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Research Papers

On the Merkel Equation: Novel ε-Number of Transfer Unit Correlations for Indirect Evaporative Cooler Under Different Lewis Numbers OPEN ACCESS

[+] Author and Article Information
M. Khamis Mansour

Department of Mechanical Engineering,
Faculty of Engineering,
Beirut Arab University,
Beirut 115020, Lebanon;
Department of Mechanical Engineering,
Faculty of Engineering,
Alexandria University,
Alexandria 21526, Egypt
e-mail: m.mansour@bau.edu.lb

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received June 1, 2016; final manuscript received February 22, 2017; published online April 19, 2017. Assoc. Editor: Srinath V. Ekkad.

J. Thermal Sci. Eng. Appl 9(4), 041005 (Apr 19, 2017) (8 pages) Paper No: TSEA-16-1159; doi: 10.1115/1.4036204 History: Received June 01, 2016; Revised February 22, 2017

An innovative relationship between the effectiveness (ε) and number of transfer unit (NTU) was presented in this work for indirect evaporative cooler (IEC). This relationship is featured by its simplicity in use and has noniterative procedure to be implemented as the traditional one in the literature. The new model can be implemented in sizing and rating design of the IEC at different Lewis numbers with a reasonable accuracy. General integral equation, which is similar to that of Merkel equation, is developed in this model. The new relationship was verified through comparison with experimental and numerical work reported in the available literature for closed or indirect cooling tower (ICT), as an example of IEC. Additionally, the predicted results of the present model were compared to those obtained from the traditional numerical models at different Lewis numbers. The simulated results from the new model show a satisfactory agreement with those obtained from the experimental work of less than 10%. The new correlations can be implemented easily in predicting the thermal design and performance of IEC in any simulation program or in real site.

FIGURES IN THIS ARTICLE
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IEC is steadily used in thermal applications as in air-conditioning systems or industrial processes to reject heat to the surrounding. The IEC is considered as heat exchanger which has three different fluids, cooling process fluid, air, and spray/deluge water. Heat and mass transfer occurred between the spray water and the air passed over a bundle of tubes, in which the cooling process fluid was sensibly cooled. It can work individually or integrated with the ordinary air-conditioning system to reject the thermal load from the building. It is usually used with the chilled beam or ceiling. The prediction of IEC's thermal performance during partial load is paramount for the thermal designer and for the simulation of the whole system integration. The simple reliable relationship which describes the heat exchanger's thermal performance, it attracts the user to implement it either in the theoretical modeling or in the practical site usage. In particular, it helps in execution of the optimization exercise or in developing building energy simulation program.

The development of theoretical models for the IEC thermal performance has attracted many researchers. Those models can be categorized into three streams: (1) numerical solution, (2) analytical work, and (3) lumped/simplified approach.

The heat exchanger is segregated into a number of segments in the numerical solution; the governing equations are solved segment-by-segment in iterative method until convergence is achieved with reasonable accuracy [1]. With this approach, the prediction of heat exchanger's thermal performance could be precisely computed at the expense of lengthy computation time [2]. Researchers [36] have adopted this approach in their works. The analytical approach is the second alternative for the numerical solution; it evaluates accurately the thermal performance of the IEC with less computational time comparable with that of the numerical solution. However, the complicated calculations which are employed in this approach such as Newton–Raphson iteration method make the prediction of IEC performance is so difficult to be practically implemented by the process/operation engineer [1,2]. Analytical solutions have been carried out and reported as in Refs. [710].

In order to evaluate the thermal performance of the IEC by simplified methodology with reasonable accuracy and certainly with less computational time, lumped solution is considered the easiest approach to do that [1,2]. In modeling simultaneous heat and mass transfer process, it introduces complexities in the heat and mass transfer calculations. Goodman [11] developed and presented the potential enthalpy approach to solve the simultaneous heat and mass transfer problem. Threlkeld [12] detailed the enthalpy potential method and presented the logarithmic mean enthalpy difference (LMED), which is analogous to logarithmic mean temperature difference for dry heat exchanger. However, the enthalpy difference is the driving force in wet cooling towers. This method (LMED) has been adopted by many authors such as Facao and Oliveira [13,14]. The second method to simulate the wet heat exchanger is the ε-NTU. One of the benefits with the ε-NTU method for dry heat exchanger is that it can be solved explicitly without iteration. Only the inlet conditions are needed to solve for the heat transfer rate. Alternatively, ε-NTU method for wet heat exchanger is, unfortunately, still an iterative process. Braun et al. [15] developed “effectiveness models” for cooling coils and cooling towers, which utilized the assumption of a linearized air saturation enthalpy and the modified definition of NTUs. The models were useful for both design and system simulation. However, Braun’s model needs iterative computation to obtain the output results and is not suitable for online optimization [16]. Stabat and Marchio [17] adapted the traditional ε-NTU for dry heat exchanger to develop a simplified model for the ICT. The simplification of their model was constructed on the simplification of energy balance and heat and mass transfer equations. The model was solved on iterative approach by assuming the output conditions of the ICT. Hasan [18] modified the traditional ε-NTU for counter/parallel sensible heat exchanger by implementing new mass flow rate parameter. There is no need for the iterative process to use the ε-NTU correlation for wet heat exchanger. The wet specific heat, which represents the iterative term of the wet ε-NTU correlation, has been replaced by the slope of saturation line. Recently, Kim et al. [19] presented an empirical equation, which correlates the effectiveness of wet/dry heat exchanger with the major design parameters through a linear regression equation. The developed correlation was proposed on 2k-factorial experiment design method to estimate the impact of the design parameters and their interactions on the effectiveness of a wet IEC. The superscript k reflects the number of parameters considered in the experiments. Most of those simplified models were developed based on assuming Lewis number of a unit value. Xia and Jacobi [20] declared that the assumption of unity value of Lewis number causes the major source of error in LMED method and a difference of 8% could be introduced in evaluating the total heat transfer rate, under the operating condition of a sensible heat ratio of 50%, as the value of Lewis Factor changed from 1 to 1.16. Recently, Xia et al. [21] suggested that the relative calculation error for the total heat transfer rate could be as high as 20% as a result of assuming Lewis number of unit value.

It can be summarized from this survey that the determination of the wet IEC performance was done by complicated numerical or analytical computation or using ε-NTU correlation for dry counter crossflow heat exchanger with some modifications with a unity value of Lewis number.

In this work, novel simplified correlations for Effectiveness-NTU of counterflow wet IEC operating with both unit and nonunit Lewis number are developed and are presented. Those correlations are handy to be used by the process engineer or IEC designer and they are featured by direct input parameters and no need for iterative process. The validation of this study is carried out on ICT as an example of IEC.

A schematic diagram of a counterflow ICT considers an increment of a cooling process as in control volume dv of Fig. 1 as adopted by Xia et al. [21], where process fluid mass flow rate mf, spray water mass flow rate ms, and air mass flow rate ma flow uniformly of plane area. All vertical sections through the coil are assumed to be the same, in which both streams move in opposite directions. Process fluid flows inside the tubes while the air is passed across the IEC.

The major assumptions that are used to derive the basic modeling equations are summarized as in Refs. [1,2]:

  1. (1)heat and mass transfer in a direction normal to the flows only and in one-dimension,
  2. (2)constant physical properties of both fluids and tube material,
  3. (3)constant heat and mass transfer coefficients throughout the cooling coil,
  4. (4)uniform cross-sectional area of the cooling tower,
  5. (5)constant value of Lewis number of throughout the tower,
  6. (6)the water film on the tubes is considered to be very thin, i.e., the air–water interface area is approximately equal to the outer surface area of dry tubes,
  7. (7)linear dependency of saturation enthalpy of air on temperature,
  8. (8)no heat transfer between the cooling tower and its surrounding occurs, and
  9. (9)complete surface wetting of the tube bundle.

The amount of heat transferred in the incremental volume of dv (Fig. 1) can be written for the air and process fluid, respectively, as Display Formula

(1)δQ=ma*(haj+dhahaj)=ma*dha
Display Formula
(2)δQ=mf*Cf*(Tfj(TfjdTf))=mf*Cf*dTf
Display Formula
(3)δQ=αo*Leeq*dAoCpa*(hsmham)
Display Formula
(4)δQ=Ui*dAi*(TfmTsm)

where Eqs. (1) and (2) are the thermodynamics equations while Eq. (3) expresses the heat and mass transfer from the wetted surface to the air. On the other hand, Eq. (4) stands for expressing the sensible heat transfer from the hot process fluid to the surface

Ui=1(1αi*dodi+1αo+do*ln(dodi)2*kp)

Equation (3) and Leeq are determined based on Xia et al. [21] as follows: Display Formula

(5)Leeq=1(SHF+Le23(1SHF))

where SHF is the sensible heat factor of the heating and humidification process, which is assumed to be constant along the entire heat exchanger surface area and was equal to the ratio of the sensible heat transfer rate to the total heat transfer rate of the entire heat exchanger [1,2] Display Formula

(6)ham=(2haj+dha)2=haj+dha2

From Eq. (1), ham=haj+(δQ/2*ma)Display Formula

(7)Tsm=(Tsj+Tsj+dTsj)2=Tsj+dTsj2
Display Formula
(8)Tfm=(Tfj+TfjdTfj)2=TfjdTfj2

Most of evaporative cooler applications in small range of process fluid temperature. This confirms the use of linear relationship between the saturated air enthalpy and its temperature, as adopted by Threlkeld [12]. Therefore, it is assumed that the saturated air enthalpy could be expressed as follows:

hsj=a+bTsj

where a and b are constants obtained from curve-fitting using least-square method between the enthalpy and saturated temperature Display Formula

(9)hsm=[(a+bTsj)+(a+b(Tsj+dTsj))]2=a+bTsj+b*dTsj2

By substituting Eqs. (7) and (8) in Eq. (4)

δQ=Ui*dAi*(TfmTsm)=Ui*dAi*[(TfjTsj)dTsj2+δQ2*mf*Cf]

Hence Display Formula

(10)dTsj2=δQUi*dAi+(TfjTsj)+δQ2*mf*Cf

and so, Eq. (9) can be formulated as follows:

hsm=a+bTsjb*δQUi*dAi+b*(TfjTsj)+b*δQ2*mf*Cf=a+bTfj+δQ*(bUi*dAi+b2*mf*Cf)

Define, hsfj=a+bTfj and hence Display Formula

(11)hsm=hsfj+δQ*(bUi*dAi+b2*mf*Cf)

By substituting Eqs. (6) and (11) in Eq. (3)

δQ=αo*Leeq*dAoCpa*[(hsfjhaj)δQ2*ma+δQ*(bUi*dAi+b2*mf*Cf)]

By elimination of δQ in one side of the previous equation

δQ*[1+αo*Leeq*dAo2*ma*Cpa+αo*LeeqUi*bCpa*dAodAiαo*Leeq*dAo2*ma*Cpa*mamf*bCf]=αo*Leeq*dAoCpa*(hsfjhaj)

Let δNTU=αo*Leeq*dAo/ma*Cpa, R=(αo*Leeq/Ui)*(b/Cpa)*(dAo/dAi), dAo/dAi=Ao/Ai.

Therefore Display Formula

(12)δQ=δNTU*ma*(hsfjhaj)[1+δNTU2+RδNTU2*mamf*bCf]
By equaling Eq. (12) to Eq. (1)Display Formula
(13)δNTU*ma*(hsfjhaj)[(1+R)+δNTU2(1mamf*bCf)]=ma*dha(1+R)dha+δNTU2*dha*(1mamf*bCf)=δNTU*(hsfjhaj)

The term δNTU*dha can be ignored as the result of its miniaturization; therefore, Eq. (13) could be reduced to Display Formula

(14)haihao(1+R)dha0AoδNTU*(hsfjhaj)

Equation (14) is quite similar to Merkel equation for direct cooling tower.

The relationship of (hsfjhaj) is proposed to be a function of the surface area as follows:

hsfjhaj=(hsfouthai)+K*A

This relationship is applied on a basis of calculations done in Khamis Mansour and Hassab [16], A is the incremental outer surface area of the ICT, K is the constant and can be determined as follows:

K=(hsfinhao)(hsfouthai)Ao=(hsfinhsfout)(haohai)Ao

The assumption of the linear relationship between the saturated air enthalpy at the wetted surface and its temperature can be exploited here; therefore, the difference between the saturated air enthalpies at the ICT entering and outlet is determined as follows: Display Formula

(15)K=1Ao*[b*(TfinTfout)(haohai)]

By using heat balance over the entire cooling tower between the air and the cooling water, Eq. (15) yields to Display Formula

(16)K=1Ao*[b*(TfinTfout)mfma*Cf*(TfinTfout)]

In this study, the cooling tower effectiveness is identified by the following equation: Display Formula

(17)ε=(TfinTfout)(TfinTwbi)

By dividing Eq. (16) over ((TfinTwbi)*b)

Kb*(TfinTwbi)=1Ao*[εmfma*Cpfb*ε]=εAo*[1Cfb*mfma]

By calling mra=mf/maandCpra=Cf/b, the above equation becomes as follows: Display Formula

(18)Kb*(TfinTwbi)=εAo*[1Cpra*mra]

By dividing Eq. (14) over (TfinTwbi)*b, the net result of integration of Eq. (14) is Display Formula

(19)(1+R)*(haohai)(TfinTwbi)*b=0Ao[(hsfouthai)(TfinTwbi)*b+K(TfinTwbi)*b*A]*αo*ηs*Leeq*dAma*Cpa

The fraction in the left term of the above equation can be rewritten as

(haohai)(TfinTwbi)*b=mra*Cpra*ε

and

(hsfouthai)(TfinTwbi)*b=(hsfinhsfout)+(hsfinhai)(TfinTwbi)*b=b*(TfinTfout)+b*(TfinTwbi)(TfinTwbi)*b=1ε

Hence, Eq. (18) can be yielded as follows:

(1+R)*mra*Cpra*ε=(1ε)*NTU+ε*[1mra*Cpra]*0.5*NTU

Therefore, the new correlations are presented as follows: Display Formula

(20)NTU=(1+R)*mra*Cpra*ε[10.5*ε*(1+mra*Cpra)]

and Display Formula

(21)ε=NTU[(1+R)*mra*Cpra+0.5*NTU*(1+Cpra*mra)]

where NTU=αo*Leeq*Ao/ma*Cpa, R=(αo*Leeq/Ui)*(ηsb/Cpa)*(Ao/Ai), and Display Formula

(22)Leeq=1(SHF+Le23(1SHF))

SHF is the incremental sensible heat ratio; it can be computed as follows:

SHF=ma*Cpa*(TaoTai)ma*(haohai)=(TaoTai)(TfinTai)*Cpa*(TfinTai)b*(TfinTwbti)*(hsfinhai)(haohai)

From definition of effectiveness Display Formula

(23)ε=(haohai)(hsfinhai)(TaoTai)(TfinTai)andthus,SHF=Cpa*(TfinTai)b*(TfinTwbti)

Equations (20)(22) are the most important findings in this work. And from those equations, by knowing the key parameters (R, mra, and Cpra), the NTU can be determined from Eq. (20) if the ε is known. Conversely, the IEC effectiveness can be computed if the key parameters and cooler NTU are known.

In this section, the results obtained from the proposed novel correlations are tested though the comparison with those obtained from the open literature either they are experimental or theoretical (numerical or analytical solution) either for rating or sizing mode. The outlet air temperature Tao and air enthalpy hao could be calculated by knowing the effectiveness of the cooling tower and use the triangle similarity between the air moist properties (enthalpy and temperature) as shown in Fig. 2.

From the definition of cooling tower effectiveness

ε=(TfinTfout)(TfinTwbi)=1(mra*Cpra)(haohai)(TfinTwbi)*b1(mra*Cpra)(haohai)(hsfinhai)

and from psychometric process similarity. Therefore Display Formula

(24)ε=(TfinTfout)(TfinTwbi)1(mra*Cpra)(haohai)(hsfinhai)1(mra*Cpra)(TaoTai)(TfinTai)

Hence, the outlet air properties could be calculated from Eq. (24).

Comparison With Experimental Work.

The simulated results of the novel correlations are compared to the test results from the experimental work done by Zheng et al. [9] for rating mode. Eight test runs at different operating conditions were selected. The geometrical configurations of the preselected ICT are given in Table 1 while the operating conditions for the eight tests are shown in Table 2. In order to make full comparison with the selected tests, the calculation of process water-side, spray/deluge water-side, and air-side heat transfers were calculated typically as reported in Ref. [9]. Those heat transfer characteristics and other parameters related to the present correlation are presented in Table 3.

Table 4 is equipped to show the comparison between the predictions of the present model with those obtained from the experimental work done by Zheng et al. [9]. The outlet temperature of the process fluid Tfout and the air outlet temperature Tao are calculated through the calculation of the ICT effectiveness and using of Eq. (24). As shown from Table 4, the results were calculated from the present model have relative deviations from those obtained from the experimental work of less than +/− 10%. The maximum deviation has been occurred in case_3 and case_6; the main reason can be explained as the reliability of assuming the linear relationship between the saturated air enthalpy and its corresponding saturated temperature is robust at narrow range of the difference between the inlet air wet bulb temperature and inlet process water temperature. The increase in this difference could participate in increasing the deviation between the predicted results and those obtained from the experimental work. The difference between the inlet air wet bulb temperature and inlet process water temperature is more than 30 K; this causes inaccurate calculations of the fictitious specific heat, b, and maximizes the deviation between both results to reach −6% as listed in Table 4.

Comparison With Traditional ε-Number of Transfer .

The geometrical and operating parameters of selected ICT of Jafari Naser and Behfar [10] are adopted in order to compare the predictions of the present model for sizing mode with that obtained of traditional ε-NTU. The comparison has been conducted to calculate the surface area of the evaporative cooler at different mass flow rates of the process cooling water as reported in Ref. [10]. The key parameters involved in the present model have been displayed in Table 5.

The use of the traditional ε-NTU method is accompanied by an iterative solution, the relation between the effectiveness and NTU in the traditional method as follows:

ε=Cw*(TfinTfout)Cmin*(TfinTwbi)=1eNTUw(1m*)1m*eNTUw(1m*)

where

Cw=mfCf,Ca=maCps and Cmin is the smallest one between Cw and Ca

Cps=(hsfinhsfout)/(TfinTfout)andm*=Cmin/Cmax

NTUw is calculated as reported in Ref. [17]. Figure 3 shows a good agreement between the simulated surface area by the present model and that calculated by the iterative traditional ε-NTU. The maximum deviation between both results is 9.37%.

Comparison With Numerical Work.

In order to enrich the test of the new correlation reliability, the predicted results of the present model are tested with those obtained from numerical modeling by Hasan and Siren [22]. They tested an ICT at inlet conditions: process water flow rate is 0.8 kg/s, air flow rate of 3.0 kg/s, 1.37 kg/s spray water flow rate, inlet process water temperature of 21 °C, and air dry bulb and wet bulb temperatures of air temperature of 20 °C and 16 °C, respectively. The heat transfer characteristics and other parameters related to the present model are listed in Table 6. Hasan and Siren [22] predicted the thermal performance of the preselected ICT incrementally, i.e., row-by-row outlet predictions (water temperature, air dry bulb temperature, and air enthalpy). Also, the results obtained from the present model are presented incrementally to achieve a complete comparison with Ref. [22].

As shown in Fig. 4, there is a good agreement between the predictions of process water temperature and air properties along the depth of ICT of the present model and those obtained from the numerical work done by Hasan and Siren [22]. The maximum deviation between both results is of 4.2%, and it is accounted for the prediction of process water temperature.

Comparison With Traditional Numerical Integration Method at Different Lewis Numbers.

In this section, the assessment of the present model is performed at different Lewis numbers by comparison with the traditional numerical integration method. This traditional method is assessed by comparing its simulated results with those obtained experimentally from Facao and Oliveira [13] at unit Lewis number as well with those obtained from the present model. After the validation of the numerical integration model, the adaptation of this model is easy to handle the different values of Lewis numbers. Figure 5 is prepared to illustrate the comparison of the two models with the experimental work of Facao and Oliveira [13] at Le = 1.

As shown in Fig. 5, both theoretical models display a good agreement with those obtained experimentally with maximum deviation of −7.3% for the present lumped model and −3.7% for the numerical integration model. Doing so, the numerical integration model is ready to be implemented as a tool for validation of the present model results at different Lewis number.

In the lumped present model, the equivalent Lewis number is calculated from Eqs. (5) and (23) and plugged in Eq. (21) to evaluate the performance of the ICT at different Lewis numbers. As noticed from Fig. 6, the present model can predict very well the thermal performance of the IEC at low Lewis number with maximum deviation of −2.7%. On the other hand, at high value of Lewis number, the accuracy of the model predictions decreases with maximum deviation of −5.9% accounted for Le = 1.6.

The main objective of this work is to present a new correlation of the effectiveness-NTU of counterflow IEC. The basic fundamentals of the energy and mass balance as well as the heat and mass transfer Equation were used to formulate the new correlation. A linear relationship between the saturated air enthalpy and its temperature was implemented and least square curve-fitting method was adopted to develop this relationship. The new correlation was tested through conducting of a series of comparisons either analytical or experimental previous work. A closed-type counterflow cooling tower is an example for an IEC. A numerical integration method has been adopted to assess the reliability of the new model accuracy at different Lewis numbers. The net outcome of the comparison results revealed that the new correlation is able to predict the thermal performance of IEC accurately with maximum deviation of 10% under different values of Lewis number. The new correlations could be used as powerful tool in finding the optimal operation of the IEC during its working through the thermal system or for developing building energy simulation program.

  • Ai =

    inner surface area, m2

  • Ao =

    outer surface area, m2

  • b =

    slope of saturation air enthalpy line, kJ/kg K

  • Cf =

    process fluid specific heat, kJ/kg K

  • Cpa =

    air specific heat, kJ/kg K

  • Cpra =

    ratio between specific heat of fluid and b constant

  • d =

    pipe diameter, m

  • ha =

    specific air enthalpy, kJ/kg

  • hs =

    specific saturated air enthalpy, kJ/kg

  • hsf =

    specific saturated air enthalpy at the process fluid temperature, kJ/kg

  • Kp =

    pipe thermal conductivity, W/m K

  • Le =

    Lewis number, defined as a ratio between thermal diffusivity and mass diffusivity of humid air

  • ma =

    air mass flow rate, kg/s

  • mf =

    process fluid mass flow rate, kg/s

  • mra =

    ratio between mass flow rate of process fluid and air

  • NTU =

    number of transfer unit

  • Q =

    heat transfer, W

  • SHF =

    sensible heat factor

  • T =

    temperature,  °C

  • Ts =

    surface temperature,  °C

  • Tfin =

    inlet process fluid temperature,  °C

  • Tfout =

    outlet process fluid temperature,  °C

  • Twbi =

    inlet air wet-bulb temperature,  °C

  • Wa =

    air humidity ratio, Kg/Kga

  • Ws =

    saturated air humidity ratio, Kg/Kga

  • Wsf =

    saturated air humidity ratio at the process fluid temperature, Kg/Kga

 Greek Symbols
  • α =

    heat transfer coefficient, W/m2 K

  • ε =

    effectiveness

 Subscripts
  • a =

    air or ambient

  • ai =

    inlet air

  • ao =

    outlet air

  • cal =

    calculated

  • f =

    process fluid

  • fm =

    mean for process fluid

  • i =

    inlet or inner

  • in =

    inlet

  • m =

    mean

  • o =

    outside or outer

  • out =

    outside

  • ref =

    reference

  • s =

    saturated or surface

  • sfin =

    saturated at inlet process fluid

  • sfout =

    saturated at outlet process fluid

  • sm =

    mean at saturated condition for air

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References

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Zheng, W.-Y. , Zhu, D.-S. , Zhou, G.-Y. , Wu, J.-F. , and Shi, Y.-Y. , 2012, “ Thermal Performance Analysis of Closed Wet Cooling Towers Under Both Unsaturated and Supersaturated Conditions,” Int. J. Heat Mass Transfer, 55(25–26), pp. 7803–7811. [CrossRef]
Jafari Nasr, M. R. , and Behfar, R. A. , 2010, “ Novel Design for Evaporative Fluid Coolers,” Appl. Therm. Eng., 30(17–18), pp. 2746–2752. [CrossRef]
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Threlkeld, J. L. , 1968, Thermal Environmental Engineering, 1st ed., Prentice-Hall, Englewood Cliffs, NJ.
Facao, J. , and Oliveira, A. C. , 2000, “ Thermal Behavior of Closed Wet Cooling Towers for Use With Chilled Ceilings,” Appl. Therm. Eng., 20(13), pp. 1225–1236. [CrossRef]
Facao, J. , and Oliveira, A. C. , 2004, “ Heat and Mass Transfer Correlations for the Design of Small Indirect Contact Cooling Towers,” Appl. Therm. Eng., 24(14–15), pp. 1969–1978. [CrossRef]
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Figures

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Fig. 1

A schematic diagram for counter-flow cooling tower

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Fig. 2

Heating and humidification process (triangle similarity between air properties)

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Fig. 3

Comparison between the present model and the traditional ε-NTU method

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Fig. 4

Comparison between the results obtained by the present model and those of Hasan and Siren [22] in terms of (a) process water temperature and (b) air temperature and enthalpy

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Fig. 5

Comparison between the results obtained by the present model, traditional integration model, and those of Facao and Oliveira [13]

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Fig. 6

Comparison between the results obtained by the present model and those obtained from the traditional integration model

Tables

Table Grahic Jump Location
Table 1 Geometrical configurations of the selected cooling tower [9]
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Table 2 Operating conditions of the selected cooling tower for the eight case studies [9]
Table Grahic Jump Location
Table 3 Heat transfer characteristics of the eight case studies [9]
Table Grahic Jump Location
Table 4 Comparison between the present model and Zheng [9] in terms of predictions of outlet process water temperature and outlet air temperature
Table Footer NoteNote: Error = (QCal−QExp)/QExp
Table Grahic Jump Location
Table 5 Heat transfer characteristics of the comparison with traditional ε-NTU method
Table Grahic Jump Location
Table 6 The calculated Heat transfer characteristics and parameters of the new correlation for the ICT of Hasan and Siren [22]

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