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\title{Experimental and Numerical Model for Thermal Design of Air Cooled Condenser}
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\begin{document}

             \author[1]{Ali Hussain  Tarrad}

             \affil[1]{  Private Consultant Engineer}

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\date{\small \em Received: 12 December 2014 Accepted: 2 January 2015 Published: 15 January 2015}

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\begin{abstract}
        


The present work outlines a simple procedure for the thermal design of air cooled heat exchanger. The step by step numerical technique is implemented a long the steam flow direction to ratea vertical orientation single pass two tube rows heat exchanger. A saturated steam at atmospheric pressure of flow rate ranged between (18-36) kg/hr was passed throughout the tubes to provide a steam velocity in the range between (3.5) and (7) m/s. The condenser entering air dry bulb temperature was ranged between (21) and (42) oCand condensation load capacity fell in the range of (11) and (22.5) kW. The air flow rate was (1200) cfm and (2400) cfm corresponding air face velocities of (3 and 6) m/s. The simulated data showed excellent agreement with the measured rating parameters regarding the heat exchanger load duty and exit air cooling temperature. The respective discrepancy for the heat duty was within (12) % and (-5) % and the exit air temperature was underestimated by (5) %.

\end{abstract}


\keywords{condensation, heat exchangers, air cooled, steam condensers, modeling.}

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\textcolor{GJBlue}{\footnotesize \\ Artificial Intelligence formulated this projection for compatibility purposes from the original article published at Global Journals. However, this technology is currently in beta. \emph{Therefore, kindly ignore odd layouts, missed formulae, text, tables, or figures.}}
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\let\tabcellsep& 	 	 		 
\section[{Introduction}]{Introduction}\par
n ACC, heat is transferred from the process fluid (steam) to the cooling medium (air) through the fin tube bundle. It depends on the temperature difference (driving force) between air and steam so that the dry bulb temperature of air is a key control of the ACC performance. Therefore, the dry cooling system with ACC is less efficient in hot ambient. \hyperref[b0]{Kutscher and Costenaro (2002)}  \hyperref[b0]{[1]}developed a model to assess the cost and performance of different methods for using supplemental evaporative cooling to boost the summer performance of air cooled condenser in geothermal power plants. A system in which water directly contacts the condensate tubes has the highest performance and is economically the most attractive. However, consideration of scaling and corrosion must be addressed.\par
Jabardo and Mamani (2003) \hyperref[b1]{[2]} developed a simulation model based on dividing the condenser into three zones as superheating, condensing and subcooling.Each region was treated as an independent heat exchanger. The discrepancy between the experimental data and the simulation results has shown a good agreement.  {\ref Gadhamshettyet al. (2006)}  \hyperref[b2]{[3]}, proposed a new approach to alleviate the performance decline in air cooled condenser with increasing the air dry-bulb temperature. A chilled water thermal energy storage system is used to pre-cool the inflow air to the ACC whenever the ambient air temperature increases above (20 o C). The proposed procedure used the test 171 MW plant saves (2.5\%) of the power (4.2MW) without using any water or incurring any water treatment cost.\par
The work of Tarrad and coworkers \hyperref[b3]{[4]}, \hyperref[b4]{[5]} and \hyperref[b5]{[6]} was concentrated on the heat transfer performance and modeling of air cooled heat exchangers. Their work showed that the thermal enhancement is a dependent measure of the fin geometric variables and row intensity of the air cooled heat exchanger. \hyperref[b6]{Tarrad (2010)}  \hyperref[b6]{[7]} developed a numerical model for performance prediction of dry cooling of the air cooled condensers applied in power plants technology. A computer code was built that depends on the idea of using the row by row technique for estimating the heat transfer coefficient, air temperature and air physical properties distribution in the air flow direction from row to row. The model results showed an improvement in the condensation load up to (23\%) when air pre-cooling mode applied to inflow air to the ACC to lower the drybulb temperature from (45) to (28) o C at air face velocity of (3.6) m/s.\par
Tarrad and Khudor(2015) \hyperref[b7]{[8]} have presented quite a simple and adaptable correlation for the air side heat transfer coefficient in the form of dimensionless group criteria. It depends on the fin geometry, row and tube intensity and operating conditions. They concluded that their correlation predicts the heat duty and overall heat transfer coefficient of the case study heat exchangers with total mean absolute errors of (13\%) and (10\%) respectively. More recently, Tarrad and Al-Nadawi (2015) \hyperref[b22]{[9]} presented a model for the air cooled condenser. Its strategy depends on the tube by tube technique implemented for a window type air conditioning unit circulating different refrigerant such as R-22, R-407C and R-407A. They postulated that the predicted heat duty of these refrigerants by their model has showed excellent agreement and was within the range of (-5\%) and (+1.7\%).\par
An experimental facility was constructed to allow two types of condensing system worked as a test arrangement, Altameemi (2007)  {\ref [10]}. Each one represents a separate unit having all the specifications and instruments which allows condensation data to be collected over a range of operating conditions, figure \hyperref[b0]{(1)}. Air cooled condenser and shell and tube heat exchanger were used as a single or in a hybrid arrangement.The experimental apparatus was modified after a first set of data to ensure an accurate operation condition compatibility to weather criteria in Iraq in hottest period. This was accomplished by adding an electrical heating coil works as air heater for a set exit temperatures. 
\section[{b) Heat Exchanger}]{b) Heat Exchanger}\par
Air cooled condenser is a finned tube heat exchanger, typically used for the process which consists of a finned-tube bundle with rectangular box headers on both ends of tubes. The "ACC" used in the present work was a vertical type, a single pass having two rows with flat side tubes occupied each rowas shown in figure \hyperref[b1]{(2)}.Flat side tube geometry used to enhance heat transfer inside tube with extra heat transfer area and reduce pressure drop outside tube. The tubes material are brass which has excellent physical properties \hyperref[b8]{[11]}, compared with other materials. The fins are constructed to the tubes so each fins row contains (70) fins attached to tube in equal pitch about (4.18) mm.The fins material is a copper, the physical characteristicand dimensions are listed in table \hyperref[b0]{(1)}.  The whole assembly is mounted on legs with a rubber and fasteners to well-set during operation. 
\section[{Global}]{Global} 
\section[{Global Journal of Researches in Engineering ( ) Volum}]{Global Journal of Researches in Engineering ( ) Volum}\par
The uncertainty percentage for the measurement was estimated to be within (± 2 \%) for the whole tests range in this work, Altameemi [10]. 
\section[{III.}]{III.} 
\section[{Model Methodology a) Model Technique and Assumptions}]{Model Methodology a) Model Technique and Assumptions}\par
The air cooled steam condenser is shown in figure \hyperref[b2]{(3)}.The steam flows inside the flat tube. The air flow is perpendicular to the tubes across the fins so that both process and service fluids pass in a cross flow pattern on both sides of the exchanger wall. A row by row technique was implemented and each row in the single pass condenser is subdivided into segments in the height direction of the heat exchanger, figure \hyperref[b2]{(3)}. Each segment is treated as a small condenser with a specified geometry. It is associated with steam parameters such as mass flow rate, pressure and temperature. The air side has also specific air mass flow rate and inlet air temperature. 
\section[{Figure (3) : A step by step modeling representation}]{Figure (3) : A step by step modeling representation}\par
The assumptions of the ACC modeling are: 1. The air mass flow rate is assumed to be distributed uniformly over the whole face of the air cooled steam condenser. To ensure this assumption, the inlet duct configuration and mal-distribution was checked. 2. Homogenous temperature distribution of air all over the frontal face area of the heat exchanger and hence for each segment. 3. The mean air exit temperature of each row is considered to be the inlet to the next row. 4. The steam temperature variations between the rows were assumed to be negligible. 5. The inlet air velocity for each row was assumed to be uniform and is represented by a specified value. 6. The steam mass flow rate from the main header is divided equally for each row. 7. Heat transferred away by convection and radiation is neglected. 8. Material properties of the finned tube bundle are constant with temperature variations. The air side dry-bulb exit temperature that leaves the condenser is considered as the target parameter of the present model. 
\section[{b) Steam Side Heat Transfer Coefficient}]{b) Steam Side Heat Transfer Coefficient}\par
i. 
\section[{Condensation Mode}]{Condensation Mode}\par
When the vapor velocity is high, the vapor will pull the liquid along the interface. This is because the vapor velocity at the interface must drop to the value of the liquid velocity. If the vapor flows downward this addition force will increase the average velocity of the liquid and thus the film thickness is decreased. This in turn, will decrease the thermal resistance of the liquid film and thus increasing heat transfer. For condensation inside tubes in air cooled condenser model the tube inside diameter is very small and the influence of tube wall curvature is important in condensation phenomenon. The correlation postulated by Boyko-Kruzhilin (1967) \hyperref[b10]{[13]} was used to estimate the mean condensing coefficient for a steam between inlet quality and outlet quality inside tubes as below:? ??,???? = ? ???? ? ?? ?? ?? ?? ? ?? +?? ?? ?? ?? ? ?? 2 ?\textbf{(1)}\par
Where:? ?? ?? ?? ? ?? = 1 + ?? ?? ??? ?? ?? ?? ?? ?? (2.a) ? ?? ?? ?? ? ?? = 1 + ?? ?? ??? ?? ?? ?? ?? ?? (2.b)\par
h lo is the sensible heat transfer coefficient assuming that the total fluid is flowing with condensate properties (condensate filled the tube and was flowing alone). This can be evaluated with the implementation of any available correlation for forced convection in tubes.\par
Boyko and kruzhilin \hyperref[b10]{[13]}suggested the following correlation:? ???? = 0.021 ? ?? ?? ?? ?? ? ???? ???? 0.8 ???? ?? 0.43\textbf{(3)}\par
In a condenser, where the inlet stream was assumed to be saturated vapor and the vapor will be totally condensed,for these conditions equation (1) becomes, \hyperref[b11]{Sinnott (2005)}  \hyperref[b11]{[14]}:? ??,???? = ? ???? ? 1+ ? ?? ?? ?? ?? 2 ?\textbf{(4)}\par
In the present work it is suggested to divide the tube length into equal increments. The quality change across each increment of length (?z) is calculated to be (?x),(x i -x e ). The heat transfer of steam in two phase region depends on the quality change as a demonstrative factor to describe the amount of heat released at constant temperature. After the determination of the quality limits at each increment, it was utilized to calculate the local condensing heat transfer coefficient at the mid-quality magnitude of each (\par
). Assuming that the local value is constant over particular quality range ( ), then: Where represents the mid-quality which is equal:? ?? ?? ?? ? ???? = 1 2 ?? ?? ?? ?? ? ?? + ? ?? ?? ?? ? ?? ?\textbf{(5.}?? ???? = (?? ?? + ?? ?? ) 2 (5.d)\par
So that equation (1) becomes:? ??,???? = ? ???? ??1 + ? ?? ?? ? ?? ?? ?? ?? ? ?? ???? ?\textbf{(6)}\par
At high condensing loads, with vapor shear dominating, tube orientation has no effect, and equation (1) may also be utilized for horizontaltubes, Perry (1999) \hyperref[b12]{[15]}.\par
ii. 
\section[{Single Phase Forced Convection Turbulent flow:}]{Single Phase Forced Convection Turbulent flow:}\par
Numerous relations have been proposed for predicting fully developed turbulent flow in uniform cross-section tubes. The Dittus and Boelter correlation is suitable for moderate temperature variation, \hyperref[b13]{Incropera and Dewitt (1996)}  \hyperref[b13]{[16]}. TheDittus-Boelter is usually given in the form:? = 0.023 ? ?? ð??"ð??" ?? ?? ? ???? 0.8 ???? ??\textbf{(7)}\par
Where Reynolds and Prandtl numbers are estimated from: For the case where the condensing load is small, vertical tube condenser may maintain sub-cooling in the bottom end of the tube. For this condition, if the temperature difference at the inlet and exit is greater than 10 o C, then the moderate temperature variation assumption is invalid. However, for flows characterized by large property variations, Sieder and Tate correlation was used to calculate the heat transfer coefficient. \hyperref[b14]{Incropera and Dewitt (2006)}  \hyperref[b14]{[17]} recommends:? = 0.027 ? ?? ð??"ð??" ?? ?? ? ???? 0.8 ???? 1 3 ? ? ?? ?? ?? ? 0.14\textbf{(9)}\par
Laminar flow: Below a Reynolds number of about (2000), the flow in pipes will be considered to fall in the laminar region.  {\ref Sieder and Tate (1930)}  \hyperref[b15]{[18]} recommends the following simple correlation:? = 1.86 (???? ????) 0.33 ? ?? ?? ?? ? 0.33 ? ?? ?? ?? ? 0.14 (10)\par
Here (L) is the length of the tube or conduits.\par
For steam condensation where the condensed fluid is water, a special correlation for water could be used for more accurate estimation for inside coefficient.  {\ref Eagle and Ferguson (1930)} \hyperref[b16]{[19]} data bank was adapted by \hyperref[b17]{Sinnott (1999)}  \hyperref[b17]{[20]} to develop specifically correlation for water as follows:? ?? = 4200 (1.35 + 0.02 ?? ?? ) ? ?? ?? 0.8 ?? ?? 0.2 ?\textbf{(11)}\par
Equation ( \hyperref[formula_10]{11}) is applicable for all range of Reynolds number. However, if the estimated inside heat transfer coefficient by this equation is large compared with another used correlation, as described above, the smallest value will be taken.\par
For noncircular tubes all the above equations may be applied by using an effective diameter as a characteristics length. It is termed as the hydraulic diameter and is defined as: Re D ? 10,000 and L/D i ? 10?? ? = 4 ?? ?? ??\textbf{(12)}\par
Where A c and P are the flow cross sectional area and wetted perimeter. 
\section[{c) Air Side Heat Transfer}]{c) Air Side Heat Transfer}\par
i. 
\section[{Heat Transfer Coefficient}]{Heat Transfer Coefficient}\par
Heat transfer performance of the tube bank is determined by flow pattern, which is strongly dependent on the arrangement of the tubes. The longitudinal tube spacing and transverse tube spacing could influence the thermal characteristics performance of heat exchanger. This has been studies by Tarrad et al. \hyperref[b5]{[6]}, Grame \hyperref[b18]{[21]} and Jones \hyperref[b19]{[22]}.On the other hand fin spacing, fin thickness and fin height also affect the performance of finned tube heat exchangers as reported by \hyperref[b20]{Briggs (1963)}  \hyperref[b20]{[23]} and Tarrad and Khodur(2015) \hyperref[b7]{[8]}.\par
In the present work, the forced convection heat transfer coefficient for the triangular fins could be predicted approximately using correlation of internal flow in ducts for laminar or turbulent flow as stated above. Reynolds number for air flow inside a triangle fin with using a hydraulic diameter approach is calculated as below:???? = ?? ?? ?????? ?? ? ?? (13.a)\par
The velocity u max is calculated at the minimum cross flow area S m in tube bundle, hence:?? ?????? = ????? ?? ?? ?? ?? (13.b)\par
In the present work minimum cross flow area was calculated according to the air side geometry as:  The tube wetted perimeter is the total tube perimeter in contact with the steam. It is given by:?? ?? =?? ?? = ?? ?? ??,?? + 2 ??? ??,?? ? ?? ??,?? ?\textbf{(15)}\par
The hydraulic diameter is given by: The tube walls wetted by direct contact with steam transfer heat directly from the steam side to the outside air,hence the heat transfer area: ?? ?? = 2 ??? ??,?? ? ?? ??,?? ??? ?? + ?? ?? ??,?? ?? ?? \hyperref[b14]{(17)} Each fin attached to the tube with approximately (1 mm) thickness along the depth. The contact area is calculated as:?? ?,?? = 4 ?? ?? ?? ??\textbf{(16}?? ?????? = ?? ?????? ?? ????????\textbf{(18)}\par
The total heat transfer area is given by:?? ??,?? = ?? ?? ? ?? ??????\textbf{(19)}\par
iii. 
\section[{Air Side Tube Characteristics}]{Air Side Tube Characteristics}\par
The cross section of the tube outer surface is shown in figure (4.b). The face area of one tube and fin set in one increment, figure (4.c) is defined as:?? ð??"ð??"?? ,?????? = ??? ???????? ,?? + ?? ? ??? ??????\textbf{(20)}\par
Therefore, the area blocked by the fins is given by:?? ???? = ?? ?????? ?? ?? ??? ð??"ð??" ?? ð??"ð??" + ?? ð??"ð??" ?? ð??"ð??" ?\textbf{(21)}\par
The area available for air flow is represented as the total area less than the area blocked by the fins together with the area occupied by the tube for steam flow as follows:?? ?? = ?? ð??"ð??"?? ,?????? ? ??? ???? + ?? ???????? ,?? ?? ?????? ?\textbf{(22)}\par
The perimeter of the tube which is directly in contact with air is given by:?? ?? = ?2 ?? ?????? ?? ?? ??? ð??"ð??" ? ?? ð??"ð??" ? + ??? ?????? ? ?? ?????? ?? ð??"ð??" ?? ?? ?? (\textbf{23})\par
The hydraulic diameter is:?? ?,?? = 4 ?? ?? ?? ??\textbf{(24)}\par
The tube wall which is in contact with steam on the inside surface and with air on the outside surface directly transfers heat from the steam to the outside air. This constitutes the heat transfer area:?? ??,?? = ?2 ??? ??,?? ? ?? ??,?? ? ?1 ? ?? ð??"ð??" ?? ?? ? + ?? ?? ??,?? ? ?? ??????\textbf{(25)}\par
The fins also confirm the heat transfer from the steam to air. Therefore fin surface area is defined as follows:?? ð??"ð??",?? = 2 ?? ?????? ?? ?? ??? ð??"ð??" ?? ð??"ð??" ?\textbf{(26)}\par
The total heat transfer area become: Here ? f is the fin efficiency, when (?? ?? = ?? ??,?? + ?? ð??"ð??" ?? ð??"ð??",??\textbf{(27)}0, dT x l dx = =\par
) then the efficiency is given by, \hyperref[b21]{Kreith (1999)}  \hyperref[b21]{[24]}. In the present work, the fin is represented by a schematic diagram shown in figure \hyperref[b4]{(5)}, hence:?? ð??"ð??" = tanh ???? ???? (28.a) ?? = ? ? ?? ?? ?? ?? ?? ?? ?? (28.b)\par
Therefore, the total surface efficiency of the fin, ? o is therefore expressed as below:?? ?? = 1 ? ?? ð??"ð??" ?? ?? ?1 ? ?? ð??"ð??" ? (29) 
\section[{d) NTU Effectiveness Relations:}]{d) NTU Effectiveness Relations:}\par
The NTU method offers more advantages for analyzing heat exchangers. It shows that iterative procedure is not required when inlet and outlet temperatures are unknown. For any heat exchanger, the total heat rejected from the hot fluid to the cold fluid is dependent on the heat exchanger effectiveness and also on the heat capacity of each fluid. This can be calculated as follows:?? = ?? ?? ?????? ??? ?,?? ? ?? ??,?? ? (30.a)\par
The heat capacity, c, the extensive equivalent of the specific heat, determines the amount of heat a substance absorbs or rejects per unit temperature change, where:?? = ??? ???? (30.b)\par
The effectiveness is the ratio of the actual amount of heat transferred to the maximum possible amount of heat transferred and defined as:?? = ?? ?? ???? ?? (31.a)\par
In the present work, the heat duty of each increment is calculated by the effectiveness-NTU method. The effectiveness relation for single-phase fluid cross flow is given below, \hyperref[b23]{Holman (2002)}  \hyperref[b23]{[25]}:?? = 1 ? ?????? ? ?????? (??? ?? ?? ??)?1 ?? ?? ?? ? (31.b)\par
And for Counter flow:?? = 1??????? [??? (1??? ?? )] 1? ?? ?? ?????? [??? (1??? ?? )]\par
(32.a)\par
Where:?? = ?? ?0.22 (32.b) ?? ?? = ?? ?????? ?? ?????? (32.c) ?? = ?????? = ???? ?? ?????? (32.d)\par
This is the effectiveness relationship for a cross flow, single-pass heat exchanger with both fluid unmixed. For tow-phase fluid flow, the effectiveness relation is:?? = 1 ? ??????(???????)\textbf{(33)}\par
The overall heat transfer coefficient (U), takes into consideration the total thermal resistance to heat transfer between two fluids. Even though the convective heat transfer coefficients may be different on the two sides of the heat exchanger, the (UA) product is the same on either side. This is because all of heat taken from hot side must be transferred to the cold side. Overall heat transfer coefficient defined as, \hyperref[b17]{Sinnott (1999)}  \hyperref[b17]{[20]}:1 ?? ?? = 1 ? ?? ?? ?? + 1 ? ð??"ð??"?? ,?? ?? ?? + ?? ?? ln ? ?? ?? ?? ?? ? 2 ?? ???????? + ? ?? ?? ?? ?? 1 ? ð??"ð??"?? ?? ?? ?? ? + ? ?? ?? ?? ?? 1 ? ?? ?? ?? ?\textbf{(34.a)}\par
By neglecting the effect of fouling on both sides of the heat exchanger, and inside surface efficiency, the overall heat transfer coefficient is reduced to:1 ?? ?? = 1 ? ?? ?? ?? + ?? ?? ln ? ?? ?? ?? ?? ? 2 ?? ???????? + ? ?? ?? ?? ?? 1 ? ?? ? (34.b) e) Model Scheme\par
The suggested model in the present work was prepared in the form of a computer program designated as ACCRP. It was written with the aid of Liberty Basic Language, \hyperref[b24]{[26]}. Multi iteration schemes were implemented to obtain the final rating data of the air cooled condenser. These were related to the air stream side and steam flow inside the tubes. A complete description and flow diagram of this code could be found in Altameemi  {\ref [10]}.\par
IV. 
\section[{Model Verification}]{Model Verification}\par
The experimental results are compared to the theoretical simulation results using the ACCRP computer program. The results showed a good agreement with the experimental data.The present model was verified by the implementation of the pressure. The model calculation scheme depends on the prediction of the air exit dry bulb temperature that on the lee side of the condenser under steady state conditions. Hence, this parameter was considered as an indication for the uncertainty percentage of the simulation process of the present model. Accordingly, the accuracy of the present row by row and step by step strategy is related to how far be the predicted air temperature and the condenser load from the experimental data. The uncertainty of each parameter and its discrepancy or scatter from the experimental data was estimated from:? ± = ? ??? ?????????????????? ?? ???????????????????????? ? ???????????????????????? (35)\par
Here ? represents either the exit air temperature or the heat duty of the condenser. 
\section[{a) Thermal Load}]{a) Thermal Load}\par
The experimental data collected in the present work showed its dependency on the air velocity and its temperature. Figure \hyperref[b5]{(6)} shows the variation of the condenser load with entering temperature at two different velocities for a steam mass flow rate of (33.5) kg/hr. It is obvious that increasing air velocity or reducing the entering condenser air temperature will enhance the condenser load.Increasing the air velocity The ACC thermal loads for different experimental conditions exhibited a maximum deviation of (+8 \%), and a minimum deviation of (-5 \%) for air velocity of (3) m/s.The corresponding values for (6) m/s, the maximum discrepancy of (+ 11 \%), as shown in figures \hyperref[b6]{(7)} and \hyperref[b7]{(8)}. It is quite clear that the uncertainty in the model prediction was better at the low air velocity than that at the higher one. Figure \hyperref[b7]{(8)} : Comparison of experimental and theoretical ACC thermal load at air velocity of (6) m/s Figure \hyperref[b22]{(9)} shows the comparison between the measured experimental heat duty and that predicted by the present modal for the entire operating conditions considered in the present work. The model predicted the condensation load with a high confidence and it lies with a scatter of (+12) \% and (-5) \% for more than (98) \% of the data points. Verification of the air exit temperature samples for (3 and 6) m/s are shown in figure  {\ref (10)}. It is obvious that all of the results are under predicted by (5 \%). The most attractive feature of the present model is its response to the variation of the operating conditions. These conditions are related to the condensation loading, air temperature and its flow rate. The distribution of the overall heat transfer coefficient with the tube length is illustrated in figures \hyperref[b8]{(11)}, \hyperref[b9]{(12)} for the ACC under low and high air velocity respectively. The present model showed that the local overall heat transfer coefficient for air cooled condenser varies with increment and row position in the air direction towards the exit side of the condenser. The variation with increment position is due to the condensation heat transfer variation with vapor fraction at each section. The variation with row position is due to the variation in air side heattransfer coefficient in the air direction.\par
It is obvious that the choice of increasing the air flow rate and flow velocities with (100\%) by fanning a higher air volumetric flow may be considered to achieve high heat transfer. This is due to the increaseof air side heat transfer coefficient, especially for hot ambient condition when performance in a credible manner was required.The air velocity is an important character in air cooled condenser overall design and determination of the face velocity. However it is usually falls within the range of (1.5) to (4) m/s, Tarrad (2010) \hyperref[b6]{[7]}. It is recommended for the face velocity of the air a value which is not exceeding (3) m/s, for pressure drop consideration, \hyperref[b25]{Wilber and Zammit (2005)}  \hyperref[b25]{[27]}.  
\section[{Conclusions}]{Conclusions}\par
The present work revealed the following findings:\par
1. Thermal rating model for the ACC has been built successfully to predict the thermal load and temperature distributions across the heat exchanger. It showed excellent agreement between the experimental and predicted data of the exit air dry bulb temperature and condensation load. \begin{figure}[htbp]
\noindent\textbf{2}\includegraphics[]{image-2.png}
\caption{\label{fig_0}Figure ( 2}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-3.png}
\caption{\label{fig_4}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-4.png}
\caption{\label{fig_5}A}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-5.png}
\caption{\label{fig_6}1 2??}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{44}\includegraphics[]{image-6.png}
\caption{\label{fig_7}Figure ( 4 ): 4 ??}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{5}\includegraphics[]{image-7.png}
\caption{\label{fig_9}Figure ( 5 ):A}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-8.png}
\caption{\label{fig_10}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{7}\includegraphics[]{image-9.png}
\caption{\label{fig_11}Figure ( 7 ):A}\end{figure}
    \begin{figure}[htbp]
\noindent\textbf{(} \par 
\begin{longtable}{P{0.08952546296296296\textwidth}P{0.5607638888888888\textwidth}P{0.11313657407407408\textwidth}P{0.08657407407407407\textwidth}}
\multicolumn{3}{l}{Experimental and Numerical Model for Thermal Design of Air Cooled Condenser}\tabcellsep \\
\tabcellsep Parameter\tabcellsep Value\tabcellsep \\
\tabcellsep Width (W), mm\tabcellsep 590\tabcellsep \\
\tabcellsep Depth (D), mm\tabcellsep 30\tabcellsep \\
\tabcellsep Height (H), mm\tabcellsep 320\tabcellsep \\
Core\tabcellsep No. of Tubes\tabcellsep 110\tabcellsep \\
\tabcellsep No. of Tubes/Row\tabcellsep 55\tabcellsep \\
\tabcellsep No. of Rows\tabcellsep 2\tabcellsep \\
\tabcellsep No. of fins/ Tube (on both sides) Transverse Distance (X T ) to flow, mm Longitudinal Distance (X L ) to flow, mm\tabcellsep 140 11.25 15\tabcellsep Year 2015\\
\tabcellsep Frontal Area (A ?ace ), m 2\tabcellsep 0.1888\tabcellsep 15\\
Fin\tabcellsep Pitch (? ? ), mm Length (l ? ), mm Thickness(t ? ), mm Area of a Single Fin (A ? ), mm 2 Material Thermal Conductivity (W/m.C), [12]\tabcellsep 4.18 8.05 0.18 36.12 Copper 388\tabcellsep XV Issue III Version I\\
Tube Area\tabcellsep Height (H t ), mm Depth (D t ), mm Thickness (t t ), mm Material Inner tube surface Thermal Conductivity (W/m. o C), [12] Total Surface Area (A total ), m 2 Total Fin Surface Area, m 2 Total Bare Tube Area, m 2\tabcellsep 2.35 12 0.24 Brass Smooth 119 3.935 3.029 0.906\tabcellsep ( ) Volume A of Researches in Engineering\\
\tabcellsep \tabcellsep \tabcellsep Global Journal\end{longtable} \par
 
\caption{\label{tab_0}Table ( 1}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{P{0.0411504424778761\textwidth}P{0.6734513274336283\textwidth}P{0.04247787610619469\textwidth}P{0.0008849557522123894\textwidth}P{0.01991150442477876\textwidth}P{0.05707964601769911\textwidth}P{0.01504424778761062\textwidth}}
\tabcellsep \multicolumn{2}{l}{Nomenclature}\tabcellsep \\
\tabcellsep \tabcellsep A\tabcellsep \tabcellsep Area\tabcellsep m 2\\
\tabcellsep \tabcellsep C r\tabcellsep 95\tabcellsep Heat Capacity Ratio\tabcellsep -\\
Year 2015 24 Global Journal of Researches in Engineering ( ) Volum A III Version I e XV Issue\tabcellsep \multicolumn{4}{l}{60 65 70 75 80 85 90 Total Surface efficiency 0 Overall cp Specific Heat at Constant Pressure 0.05 0.1 0.15 Tube Length (m) 0.2 D Diameter or Depth F p Fin Pitch g Gravitational Acceleration h Specific Enthalpy h c Steam Condensing Heat Transfer Coefficient 0.25 h o Outside Heat Transfer Coefficient Heat Transfer Coefficient (W/m2.°C) H Height k Thermal Conductivity L Tube Length l f Fin Length Fluid Mass Flow Rate ??Q? n Parameter Defined by Equation (32.b), Correlation index 0.3 Row 1 Row 2 N Number Nu Nusselt Number p Operating Absolute Pressure of Steam P Perimeter of Tube Pr Prandtle Number Condensation Load ?reek Re Reynolds Number S m Hollow Fin Cross Sectional Area t Thickness T Fluid Temperature T ? Temperature Difference u Fluid Velocity U o Overall Heat Transfer Coefficient W Air Cooled Condenser Width Steam Local Quality x eq X T Transverse Tube Pitch to the Flow Direction X L Longitudinal Tube Pith in Flow Direction z Heat Exchanger Cooled Length Symbols Fin Efficiency Effectiveness of the Condenser est. Estimated Value f Fouling , Fin or fluid g gas h Hydraulic diameter, hot fluid 0.35 J/kg.°C m m m/s 2 kJ/kg W/m 2 °C W/m 2 °C m W/m °C m m kg/s ---bar m -kW -m 2 m °C or K °C m/s W/m 2 °C m -m m m i Inside or Inlet Density (kg/m 3 ) µ Viscosity (kg/m.s) f ? o ? ? ? ? Parameter defined by eq. (35) Subscripts inc increment l Liquid lo Liquid Only m mean max maximum a Air min minimum}\tabcellsep Year 2015 25 XV Issue III Version I ( ) Volume A of Researches in Engineering Global Journal\\
\tabcellsep ass. att.\tabcellsep Assumed Value Attached\tabcellsep \tabcellsep o r\tabcellsep Outside ratio,row\\
\tabcellsep c\tabcellsep Condensate , cold\tabcellsep \tabcellsep row\tabcellsep Row Value\\
\tabcellsep \multicolumn{4}{l}{cBK Boyko-Kruzhilin condensation coefficient}\tabcellsep s\tabcellsep Steam Value or Surface\\
\tabcellsep cal.\tabcellsep Calculated Value\tabcellsep \tabcellsep t\tabcellsep Tube\\
\tabcellsep \multicolumn{4}{l}{cond Condenser, Condensation}\tabcellsep tr\tabcellsep tube per row\\
\tabcellsep e\tabcellsep Exit or Equivalent\tabcellsep \tabcellsep Tube Tube Value\\
\tabcellsep eff.\tabcellsep Effective\tabcellsep \\
\tabcellsep eq.\tabcellsep Equivalent\tabcellsep \end{longtable} \par
  {\small\itshape [Note: ? Vapor w Wall Value]} 
\caption{\label{tab_1}}\end{figure}
 			\footnote{© 2015 Global Journals Inc. (US) Experimental and Numerical Model for Thermal Design of Air Cooled Condenser} 			\footnote{© 20 15 Global Journals Inc. (US)} 			\footnote{© 2015 Global Journals Inc. (US)} 		 		\backmatter  			  				\begin{bibitemlist}{1}
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