals to , as shown in Figs. 13, 14, and 15, respectively. Compared with regression output, it is clear that mean square error equals to 0.01 for T e, T c, and T g, respectively. However, in fuzzy system logic, new modeling system is acquired by interaction of three inputs with minimum least square error equals to In the experimental case, each input variable acquires mean square error, and it equals to for T c and T g, respectively, at T e =0 C. In fuzzy system, logic acquires new modeling system by interaction of two inputs with minimum LSE error equals to However, fuzzy logic technique showed excellent accuracy than the regression model compared to collected data. After approaching a minimum least square error, we will get a suitable function of COP with respect to variable inputs data, as clearly shown in Figs. 16 and 17. Finally, a new modeling system from training data using fuzzy clustering and adaptive neuro-fuzzy techniques (based on the ANFIS architecture) was generated. For theoretical collected data, the optimization new modeling generated an output COP equal to and three inputs, evaporating, condensing, and generating temperature (T e =0 C, T c =35 C, and T g =107 C). On the other hand, for experimental collected data, the optimization new modeling generated an output COP equal to and two inputs, condensing and generating temperature (T c =35 C and T g =107 C). Conclusions A multi-dimensional curve-fitting procedure was used to fit experimental as well as theoretical data relating the COP value to one of the three temperature variables (condensation, evaporation, or generation temperatures). Consequently, the curve-fitting procedure is an attempt to provide us with a simple mathematical model that can relate COP value to the three temperature variables at the same instant. Multidimensional regression analysis and Guassian fuzzy logic techniques were utilized to build different models between COP and the three temperatures, T c, T e, and T g. Both models result into a promising model that can be implemented to predict COP accurately. The mean square error from both models in the comparison process did not exceed the values of 0.01 and 0.001, respectively. However, the fuzzy logic model gives excellent accuracy results when compared with regression, due to the optimum nature of its procedure in developing the mathematical model for any given problem. Furthermore, this work should be validated in the future by experimental work setup that has the facility of determining COP for different input variables, T c, T e, and T g, under the same conditions. References Anyanwu, E. E. (2000). Review of solid adsorption solar refrigeration II. An overview of the principles and theory. Energy Conversion and Management, 45, Anyanwu, E. E., & Ezekwe, C. I. (2003). Design, construction and test run of a solid adsorption solar refrigerator using activated carbon/methanol, as adsorbent/adsorbate pair. Energy Conversion and Management, 44, Boubakri, A., Arsalane, M., Yous, B., Alimoussa, L., Pons, M., Meunier, F., et al. (1992). Experimental study of adsorptive solar-powered ice makers in Agadir (Morocco) 1. Performance in actual site. Renewable Energy, 2, Boubakri, A., Grenier, P., & Pons, M. (1985). Utilization of activated carbon and methanol pair to solar ice production. In Proceedings of the JITH Conference, 1, Rabat, Morocco. Boubakri, A., Guilleminot, J. J., & Meunier, F. (2000). Adsorptive solar powered ice maker: experiments and model. Solar Energy, 69(3), Duffie, J. A., & Beckman, W. A. (1991). Solar engineering of thermal processes (2nd ed.). New York: Wiley/Interscience. Enrique Vladimir, E. (1995). A practical approach to the use of silica gel-water pair in adsorption heat pumps. Flores, MSc thesis. Cranfield: Cranfield University. Fan, Y., Luo, L., & Souyri, B. (2007). Review of solar sorption refrigeration technologies: development and applications. Renewable & Sustainable Energy Reviews, 11, Furinwata, S. S., & Langari, R. (2000). Fuzzy control synthesis and analysis (1st ed.). Chichester, U.K.: Wiley, pp

10 256 Energy Efficiency (2011) 4: Grenier, P., & Pons, M. (1983). Experimental and theoretical results on the use of an activated carbon+methanol cycle for the application to a solar powered ice maker. In Proceedings of the ISES Conference, Perth. New York: Pergamon. Guilleminot, J. J., & Meunier, F. (1981). Etude expe'rimentale d'une glacie're solaire utilisant le cycle ze'olitheeau. Revue Generale de Thermique, 239, Hao Ying, J. (2000). Theory and application of a novel fuzzy PID controller using a simplified Takagi-Sugeno rule scheme. Information Sciences, 123, Jang, J. R. (1993). ANFIS: Adaptive Network Based Fuzzy Inference System. IEEE Transactions on Systems, Man, and Cybernetics, 23(3), Kima, D. S., & Infante Ferreira, C. A. (2008). Solar refrigeration options a state-of-the-art review. International Journal of Refrigeration, 31, Li, M., & Wang, R. Z. (2002). A study of the effects of collector and environment parameters on the performance of a solar powered solid adsorption refrigerator. Renewable Energy, 27, Li, M., Wang, R. Z., Xu, Y. X., Wu, J. Y., & Dieng, A. O. (2002). Experimental study on dynamic performance analysis of flat-plate solar solid-adsorption refrigeration for ice maker. Renewable Energy, 27, Mamdani, E. H., & Assilian, S. (1975). An experiment in linguistic synthesis with a fuzzy logic controller. International Journal of Man-Machine Studies, 7, Meunier, F. (1978). Utilisations des cycles adsorption pour la re'frige'ration solaire. J AFEDES Feb 16, Cahier AFEDES. Miller, E. B. (1929). The development of silica gel, refrigerating engineering. The American Society of Refrigerating Engineering, 17(4), Pons, M., & Guilleminot, J. J. (1986). Design of an experimental solar-powered solid adsorption ice maker. Journal of Solar Energy Science and Engineering, 108, Ross, T. J. (1995). Fuzzy logic with engineering applications (2nd ed.). New York: McGraw Hill Companies Inc. Sugeno, M., & Kang, G. T. (1988). Structure identification of fuzzy model. Fuzzy Sets and Systems, 28, Takagi, T., & Sugeno, M. (1985). Fuzzy identification of systems and its application to modeling and control. IEEE Transactions on Systems, Man, and Cybernetics, 15(1), Tchernev, D. I. (1974). Solar energy cooling with ze'olithes. Proceedings of the NSF/RANN. New York: Solar Collector Workshop. Yeung, K. H., & Sumathy, K. (2003). Thermodynamic analysis and optimization of a combined adsorption heating and cooling system. International Journal of Energy Research, 27, Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, Zhang, X. J., & Wang, R. Z. (2002). Anew adsorption-ejector refrigeration and heating hybrid system powered by solar energy. Applied Thermal Engineering, 22, Zigler, F. (1999). Recent development and future prospects of sorption heat pump systems. International Journal of Thermal Sciences, 38,