Computational and Artificial Intelligence Study of the Parameters Affecting the Performance of Heat Recovery Wheels
Ahmed F. Abdel Gawad, Muhammad N. Radhwi, Asim M. Wafiah, Ghassan J. Softah
Mech. Eng. Dept., College of Eng. & Islamic Archit., Umm AlQura Univ., Makkah, Saudi Arabia
Email address:
afaroukg@yahoo.com (A. F. A. Gawad), mnradhwi@uqu.edu.sa (M. N. Radhwi), am907@hotmail.com (A. M. Wafiah), gjs_1982@hotmail.com (G. J. Softah)
To cite this article:
Ahmed F. Abdel Gawad, Muhammad N. Radhwi, Asim M. Wafiah, Ghassan J. Softah. Computational and Artificial Intelligence Study of the Parameters Affecting the Performance of Heat Recovery Wheels. American Journal of Energy Engineering. Special Issue: Fire, Energy and Thermal Reallife Challenges. Vol. 3, No. 41, 2015, pp. 7994. doi: 10.11648/j.ajee.s.2015030401.16
Keywords: Heat Recovery Wheels, Air Handling Units, Computational Study, Artificial Intelligence
1. System Description
1.1. Heat Recovery System
Figure1 shows a typical heat recovery system installed in a ventilation system. In the core, the fresh air stream is automatically preheated or precooled (depending on the season) by the exhausted air and redirected to the cooling, heating or any demanding alternatives. The outgoing and incoming air streams pass next to each other but do not mix in the heat wheel; this providing guaranteed contaminantfree preheated or precooled fresh air.
1.2. Heat Recovery Wheel
A thermal wheel consists of a matrix of heatabsorbing material, Fig. 2, which is slowly rotated within the supply and exhaust air streams of an air handling system. When cooling the interior of a building, as the thermal wheel rotates, heat is picked up from the fresh air stream in onehalf of the rotation, and given up to the exhaust air stream in the other half of the rotation. Thus, heat energy from the hot fresh air stream is transferred to the matrix material and then from the matrix material to the cool exhaust air stream lowering the temperature of the supply air stream by an amount proportional to the temperature differential between air streams, or 'thermal gradient', and depending upon the efficiency of the device. Heat exchange is most efficient when the streams flow in opposite directions (counter flow), since this causes a favorable temperature gradient across the thickness of the wheel.
Because of the nature of thermal wheels in the way that heat is transferred from one stream to another without having to pass directly through or via an exchange medium, the gross efficiencies are usually much higher than that of any other airside heat recovery system [3,4].
The heat recovery wheel consists of air channels and exchanger walls, which contain not only the adsorbent but also the base materials or the binders. The base material of the exchanger wall may be metal or fiberglass. As an example, the matrix pictures of exchanger wheels and the closeup of the front surface are shown in Fig. 3. As can be seen, they may have different values of width (20, 60,100, 200, 400 mm) for the diameter of 350 mm [5].
The major advantages of heat recovery wheel are [6]:
1. The system significant electrical power savings.
2. Chlorofluorocarbons (CFCs) free; thus, the system is environmentally friendly.
3. Construction and maintenance are simple.
2. Background
2.1. Previous Investigations
The design of HVAC (Heating, ventilation and air conditioning) systems for thermal comfort requires increased attention, especially matters arising from recent regulations and standards on ventilation [7]. The optimum temperature and humidity range for human comfort is presented by ASHRAE [8]. Building energy consumption and savings were highlighted by some investigators [911]. Much effort was devoted to the research and application of heat conservation wheel components, especially desiccant wheels [2,12,24]. Also, many studies concentrated on the potential use of heat conservation wheel systems in various locations in the USA and Europe [5,6,9,25,28]. Other researchers considered the mathematical models of rotary wheels [20,28,30]. Moreover, artificial neural network (ANN) and adaptive neurofuzzy inference system (ANFIS) techniques were used by researchers in air conditioned systems [3135] and other mechanical applications [3642].
2.2. Present Work
In the present investigation, a computational study of the channels of heat recovery wheels was carried out for different materials and shapes. The commercial softwarepackage (ANSYSFluent 13) was exploited for parametric study of the influence of different parameters on heat transfer performance.
The investigated channels of the heat conservation wheel had five crosssectional shapes, namely: circular, hexagonal, quadrangular, lozenge and sinusoidal. In addition, four different materials; steel, aluminium, nickel and copper were considered at different values of Reynolds number.
On the other hand, both the artificial neural network (ANN) and adaptive neurofuzzy inference system (ANFIS) methods were adapted to predict the important thermal characteristics. The present computational results were used as training and verification data for the artificial intelligence models.
3. Mathematical Model and Computational Features
3.1. Mathematical Model of Flow and Heat
It is assumed that the flow is incompressible, onedimensional and turbulent through a straight channel, Fig.4. Thermal properties of the fluid (such as specific heat, thermal conductivity, density) are assumed to have bulk average values and be uniform at any crosssection. Mass flow rate is constant. Heat transfer is in the flow direction.
Based on these assumptions, differential equations relating the flow and thermal fields can be derived from the energy balance applied to a unit element through the channel of the heat wheel as a control volume. The details of the mathematical model can be found in [4345].
3.2. Turbulence Modeling
The realizable ke turbulence model was used in the present study. The realizable ke model differs from the standard ke model in two important aspects: (i) the realizable ke model contains an alternative formulation for the turbulent viscosity. (ii) A modified transport equation for the dissipation rate,, has been derived from an exact equation for the transport of the meansquare vorticity fluctuation. Further details about the realizable k turbulence model are found in [46].
3.3. Computational Domain and Boundary Conditions
The conservation wheel contains flow passages that form a matrix of similar channels. The present study concerns the flow and thermal fields through these channels. As these channels are similar, only one complete channel is considered. The flow was treated as steady without the effect of wheel rotation. The flow in the channel was kept hotter than the surroundings.
The computational domain, for all test cases, is a three dimensional (3D) domain, Fig. 5. The ratio between the length of the channel and its hydraulic diameter (L/d) is (100/3).
Typically, there are three types of boundary conditions that can be listed as:
• Inlet boundary condition: inlet uniform velocity is specified at the entrance of the channel. According to ASHRAE handbook 2005 [47], the inlet temperature was taken as 319. This temperature value represents the annual average ambient temperature in Makkah.
• Outlet boundary condition: Pressure outlet flow condition and temperature of 300 K as outlet temperature.
• Wall boundary condition: the walls of the channel were treated as smooth. The nopenetration and nosliding conditions were applied at the channel walls. The temperature at the inner surface of the walls was kept at 309 K for all test cases. This makes a temperature difference of 10 K between the inlet flow and the inner surface. This difference value was recommended in the literature [43]. As will be seen in the following sections, the wall material changes depending on the test case.
3.4. Computational Grid (Mesh)
Due to the complexity of the shapes of the channels, the computational domain was discretized using unstructured grids. This type of grids usually guarantees the flexibility to generate enough computational points in locations of severe gradients. Unstructured grids adopt themselves easily to irregular geometries with minimum programmer's effort.
The computational domain was covered by tetrahedralshaped elements, (Fig. 6). The grid is very fine next to the solid boundary. The dimensionless distance between the wall and first computational point is y+ ≈ 2. y+ is calculated as . Where, y is the distance to the first point off the wall, is the kinematic viscosity, is the friction velocity (), is the wall shear stress, and is the flow density. The value of y+ = 2 ensures the resolution of the complex turbulent flow [44, 45].
Careful consideration was paid to ensure the gridindependency of the computational solution. Thus, three grid sizes were used to test the gridindependency, namely: 100,000,150,000 and 200,000 elements (cells). The results of both the flow and thermal fields show that the difference between the results of the second and third grid is in the range of 12 %. Thus, the second grid size (150,000) was used for all the test cases.
3.5. Numerical Treatment
SIMPLE (semiimplicit method for pressurelinked equations) algorithm was employed to solve both the velocity and pressure fields. Each equation of the momentum and energy was solved by "firstorder upwind" scheme. The "standard wall function" was used as the nearwall treatment technique in the turbulence model. The solution continues until the numerical residual (error) of all quantities gets below.
3.6. Test Cases
A parametric study was carried out to obtain the best case for optimum operation. Different cases were computationally tested and evaluated. The parametric study covered the shape of the channel crosssection, the wall material, and the flow Reynolds number.
Five crosssectional shapes were considered; circular, hexagonal, quadrangular, lozenge, and sinusoidal. The sinusoidal crosssection is widely used in conservation wheels. It is used here mainly for comparison. The other four shapes are proposed by the authors. The circular shape has good characteristics when considering flow and thermal fields. On the other hand, the hexagonal, quadrangular, and lozenge shapes have good structural properties.
Four materials were tested as wall of the channels, namely: copper, aluminium, nickel and steel. The calculations were performed at six values of Reynolds numbers; 1200, 1540, 1830, 1950, 2200, and 2300. Reynolds number is calculated based on inlet velocity and the hydraulic diameter of the channel, i.e., . Where, , is the hydraulic diameter (3 mm), is the kinematic viscosity. This combination of parameters leads to twenty four (24) test cases. Table.1 shows a summary of all the studied test cases.
Shape  Material  Reynolds Number 
Circular
 Copper  1540 
Aluminium  1950  
Nickel  
Steel  2300  
Hexagonal
 Copper  1540 
Aluminium  1950  
Nickel  
Steel  2300  
Quadrangular
 Copper  1200 
Aluminium  1830  
Nickel  
Steel  2200  
Lozenge
 Copper  1200 
Aluminium  1830  
Nickel  
Steel  2200  
Sinusoidal
 Copper  1200 
1540  
Aluminium  1830  
Nickel  1950  
Steel  2200  
2300 
3.7. Validation of the Numerical Results
The present numerical results compare very well to the data obtained by others [5] as shown in Fig. 7 for the temperature contours. Generally, the same trend of temperature distribution and gradient is obtained in both Figs. 7a and 7b. The red color means the highest temperature and the blue color means the lowest temperature. More gradient contours appear in Fig. 7b. This may be attributed to the secondary flow that is not considered in the present computational investigation.


4. Computational Results and Discussions
This section demonstrates the results of the computations of the test cases that were mentioned in Sec. 3.6 and Table 1. The carriedout parametric study aims to find the combination of parameters that gives the optimum performance of the wheel. Optimum performance, here, means best heat transfer exchange rate. However, the results must cover both the flow and thermal fields. The flow filed concerns the working fluid (air) that transfers heat. Thus, the flow field of the different cases is presented firstly. Then, the thermal filed results are presented. Naturally, concentration is paid to the thermal filed as heat transfer optimization is the principal goal of the study.
4.1. Flow Field
Figure 8 shows the velocity contours along the channels as well as at the entrance and exit of the channel for different crosssections (shapes) and Reynolds number (Re) with aluminium wall. It is clear from the velocity contours at exit that the flow becomes fullydeveloped before the channel exit. For noncircular crosssections, the highest velocity is seen in the middle of the channel crosssection. The same pattern is repeated typically for all test cases in Fig. 8. This ensures the fullydeveloped nature of the flow inside the channel. However, the entrance length may vary from one case to another. This variation of entrance length affect greatly the thermal filed as will be explained in the coming sections.
Figure 9 shows the pressure distribution along the channels as well as at entrance and exit for different crosssections (shapes) and Reynolds number (Re) with aluminium wall. It is clear from Fig. 9 that the flow in the channel causes a considerable pressure drop from the entrance to the exit. The same pattern is repeated typically for all test cases in Fig. 9.










Fig. 8. Velocity contours, aluminium wall.  Fig. 9. Pressure contours, aluminium wall. 
4.2. Thermal Field
To estimate the effect of different parameters on the heat transfer along the channel a certain criterion should be established. This criterion concerns the different thermal zones along the channel in the streamwise direction. Thus, the length of the channel was divided into three consequence zones; hot, middle and cold. For generality the lengths of the three zones are normalized by the total length of the channel. Hence, these lengths can be defined as, Fig. 10:
• Hot zone percentage relative length:
• Middle (Transitional) zone percentage relative length:
• Cold zone percentage relative length:
Apparently, the greater the value of , the better the heat transfer process is. This criterion was implemented in the present study to determine the combination of parameters that gives the optimum heat transfer process.
Figure 11 shows the temperature results for the different crosssections (shapes) at corresponding values of Reynolds number with various wall materials. The results cover temperature contours as well as the relative lengths of the three thermal zones along the channels.
The first column of Fig. 11 shows the temperature contours along the channel as well as at entrance and exit sections at the corresponding Reynolds number and aluminium wall. Generally, the temperature inside the channel drops from the inlet temperature to the wall temperature wellbefore exiting the channel. The pattern of temperature contours at entrance and exit of the channel is repeated for all cases. However, the temperature contours along the channel length changes from one case to another depending on the case parameters. The second column of Fig. 11 shows the temperature contours along the channel length for all cases. Based on the results of the second column of Fig. 11, the percentage relative lengths of the thermal zones along the channel for different cases are shown in the third column of Fig. 11.
Figure 11a shows the results of the temperature contours along the channel as well as at entrance and exit sections for the circular crosssection. It is clear that L_{c} represents most of the length of the channel for all cases. The maximum value of L_{c} is 0.91 at Re = 1540 with aluminium wall. Hence, the circular shape gives a noticeable good thermal performance.
Figure 11b shows the results for the hexagonal crosssection. Figure 11b(iii) shows that, at the same Reynolds number of 1950, the longest cold zone has a percentage relative lengths of L_{c} = 25% and L_{h} = 59% for the copper material. When considering aluminium as the wall material at different values of Reynolds number, the longest cold zone has a percentage relative lengths of L_{c} = 31% and L_{h} = 58% at Re = 1540.
Figure 11c shows the results for the quadrangular crosssection. It is clear from Fig. 11c(iii) that, at the same Reynolds number of 1830, the longest cold zone has a percentage relative length of L_{c} = 94% with corresponding length of hot zone L_{h} = 3% for the copper material. When considering aluminium as the wall material at different values of Reynolds number, the longest cold zone has a percentage relative length of L_{c} = 95% with corresponding length of hot zone L_{h} = 3% at Re = 1200.
Figure 11d shows the results for the Lozenge crosssection. It is obvious from Fig. 11d(iii) that, at the same Reynolds number of 1830, the longest cold zone has a percentage relative length of L_{c} = 21% with corresponding length of hot zone L_{h}=71% for copper. When considering aluminium as the wall material at different values of Reynolds number, the longest cold zone has a percentage relative length L_{c} = 75% with corresponding length of hot zone L_{h} = 15% at Re = 1200.
Figure 11e shows the results for the sinusoidal crosssection at Re = 1830 and 1950. Figure 11e(iii) illustrates that, at the same Reynolds numbers of 1830 and 1950, the longest cold zone has a percentage relative length of L_{c} = 65% with corresponding length of hot zone L_{h} = 18% for copper. When considering aluminium as the wall material at different values of Reynolds number, the longest cold zone has a percentage relative length of L_{c} = 88% with corresponding length of hot zone L_{h} = 7% at Re = 1200 and 1540, while for Re = 2200, L_{c} = 35% and L_{h} = 45%.



Fig. 11a. Circular crosssection.  



Fig. 11b. Hexagonal crosssection.  



Fig. 11c. Quadrangular crosssection.  



Fig. 11d. Lozenge crosssection.  




 
Fig. 11e. Sinusoidal crosssection.  
Fig. 11. Temperature results. 
4.3. Overall View of All Cases
Based on the results of the previous section an overall view of all cases can be demonstrated. Table 2 illustrates overall results of the percentage relative lengths of all cases.
Shape  Material  Length of Cold Zone (%)  Length of Middle Zone (%)  Length of Hot Zone (%) 
Circular
 Copper Re = 1950  81  9  10 
Aluminium Re = 1950  74  12  14  
Nickel Re = 1950  68  15  17  
Steel Re = 1950  67  13  20  
Aluminium Re = 1540  91  4  5  
Aluminium Re = 2300  60  18  22  
Hexagonal
 Copper Re = 1950  25  16  59 
Aluminium Re = 1950  19  11  70  
Nickel Re = 1950  19  12  69  
Steel Re = 1950  14  14  72  
Aluminium Re = 1540  31  11  58  
Aluminium Re = 2300  16  12  71  
Quadrangular
 Copper Re = 1830  94  3  3 
Aluminium Re = 1830  90  4  9  
Nickel Re = 1830  88  5  7  
Steel Re = 1830  87  4  9  
Aluminium Re = 1200  95  2  3  
Aluminium Re = 2200  87  5  8  
Lozenge
 Copper Re = 1830  21  8  71 
Aluminium Re = 1830  19  6  75  
Nickel Re = 1830  14  8  78  
Steel Re = 1830  10  7  83  
Aluminium Re = 1200  75  10  15  
Aluminium Re = 2200  30  15  55  
Sinusoidal
 Copper Re = 1830, 1950  65  17  18 
Aluminium Re = 1830, 1950  59  18  23  
Nickel Re = 1830  52  20  28  
Steel Re = 1830, 1950  50  19  31  
Aluminium Re = 1200, 1540  88  5  7  
Aluminium Re = 2200, 2300  35  20  45 
From Table 2, the value of decreases with Reynolds number. Thus, decreasing the value of Reynolds number improves the heat transfer process. However, the value of Reynolds number is controlled by the actual operating conditions of the heat recovery wheel. In addition, at the same Reynolds number, copper shows the best heat transfer performance. Nevertheless, copper is more expensive than aluminium.
Generally, the "Circular" and "Quadrangular" are the two shapes that give the best heat transfer response in comparison to the "Sinusoidal" shape, which is commonly used. However, they may be not considered as the optimum choice from construction point of view.
It is concluded that the optimum thermal cooling cases can be stated as:
1. When considering the same range of Reynolds number (18301950) with different materials: Re = 1830, copper wall, quadrangular shape, L_{c} = 94%.
2. When considering the same material (aluminium) with different Reynolds numbers: Re = 1200, quadrangular shape, L_{c} = 95%.
5. Artificial Intelligence (AI)
Both the two artificial intelligence techniques (AI); artificial neural network (ANN) and adaptive neurofuzzy inference system (ANFIS) were used to predict the heat transfer performance of the present cases. This strategy was intended to demonstrate and judge the ability of both ANN and ANFIS to predict the heat transfer performance. Moreover, the advantages/disadvantages of the two AI techniques can be clearly noticed. Thus, the predictions of the investigated cases were divided between the two AI techniques. The results of the present computations were used as input data to the two AI techniques in their training phase.
5.1. Artificial Neural Network (ANN)
An ANN was used to predict the percentage relative length L_{c} for different materials (copper, aluminium, nickel, steel), different Reynolds numbers (1540, 1950, 2300), and different shapes (circular, hexagonal, sinusoidal). A robust learning heuristic for multilayered feedforward neural network, called the Generalized Delta Rule (GDR) or "Back Propagation Learning Rule", was implemented in the present work. The back propagation learning rules are used to adjust the weights and biases of ANNs to minimize the sumsquared error of the network. This is done by continually changing the values of the network weights and biases in the direction of steepest descent with respect to error. The used back propagation of a multilayer ANN is shown in Fig. 12.
The neural network toolbox of the Matlab 7.6 package was chosen to train the ANN [48]. The input data comprises three groups (vectors) of data, which are wall materials, Reynolds numbers, and shapes. The output data comprises one group (vector) of data, which is L_{c}. The computational input and output data were used to train the ANN till it can approximate a function that associates input vectors with specific output. The initial weights as well as the initial biases employed random values between 1 and 1. The nodes in the hidden layer were varied from 2 to 18 for every input pattern and the evaluation of the performance of the network in determining the optimum hidden nodes was carried out. Also, many training cases were operated to get the optimum transfer functions arrangement.
ANN was trained for eighteen different cases. After the ANN was trained, a separate set of unseen test data was supplied as input to the ANN and its performance was evaluated. Table 3 shows the input and the output for each training case. Results for many training cases that were carried out are presented in Table 4. These results are obtained after 1000 epochs. The epoch is a complete iteration of ANN.
Case  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18 
Shape  Circular  Hexagonal  Sinusoidal  
Input1  0.1  0.1  0.1  0.1  0.1  0.1  0.2  0.2  0.2  0.2  0.2  0.2  0.3  0.3  0.3  0.3  0.3  0.3 
Input2  1  2  3  4  2  2  1  2  3  4  2  2  1  2  3  4  2  2 
Input3  1950  1950  1950  1950  1540  2300  1950  1950  1950  1950  1540  2300  1950  1950  1950  1950  1540  2300 
Output  81  74  68  67  91  60  25  19  19  14  31  16  65  59  52  50  88  35 
Key: Input1 (Shape): (0.1) Circular, (0.2) Hexagonal, (0.3) Sinusoidal. Input2 (Material): (1) Copper, (2) Aluminium, (3) Nickel, (4) Steel. Input3 (Reynolds number): 1540, 1950, 2300. Output: L_{c}.
CASE  F1  F2  S1  SSE  SSET 
Circular  Logsig  Purelin  6  0.0573  0.0734 
Hexagonal  Logsig  Purelin  6  0.0607  0.0764 
Sinusoidal  Logsig  Purelin  6  0.0418  0.0697 
All Shapes  Logsig  Purelin  18  0.0217  0.0415 
Key: F1: Transfer function of the first layer. F2: Transfer function of the second layer. S1: Number of neurons in the hidden layer. SSE: Sumsquared error for training vector. SSET: Sumsquared error for testing vector.
It is obvious from table 4 that the increase of number of neurons in the hidden layer (S1) enhances the performance of ANN. Thus, when training cases of "All Shapes" are considered, the lowest values of errors (SSE, SSET) are obtained. The predictions of L_{c} based on new set of input data that has not been used in the training of the neural networks are shown in Table 5.
Figure 13 shows a comparison between computational results and ANN predictions. Based on the results (outputs) of Table 5, Fig. 13, and the previous Tables 3 and 4, it can be said with confidence that the predictions of Table 5 are very good and acceptable. Hence, ANNs are attractive tools for quick and reliable prediction.
Inputs  Output  
Material  Reynolds number  Channel shape  Lc (%) 
2  1600  0.3  84 
2  2000  0.3  56 
1  2000  0.3  61 
2  1600  0.2  27 
2  1850  0.2  22 
1  1850  0.2  28 
2  1440  0.1  93 
2  1850  0.1  77 
1  2000  0.1  78 
Key: Material: (1) Copper, (2) Aluminium, (3) Nickel, (4) Steel. Reynolds number: 1540, 1950, 2300. Channel shape: (0.1) Circle, (0.2) Hexagonal, (0.3) Sinusoidal.
5.2. Adaptive NeuroFuzzy Inference System (ANFIS)
The basic structure of the fuzzy inference system (FIS), Fig. 14, is a model that maps input characteristics to input membership functions (MF), input membership function to rules, rules to a set of output characteristics, output characteristics to output membership functions (MF), and the output membership functions to a singlevalued output or a decision associated with the output [48].
The parameters (e.g., material, Reynolds number, and channel shape) associated with a given membership function could be chosen so as to tailor the membership functions to a collection of input/output data in order to account for the variations in the data values. This is where the socalled neuroadaptive learning techniques can help. These techniques provide a method for the fuzzy modeling procedure to learn information about a data set in order to compute the best membership function parameters.
In the present study, four ANFIS models were developed to predict the performance of a heat recovery wheel in terms of its heat transfer efficiency (output) using the toolbox of Matlab 7.6 [48]. The predictions were based on the present computational results. There are three input sets to the ANFIS predictors, namely: material (Input 1), Reynolds number (Input 2), and channel shape (Input 3). The output of the ANFIS is the length of cold zone (L_{c}). Table 6 shows the input and the output for each training case. The different parameters of the ANFIS models are given in Table 7. All the four ANFIS models were trained until the sum of the squared error reaches 0.006. Thirty epochs were sufficient for the four models.
Case  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18 
Shape  Quadrangular  Lozenge  Sinusoidal  
Input1  1  2  3  4  2  2  1  2  3  4  2  2  1  2  3  4  2  2 
Input2  1830  1830  1830  1830  1200  2200  1830  1830  1830  1830  1200  2200  1830  1830  1830  1830  1200  2200 
Input3  0.4  0.4  0.4  0.4  0.4  0.4  0.5  0.5  0.5  0.5  0.5  0.5  0.6  0.6  0.6  0.6  0.6  0.6 
Output  94  90  88  87  95  87  21  19  14  10  75  30  65  59  52  50  88  35 
Key: Input1 (Materials): (1) Copper, (2) Aluminium, (3) Nickel, (4) Steel. Input2 (Reynolds number): 1200, 1830, 2200. Input3 (Channel shape): (0.4) Quadrangular, (0.5) Lozenge, (0.6) Sinusoidal. Output: L_{c}
ANFIS Model  Number of MF (Inputs)  Input MF type  Output MF type  Rules of Fuzzy  Optimization Method  No. of Epochs 
Quadrangular  2 ´ 6  Gaussmf  Linear Grid  Partition  Hybrid  30 
Lozenge  2 ´ 6  Gaussmf  Linear Grid  Partition  Hybrid  30 
Sinusoidal  2 ´ 6  Gaussmf  Linear Grid  Partition  Hybrid  30 
All Shapes  3 ´ 18  Gaussmf  Linear Grid  Partition  Hybrid  30 
The structure of the ANFIS model for quadrangular shape (as an example of the four ANFIS models) is shown in Fig. 15. The output surface of performance, Fig. 16, explains the variation of quadrangular predictions with the three inputs (material, channel shape, Reynolds number).
After ANFIS had been trained, it was tested by checking its predictions by a set of data that had not been seen by ANFIS before, Table 8. The comparison between present computational results and ANFIS predictions for values of L_{c} is shown in Fig. 17.
When comparing the results (output) of Table 8 and Fig. 17, with the training Table 6, it is clear that the results (output) of Table 8 was very reasonable and wellaccepted. Thus, ANFIS proves to be an effective and easytouse prediction technique.
Inputs  Output  
Material  Reynolds number  Channel shape  Lc (%) 
2  1300  0.6  82 
2  1750  0.6  61 
1  1900  0.6  62 
2  1100  0.4  96 
2  1750  0.4  92 
1  1750  0.4  96 
2  1300  0.5  70 
2  1900  0.5  15 
1  1900  0.5  19 
Key: Materials: (1) Copper, (2) Aluminium, (3) Nickel, (4) Steel. Reynolds number: 1100, 1300, 1750, 1900. Channel shape: (0.4) Quadrangular, (0.5) Lozenge, (0.6) Sinusoidal.
6. Conclusions
In the present investigation, a computational study of heat recovery wheel was carried out for different materials and crosssectional shapes. Also, the Reynolds number of flow was considered as important parameter. The main objective of the study is to find the combination of parameters that give the optimum performance (best heat transfer). The performance was evaluated by modeling the channel flow of the wheels. Also, artificial intelligence techniques (ANN, ANFIS) were proposed to predict the thermal behavior of the investigated cases.
Based on the above discussions, the following concluding points can be stated:
1. The present computational model and solution scheme were effectively validated. Hence, the outputs of present study are to be considered with confidence.
2. Generally, the circular and quadrangular shapes are the two shapes that give the finest heat transfer response in comparison to the "Sinusoidal" shape, which is commonly used. However, they may be not considered as the optimum choice from construction point of view.
3. It can be stated that the optimum thermal cooling cases are as follows:
• When considering the same range of Reynolds number (18301950) with different materials: Re = 1830, copper material, quadrangular shape, L_{c} = 94%.
• When considering the same material (aluminium) with different Reynolds numbers: Re = 1200, quadrangular shape, L_{c} = 95%.
4. Although the hexagonal shape has good structural advantages, it is not the best choice when concerning the thermal performance.
5. The circular crosssection (shape), which is simple, gives much better thermal performance than the sinusoidal crosssection that is commonly used in heat exchange wheels. However, when using circular channels to construct the recovery wheel, there will be channels between them that are not circular. Thus, the overall performance may deteriorate.
6. For all cases, the wall materials can be arranged from best to worst as: copper, aluminium, nickel, and steel when considering the thermal performance.
7. It is very important to state that the above concluding points are based on the stated flow and thermal fields. Other concluding remarks may be obtained for other operating conditions.
8. The artificial intelligence techniques (ANN, ANFIS) proved to be very effective in predicting the thermal characteristics. They are much easier to program and operate than other computational techniques. However, they need computational and/or experimental data for training.
9. Energy saving approach adapted in this study guarantees contaminantfree preheated or precooled fresh air, which is the major concern in health care facilities and large crowded commercial structures.
Nomenclature
d  : Channel hydraulic diameter 
F1  : Transfer function of the first layer 
F2  : Transfer function of the second layer 
L  : Channel length 
 : Cold zone percentage relative length: 
 : Hot zone percentage relative length: 
 : Middle zone percentage relative length: 
 : Reynolds number 
S1  : Number of neurons in the hidden layer 
 : friction velocity 
 : Inlet velocity 
y  : Distance to the first computational point off the wall 
y+  : Dimensionless distance between the wall and first computational point 
Greek  
 : Kinematic viscosity 
 : Flow density 
 : Wall shear stress 
Abbreviations  
AHU  : Air Handling Unit 
AI  : Artificial intelligence 
ANFIS  : Adaptive neurofuzzy inference system 
ANN  : Artificial neural network 
ASHRAE  : American Society of Heating, Refrigerating and Air Conditioning Engineers 
CFC  : Chlorofluorocarbons 
FIS  : Fuzzy inference system 
GDR  : Generalized delta rule 
HVAC  : Heating, Ventilation and Air Conditioning 
MF  : Membership functions 
SIMPLE  : Semiimplicit method for pressurelinked equations 
SSE  : Sumsquared error for training vector 
SSET  : Sumsquared error for testing vector 
References