13_Chapter One - Six

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CHAPTER ONE

1. INTRODUCTION

Cooling tower are widely used in large air-conditioning installations to recycle

condenser cooling tower. The performance of cooling towers are often

expressed as Number of Transfer Unit (NTU).

A widely used method of calculating NTU is based on Merkel’s theory.

The theory is applicable to both counter flow and cross flow direct-contact

forced-draft air-water cooling towers as described by Stoecker and Jones

(1982).

Manual calculation of NTU is tedious and time-consuming. In this

research, computerized calculation are made to calculate the NTU of cross

flow cooling towers using Stoecker and Jones (1982), for a range of tower inlet

water temperature (tw1), outlet water temperature (tw2), ambient air wet bulb

temperature (twB) and ratio of water to air mass flow rate (L/G).

Multi-linear regression is then made to obtain correlations in the form

of :

NTU = a0. tw1a1.tw2a2.twba3(L/G)a4



Figure 1.1 A cross flow cooling tower by dividing it into sections.

. Objective

To obtain theoretical correlations for cross flow cooling towers for the tower NTU as a

function of inlet water temperature, outlet water temperature, ambient air wet bulb

temperature, air flow rate and water flow rate.

1.2 Scope

Steady-state analysis of crossflow air-water cooling towers

Use of Merkel theory



CHAPTER TWO

2. LITERATURE REVIEW

Cooling towers are widely used in air-conditioning applications for reducing the

temperature of circulating water for reuse in condensers. A cooling tower is an

evaporative cooling device where a circulating water is cooled by direct contact

with atmospheric air, where some of water is evaporated. Direct-contact

forced-draft air-water cooling towers involve the transfer of mass and hear

between the hot water and ambient air flowing in counter flow and cross flow

configurations.

A simplified cooling tower analysis is often made using Merkel’s (1925)

theory. The model is based on the enthalpy difference between the saturated air

enthalpy or the air water interface and the enthalpy of the surrounding air as the

driving potential for energy transfer.

Baker and Shryrock (1961) have discussed Merkel’s theory and suggested

the use of on offset ratio refers to the ratio between the true enthalpy potential

and the difference in the air/water interface temperature and the bulk water

temperature. They also studied the effects of neglecting the evaporative water

loss and the liquid side thermal resistance on the cooling tower performance.

The liquid side thermal resistance was considered in a cross flow cooling

tower analysis, they have also shown that the true driving potential was lower

than that without the liquid side thermal resistance. By considering

evaporative water loss and the liquid side thermal resistance, the resulting

“true” NTUs were also shown to be greater than those calculated using

Merkel’s theory for an experimental cross-flow cooling tower.

Osterle (1991) presented a tower model for which the Merkel equations

were corrected to account for mass of water lost by evaporation. The corrected

NTUs were evaluated by solving a set of differential equations.



Majumdar et. al (1983) have developed a two –dimensional model that

coupled the thermodynamics and hydrodynamics for simulating cooling

tower performance in either a counter-flow or cross-flow configuration. The

governing partial differential equations have been solved using finitedifference techniques in a computer code.

Bernier (1994) analysing the cooling tower heat rejection performance

must be obtained experimentally, where the NTU is evaluated using several

theories and models. The product of Ka in the NTU definition represents

average values of K and a in the tower, where K is the mass transfer

coefficient, and a is the air/water contact area per unit of tower volume. The

simplest and widely used theory for cooling tower analysis has been proposed

by Merkel in 1925.

Maiya (1995) analysing the performance of modified counter-flow

cooling tower. Bedekar (1998) investigation on the performance of a

counter-flow, packed-bed cooling tower.



CHAPTER THREE

3. METHODOLOGY

In a cooling tower, heat and mass are transferred from water to air. A cooling tower

with an effectiveness of 100% would exhaust saturated air from the tower at the

temperature of the entering water. In actual towers, the air leaves at a temperature

less than the entering water temperature and a relative humidity less than 100%

because the airflow is too high and the heat transfer area is too small. Effectiveness,

εa, is defined10 in terms of the enthalpy of moist air as follows:

ε a = (hi,in -hi,out) / (t w2 –t w1) (3-1)

In Equation (1), hi,in and hi,out are the enthalpies of the air into and out of the tower, and

t w2 is the enthalpy of air saturated with water at the inlet water temperature.

Effectiveness is a dimensionless variable which can be determined from knowledge of

only two additional dimensionless variables, NTU.

NTU = (h c A) / (C pmL ) (3-2)

From Equation (3-7), NTU depends on the heat transfer coefficient, h c, the heat transfer

surface area, A, and the specific heat, C pm. Energy efficient cooling towers with large heat

transfer surfaces and small fans might have nominal NTU values of 4.5 or more. Low initial

cost towers with small heat transfer surfaces and large fans might have nominal NTU

values of 1.5 or less.

Since h c depends on the airflow rate and the water flow rate, the NTU value of a tower



operating at off-design conditions will not be the same as the NTU value at design

conditions. An empirical equation useful for predicting NTU at off-design conditions is:

NTU = = 4.19 (3-3)

The constants, a, m, and n, in Equation (3-3) are to be determined from published

performance data. In some cases, this data is unavailable.

The heat exchangers are usually characterized by the Number of Transfer Unit NTU.

Since the tower has similar hydrothermal operation, then it is possible to characterize

the tower performance using the NTU as following.

Since NTU are known for a particular cooling tower, the cooling tower

performance can be predicted at any operating condition using;

Multi Linear Regression ;

NTU = a0. tw1a1.tw2

a2.twba3(L/G)a4 (3-4)

Estimate;

NTU = 1 -number of unit transfer

tw1 = 37oC -entering water temperature

tw2 = 35oC -leaving water temperature

twb = 25oC -temperature wet bulb entering air

= 1.0

n x n = 10 x 10 -dividing section in cross flow cooling tower

calculate using eq.(3-9)

1= c.(37)c(35)c(25)c(1.0)c

a=9.2592 * 10-3 …….into eq.(3.9) to get the actual NTU

So,



NTU actual = 0.0101

Although the counter flow cooling tower is widely used in industrial services, another

configuration is the cross flow tower, in which the air passes horizontally through the

falling water sprays. Cooling towers used for air-conditioning systems are often

located atop buildings, and cross flow cooling tower usually has a lower profile,

which lends itself better to architectural treatment.

The same principles of heat and mass transfer and balance of energy apply to a

cross flow tower and to the counter flow type, but the geometric treatment of the

cross flow tower is different. Figure 3-1 showns a cross flow tower divided into 12

sections for purposes of analysis. Water enters the top at a temperature tin while air

enters from the left with an enthalpy hin. In section 1 air enters at enthalpy hin and

leaves with enthalpy h1. Also in section 1 water entera at tin and leaves at t1. The

enthalpy of air entering section 2 is h1, and the water enters section 5 with a

temperature t1. The temperature of water leaving sections 9, 10, 11, and 12 at the

bottom of the tower are t9, t10, t11, and t12, respectively. These temperatures are all

different, and the streams combine to form one stream of temperature tout.

If the value of hc A/C pm is known for the entire cooling tower, the outlet water

temperature can be predicted when the inlet water temperature, inlet air enthalpy,

and the flow rates of water and air are known. The tower can be divided into a

number of small increments (12 increment, for example, in Fig 2-1) and (hc A/C pm )/12

assigned to each increment. Let

=



Figure 2.1 Analysis a cross flow cooling tower by dividing it into sections.

Divide tower into 3 rows, 4 columns. Total cells = 12.

Given;

tin : 37oC

twb : 25oC

Total cells : 3 x 4 = 12

air flow, L : 24 kg/s

water flow, G : 15 kg/s

hin : 80.8

1. Divide whole tower NTU into cellular NTU e

Guess NTU = 10

[kW/kJ.K]

[kW/kJ.K]

NTU e = 20



2. [kg/s]

[kg/s]

Ge = 5 [kg/s]

3. [kg/s]

[kg/s]

Le = 6 [kg/s]

4. Calculate saturated air specific enthalpy at inlet water temperature tin

hi,in = 4792.6 + 2568tin – 29.834tin2 + 1.6657 tin

3 [J/kg]

hi,in = 4792.6 + 2568(37) – 29.834(372) + 1.6657(373)

hi,in = 143338.5561 [J/kg]

5. Let

t1 = 37 + 0.1 = 37.1oC

6. Calculate saturated air specific enthalpy at outlet water temperature t1

hi,out = 4792.6 + 2568tin – 29.834tin2 + 1.6657 tin

3 [J/kg]

hi,out = 4792.6 + 2568(37.1) – 29.834(37.12) + 1.6657(37.13)

hi,out = 144060.2397 [J/kg]

[oC]

Calculate specific heat of outlet air



[J/kg]

h1 = 153938.8348 [J/kg]

Heat gain by air

[W]

dq = 5 (162-80.8) [W]

dq = 438833.0088 [W]

equals heat loss from falling water:

[oC]

[oC]

t1 = 16.0333 [oC]

7. If repeat step 6.

t1 - t1,old = 16.0333 - 37.1

t1 - t1,old = -21.0667

8. Repeat calculations (steps 4–6) for the other cells.

9. At the bottom of tower calculate the average exit water temperature tout



CHAPTER FOUR

4. DATA ANALYSIS AND RESULTS

A computer program has been written to calculate the NTU of cross flow cooling

towers using Merkel’s theory as described by Stocker and Jones (1982). The inputs to

the program are inlet water temperature (tw1), outlet water temperature (tw2),



ambient air wet bulb temperature (twB) and the ratio of water to air mass flow rate

(L/G). The program calculates the NTU as described in Chapter 3.

Correlation are developed for the following conditions;

(a) Atmospheric pressure, 101 325 Pa.

(b) Tower divided into 10 rows and 10 columns (i.e. 100 cells)

(c) 34.5 oC < tw1 < 35.5 oC

(d) 29 oC < tw2 < 30 oC

(e) 25 oC < twB < 26 oC

(f) 0.5 < L/G < 1.5

4.1 L/G between 0.5 and 0.7

Table 4.1 shows the true NTU as calculated using Merkel’s theory and

NTU estimated from the correlation:

NTU = 6.800115. tw15.403319.tw2

-10.30583.twb2.785535 (L/G)0.4895199

The maximum single-point error when using the correlation is -4.5%. Figure4.1 shows that NTUcorrelation is in good agreement with the true NTU. Figure

4.2 gives the percentage error distribution for all NTUcorrelation where the

errors range from -4.5% to 3.6%.

Table 4.1 NTU for 0.5 < L/G < 0.7

tw1 tw2 twB L/G NTUtrue

NTUregression

% Error

34.5 29 25 0.5 0.94 0.9306 -1

34.5 29 25 0.6 0.99 0.9853 -0.48

34.5 29 25 0.7 1.046 1.034 -1.1534.5 29 25.5 0.5 1.039 1.0334 -0.54



34.5 29 25.5 0.6 1.1 1.0941 -0.53

34.5 29 25.5 0.7 1.17 1.1483 -1.86

34.5 29 26 0.5 1.166 1.1453 -1.78

34.5 29 26 0.6 1.243 1.2126 -2.45

34.5 29 26 0.7 1.332 1.2726 -4.46

34.5 29.5 25 0.5 0.777 0.7583 -2.4

34.5 29.5 25 0.6 0.811 0.8029 -1

34.5 29.5 25 0.7 0.849 0.8426 -0.75

34.5 29.5 25.5 0.5 0.849 0.8421 -0.81

34.5 29.5 25.5 0.6 0.89 0.8916 0.18

34.5 29.5 25.5 0.7 0.935 0.9357 0.08

34.5 29.5 26 0.5 0.94 0.9333 -0.71

34.5 29.5 26 0.6 0.989 0.9881 -0.09

34.5 29.5 26 0.7 1.046 1.037 -0.86

34.5 30 25 0.5 0.643 0.6201 -3.56

34.5 30 25 0.6 0.665 0.6565 -1.27

34.5 30 25 0.7 0.69 0.689 -0.14

34.5 30 25.5 0.5 0.696 0.6886 -1.0634.5 30 25.5 0.6 0.723 0.7291 0.84

34.5 30 25.5 0.7 0.753 0.7652 1.61

34.5 30 26 0.5 0.761 0.7632 0.29

34.5 30 26 0.6 0.794 0.808 1.77

34.5 30 26 0.7 0.83 0.848 2.17

35 29 25 0.5 1.004 1.0103 0.63

35 29 25 0.6 1.061 1.0697 0.82

35 29 25 0.7 1.125 1.1226 -0.21

35 29 25.5 0.5 1.108 1.122 1.26

35 29 25.5 0.6 1.177 1.1879 0.93

35 29 25.5 0.7 1.257 1.2467 -0.82

35 29 26 0.5 1.242 1.2434 0.1235 29 26 0.6 1.329 1.3165 -0.94

35 29 26 0.7 1.43 1.3816 -3.38

35 29.5 25 0.5 0.837 0.8233 -1.64

35 29.5 25 0.6 0.876 0.8717 -0.49

35 29.5 25 0.7 0.92 0.9148 -0.56

35 29.5 25.5 0.5 0.914 0.9143 0.03

35 29.5 25.5 0.6 0.961 0.968 0.73

35 29.5 25.5 0.7 1.014 1.0159 0.19

35 29.5 26 0.5 1.009 1.0133 0.42

35 29.5 26 0.6 1.067 1.0728 0.55

35 29.5 26 0.7 1.132 1.1259 -0.54

35 30 25 0.5 0.699 0.6732 -3.69

35 30 25 0.6 0.726 0.7128 -1.82

35 30 25 0.7 0.756 0.7481 -1.05

35 30 25.5 0.5 0.756 0.7476 -1.11

35 30 25.5 0.6 0.788 0.7916 0.45

35 30 25.5 0.7 0.824 0.8307 0.82

35 30 26 0.5 0.826 0.8286 0.31


NTUregression

% Error

35

30 26 0.7 0.907 0.9207 1.51

35.5 29 25 0.5 1.065 1.0956 2.87



35.5 29 25 0.6 1.129 1.16 2.75

35.5 29 25 0.7 1.202 1.2174 1.28

35.5 29 25.5 0.5 1.174 1.2167 3.64

35.5 29 25.5 0.6 1.252 1.2882 2.89

35.5 29 25.5 0.7 1.342 1.3519 0.74

35.5 29 26 0.5 1.314 1.3484 2.62

35.5 29 26 0.6 1.412 1.4277 1.11

35.5 29 26 0.7 1.525 1.4983 -1.75

35.5 29.5 25 0.5 0.894 0.8928 -0.13

35.5 29.5 25 0.6 0.939 0.9453 0.67

35.5 29.5 25 0.7 0.99 0.9921 0.21

35.5 29.5 25.5 0.5 0.975 0.9915 1.69

35.5 29.5 25.5 0.6 1.029 1.0498 2.02

35.5 29.5 25.5 0.7 1.089 1.1017 1.17

35.5 29.5 26 0.5 1.076 1.0988 2.12

35.5 29.5 26 0.6 1.141 1.1634 1.96

35.5 29.5 26 0.7 1.216 1.221 0.41

35.5 30 25 0.5 0.753 0.7301 -3.0435.5 30 25 0.6 0.785 0.773 -1.53

35.5 30 25 0.7 0.82 0.8112 -1.07

35.5 30 25.5 0.5 0.814 0.8108 -0.4

35.5 30 25.5 0.6 0.851 0.8584 0.87

35.5 30 25.5 0.7 0.892 0.9009 0.99

35.5 30 26 0.5 0.888 0.8985 1.19

35.5 30 26 0.6 0.933 0.9513 1.96

35.5 30 26 0.7 0.982 0.9984 1.67



Figure 4.1 NTU_correlation versus NTU_true for L/G 0.5 – 0.7



Figure 4.2 Percentage error in NTUcorrelation for L/G 0.5 – 0.7






NTU = 6.661408. tw13.968963.tw2

-8.622578.twb2.638664(L/G)0.3987166

The maximum single-point error when using the correlation is -5.5%. Figure 4.

3 shows that NTUcorrelation is in good agreement with the true NTU. Figure 4.

3 gives the percentage error distribution for all NTUcorrelation where the


Table 4.2 NTU for 0.7 < L/G < 0.9


NTUregression

% Error

34.5 29 25 0.7 1.046 1.0367 -0.89

34.5 29 25 0.8 1.11 1.1056 -0.4

34.5 29 25 0.9 1.183 1.1702 -1.08

34.5 29 25.5 0.7 1.17 1.1654 -0.39

34.5 29 25.5 0.8 1.25 1.2429 -0.57

34.5 29 25.5 0.9 1.343 1.3156 -2.04

34.5 29 26 0.7 1.332 1.3071 -1.8734.5 29 26 0.8 1.436 1.3941 -2.92

34.5 29 26 0.9 1.558 1.4756 -5.29

34.5 29.5 25 0.7 0.849 0.8251 -2.81

34.5 29.5 25 0.8 0.89 0.88 -1.12

34.5 29.5 25 0.9 0.937 0.9314 -0.59

34.5 29.5 25.5 0.7 0.935 0.9276 -0.79

34.5 29.5 25.5 0.8 0.986 0.9893 0.33

34.5 29.5 25.5 0.9 1.044 1.0471 0.3

34.5 29.5 26 0.7 1.046 1.0404 -0.53

34.5 29.5 26 0.8 1.109 1.1096 0.06

34.5 29.5 26 0.9 1.183 1.1745 -0.72

34.5 30 25 0.7 0.69 0.6593 -4.45

34.5 30 25 0.8 0.718 0.7031 -2.07

34.5 30 25 0.9 0.748 0.7442 -0.5

34.5 30 25.5 0.7 0.753 0.7411 -1.57

34.5 30 25.5 0.8 0.785 0.7904 0.69

34.5 30 25.5 0.9 0.821 0.8366 1.91

34.5 30 26 0.7 0.83 0.8313 0.16

34.5 30 26 0.8 0.869 0.8866 2.02

34.5 30 26 0.9 0.914 0.9384 2.67

35 29 25 0.7 1.125 1.1358 0.96

35 29 25 0.8 1.199 1.2114 1.03

35 29 25 0.9 1.284 1.2822 -0.1435 29 25.5 0.7 1.257 1.2769 1.58



35 29 25.5 0.8 1.349 1.3618 0.95

35 29 25.5 0.9 1.457 1.4414 -1.07

35 29 26 0.7 1.43 1.4322 0.15

35 29 26 0.8 1.549 1.5274 -1.39

35 29 26 0.9 1.69 1.6167 -4.34


NTUregression

% Error

3529.5 25 0.8 0.969 0.9642 -0.5

35 29.5 25 0.9 1.025 1.0205 -0.44

35 29.5 25.5 0.7 1.014 1.0163 0.23

35 29.5 25.5 0.8 1.073 1.0839 1.02

35 29.5 25.5 0.9 1.142 1.1473 0.46

35 29.5 26 0.7 1.132 1.1399 0.7

35 29.5 26 0.8 1.207 1.2157 0.72

35 29.5 26 0.9 1.293 1.2868 -0.48

35 30 25 0.7 0.756 0.7223 -4.45

35 30 25 0.8 0.789 0.7704 -2.36

35 30 25 0.9 0.825 0.8154 -1.16

35 30 25.5 0.7 0.824 0.812 -1.45

35 30 25.5 0.8 0.863 0.866 0.35

35 30 25.5 0.9 0.906 0.9167 1.18

35 30 26 0.7 0.907 0.9108 0.42

35 30 26 0.8 0.955 0.9714 1.72

35 30 26 0.9 1.008 1.0282 2

35.5 29 25 0.7 1.202 1.2428 3.4

35.5 29 25 0.8 1.286 1.3255 3.07

35.5 29 25 0.9 1.384 1.403 1.37

35.5 29 25.5 0.7 1.342 1.3972 4.1135.5 29 25.5 0.8 1.446 1.4901 3.05

35.5 29 25.5 0.9 1.57 1.5772 0.46

35.5 29 26 0.7 1.525 1.5671 2.76

35.5 29 26 0.8 1.659 1.6713 0.74

35.5 29 26 0.9 1.819 1.769 -2.75

35.5 29.5 25 0.7 0.99 0.9892 -0.08

35.5 29.5 25 0.8 1.047 1.055 0.77

35.5 29.5 25 0.9 1.111 1.1167 0.51

35.5 29.5 25.5 0.7 1.089 1.1121 2.12

35.5 29.5 25.5 0.8 1.158 1.186 2.42

35.5 29.5 25.5 0.9 1.238 1.2554 1.4

35.5 29.5 26 0.7 1.216 1.2473 2.5835.5 29.5 26 0.8 1.302 1.3303 2.17

35.5 29.5 26 0.9 1.402 1.408 0.43

35.5 30 25 0.7 0.82 0.7904 -3.61

35.5 30 25 0.8 0.858 0.843 -1.75

35.5 30 25 0.9 0.902 0.8922 -1.08

35.5 30 25.5 0.7 0.892 0.8885 -0.39

35.5 30 25.5 0.8 0.939 0.9477 0.92

35.5 30 25.5 0.9 0.99 1.003 1.32

35.5 30 26 0.7 0.982 0.9966 1.49

35.5 30 26 0.8 1.038 1.0629 2.4

35.5 30 26 0.9 1.102 1.125 2.09






Figure 4.4 Percentage error in NTUcorrelation for for L/G 0.7 – 0.9






NTU = 7.26992. tw14.627645.tw2

-9.369511.twb2.502056(L/G)0.5178051

The maximum single-point error when using the correlation is -6.43%. Figure

4.3 shows that NTUcorrelation is in good agreement with the true NTU. Figure



Table 4.3 NTU for 0.9 < L/G < 1.1


NTUregression

% Error

34.5 29 25 0.9 1.183 1.1741 -0.75

34.5 29 25 1 1.268 1.2654 -0.2

34.5 29 25 1.1 1.368 1.3541 -1.02

34.5 29 25.5 0.9 1.343 1.3406 -0.18

34.5 29 25.5 1 1.452 1.4449 -0.49

34.5 29 25.5 1.1 1.582 1.5462 -2.27

34.5 29 26 0.9 1.558 1.5268 -2

34.5 29 26 1 1.704 1.6456 -3.43

34.5 29 26 1.1 1.882 1.7609 -6.4334.5 29.5 25 0.9 0.937 0.9067 -3.24

34.5 29.5 25 1 0.99 0.9772 -1.3

34.5 29.5 25 1.1 1.05 1.0457 -0.41

34.5 29.5 25.5 0.9 1.044 1.0353 -0.84

34.5 29.5 25.5 1 1.11 1.1158 0.52

34.5 29.5 25.5 1.1 1.186 1.194 0.67

34.5 29.5 26 0.9 1.183 1.179 -0.33

34.5 29.5 26 1 1.267 1.2707 0.3

34.5 29.5 26 1.1 1.366 1.3598 -0.45

34.5 30 25 0.9 0.748 0.7032 -5.99

34.5 30 25 1 0.781 0.7579 -2.96

34.5 30 25 1.1 0.818 0.811 -0.86

34.5 30 25.5 0.9 0.821 0.8029 -2.2

34.5 30 25.5 1 0.861 0.8654 0.51

34.5 30 25.5 1.1 0.907 0.926 2.1

34.5 30 26 0.9 0.914 0.9144 0.05

34.5 30 26 1 0.964 0.9856 2.24

34.5 30 26 1.1 1.021 1.0547 3.3

35 29 25 0.9 1.284 1.3013 1.35

35 29 25 1 1.384 1.4025 1.34

35 29 25 1.1 1.502 1.5008 -0.08

35 29 25.5 0.9 1.457 1.4858 1.98

35 29 25.5 1 1.585 1.6014 1.0335 29 25.5 1.1 1.739 1.7137 -1.46



35 29 26 0.9 1.69 1.6922 0.13

35 29 26 1 1.86 1.8238 -1.94

35 29 26 1.1 2.069 1.9517 -5.67

tw1 tw2 twB L/G NTUtru

e

NTUregressio

n

% Error

3529.5 25 1 1.088 1.083 -0.46

35 29.5 25 1.1 1.161 1.1589 -0.18

35 29.5 25.5 0.9 1.142 1.1474 0.47

35 29.5 25.5 1 1.22 1.2366 1.36

35 29.5 25.5 1.1 1.312 1.3233 0.86

35 29.5 26 0.9 1.293 1.3068 1.06

35 29.5 26 1 1.394 1.4084 1.03

35 29.5 26 1.1 1.513 1.5071 -0.39

35 30 25 0.9 0.825 0.7794 -5.53

35 30 25 1 0.866 0.84 -3.01

35 30 25 1.1 0.911 0.8989 -1.33

35 30 25.5 0.9 0.906 0.8899 -1.78

35 30 25.5 1 0.956 0.9591 0.33

35 30 25.5 1.1 1.011 1.0263 1.52

35 30 26 0.9 1.008 1.0135 0.55

35 30 26 1 1.07 1.0923 2.09

35 30 26 1.1 1.14 1.1689 2.54

35.5 29 25 0.9 1.384 1.4401 4.06

35.5 29 25 1 1.499 1.5521 3.54

35.5 29 25 1.1 1.637 1.6609 1.46

35.5 29 25.5 0.9 1.57 1.6444 4.74

35.5 29 25.5 1 1.717 1.7723 3.22

35.5 29 25.5 1.1 1.895 1.8965 0.0835.5 29 26 0.9 1.819 1.8728 2.96

35.5 29 26 1 2.014 2.0184 0.22

35.5 29 26 1.1 2.255 2.1599 -4.22

35.5 29.5 25 0.9 1.111 1.1121 0.1

35.5 29.5 25 1 1.186 1.1986 1.06

35.5 29.5 25 1.1 1.272 1.2826 0.83

35.5 29.5 25.5 0.9 1.238 1.2698 2.57

35.5 29.5 25.5 1 1.33 1.3686 2.9

35.5 29.5 25.5 1.1 1.438 1.4645 1.85

35.5 29.5 26 0.9 1.402 1.4462 3.15

35.5 29.5 26 1 1.519 1.5587 2.61

35.5 29.5 26 1.1 1.66 1.668 0.4835.5 30 25 0.9 0.902 0.8625 -4.38

35.5 30 25 1 0.95 0.9296 -2.15

35.5 30 25 1.1 1.005 0.9948 -1.02

35.5 30 25.5 0.9 0.99 0.9849 -0.52

35.5 30 25.5 1 1.049 1.0615 1.19

35.5 30 25.5 1.1 1.116 1.1359 1.78

35.5 30 26 0.9 1.102 1.1217 1.78

35.5 30 26 1 1.175 1.2089 2.88

35.5 30 26 1.1 1.259 1.2936 2.75












NTU = 8.420994. tw14.314386.tw2

-9.973997.twb3.167216(L/G)0.7143654





Table 4.4 NTU for 1.1 < L/G < 1.3


NTUregression

% Error

34.5 29 25 1.1 1.368 1.3598 -0.6

34.5 29 25 1.2 1.486 1.4872 0.08

34.5 29 25 1.3 1.629 1.6148 -0.87

34.5 29 25.5 1.1 1.582 1.5851 0.2

34.5 29 25.5 1.2 1.74 1.7335 -0.37

34.5 29 25.5 1.3 1.934 1.8823 -2.67

34.5 29 26 1.1 1.882 1.8423 -2.11

34.5 29 26 1.2 2.101 2.0148 -4.1

34.5 29 26 1.3 2.381 2.1877 -8.1234.5 29.5 25 1.1 1.05 1.0087 -3.93

34.5 29.5 25 1.2 1.119 1.1032 -1.42

34.5 29.5 25 1.3 1.199 1.1978 -0.1

34.5 29.5 25.5 1.1 1.186 1.1758 -0.86

34.5 29.5 25.5 1.2 1.274 1.2859 0.94

34.5 29.5 25.5 1.3 1.378 1.3963 1.33

34.5 29.5 26 1.1 1.366 1.3666 0.04

34.5 29.5 26 1.2 1.483 1.4945 0.78

34.5 29.5 26 1.3 1.625 1.6228 -0.14

34.5 30 25 1.1 0.818 0.752 -8.07

34.5 30 25 1.2 0.859 0.8224 -4.26

34.5 30 25 1.3 0.905 0.893 -1.32

34.5 30 25.5 1.1 0.907 0.8766 -3.35

34.5 30 25.5 1.2 0.958 0.9587 0.07

34.5 30 25.5 1.3 1.016 1.041 2.46

34.5 30 26 1.1 1.021 1.0188 -0.21

34.5 30 26 1.2 1.086 1.1142 2.6

34.5 30 26 1.3 1.161 1.2098 4.21

35 29 25 1.1 1.502 1.53 1.86

35 29 25 1.2 1.644 1.6732 1.78

35 29 25 1.3 1.817 1.8168 -0.0135 29 25.5 1.1 1.739 1.7834 2.56



35 29 25.5 1.2 1.927 1.9504 1.22

35 29 25.5 1.3 2.162 2.1178 -2.04

35 29 26 1.1 2.069 2.0728 0.18


NTUregression

% Error

35 29 26 1.3 2.668 2.4614 -7.74

35 29.5 25 1.1 1.161 1.1349 -2.25

35 29.5 25 1.2 1.245 1.2412 -0.31

35 29.5 25 1.3 1.345 1.3477 0.2

35 29.5 25.5 1.1 1.312 1.3229 0.83

35 29.5 25.5 1.2 1.42 1.4468 1.89

35 29.5 25.5 1.3 1.549 1.571 1.42

35 29.5 26 1.1 1.513 1.5376 1.62

35 29.5 26 1.2 1.656 1.6815 1.54

35 29.5 26 1.3 1.83 1.8258 -0.23

35 30 25 1.1 0.911 0.8461 -7.12

35 30 25 1.2 0.963 0.9253 -3.91

35 30 25 1.3 1.021 1.0047 -1.59

35 30 25.5 1.1 1.011 0.9863 -2.44

35 30 25.5 1.2 1.075 1.0786 0.34

35 30 25.5 1.3 1.148 1.1712 2.02

35 30 26 1.1 1.14 1.1463 0.55

35 30 26 1.2 1.221 1.2536 2.67

35 30 26 1.3 1.316 1.3612 3.44

35.5 29 25 1.1 1.637 1.7185 4.98

35.5 29 25 1.2 1.803 1.8794 4.2435.5 29 25 1.3 2.009 2.0407 1.58

35.5 29 25.5 1.1 1.895 2.0032 5.71

35.5 29 25.5 1.2 2.115 2.1908 3.58

35.5 29 25.5 1.3 2.395 2.3788 -0.67

35.5 29 26 1.1 2.255 2.3282 3.25

35.5 29 26 1.2 2.561 2.5462 -0.58

35.5 29 26 1.3 2.96 2.7647 -6.6

35.5 29.5 25 1.1 1.272 1.2748 0.22

35.5 29.5 25 1.2 1.373 1.3941 1.54

35.5 29.5 25 1.3 1.493 1.5138 1.3935.5 29.5 25.5 1.1 1.438 1.486 3.34

35.5 29.5 25.5 1.2 1.567 1.6251 3.71

35.5 29.5 25.5 1.3 1.723 1.7646 2.41

35.5 29.5 26 1.1 1.66 1.727 4.04

35.5 29.5 26 1.2 1.83 1.8887 3.21

35.5 29.5 26 1.3 2.04 2.0509 0.53

35.5 30 25 1.1 1.005 0.9504 -5.44

35.5 30 25 1.2 1.068 1.0394 -2.68

35.5 30 25 1.3 1.14 1.1286 -1

35.5 30 25.5 1.1 1.116 1.1078 -0.73

35.5 30 25.5 1.2 1.194 1.2116 1.47



35.5 30 25.5 1.3 1.284 1.3155 2.46

35.5 30 26 1.1 1.259 1.2875 2.27

35.5 30 26 1.2 1.357 1.4081 3.77

35.5 30 26 1.3 1.475 1.529 3.66










NTU = 9.458658. tw14.383413.tw2-11.27517.twb4.164945(L/G)0.8327527





Table 4.5 NTU for 1.3 < L/G < 1.5

tw1 tw2 twB L/G NTUtru

e

NTUregressio

n

% Error

34.5 29 25 1.3 1.629 1.6242 -0.29

34.5 29 25 1.4 1.804 1.817 0.72

34.5 29 25 1.5 2.026 2.017 -0.45

34.5 29 25.5 1.3 1.934 1.9498 0.82

34.5 29 25.5 1.4 2.18 2.1812 0.06

34.5 29 25.5 1.5 2.501 2.4213 -3.19

34.5 29 26 1.3 2.381 2.3324 -2.04

34.5 29 26 1.4 2.748 2.6092 -5.05

34.5 29 26 1.5 3.253 2.8964 -10.96

34.5 29.5 25 1.3 1.199 1.1381 -5.08

34.5 29.5 25 1.4 1.294 1.2732 -1.61

34.5 29.5 25 1.5 1.407 1.4133 0.4534.5 29.5 25.5 1.3 1.378 1.3663 -0.85

34.5 29.5 25.5 1.4 1.504 1.5284 1.62

34.5 29.5 25.5 1.5 1.657 1.6967 2.39

34.5 29.5 26 1.3 1.625 1.6344 0.58

34.5 29.5 26 1.4 1.799 1.8283 1.63

34.5 29.5 26 1.5 2.018 2.0296 0.57

34.5 30 25 1.3 0.905 0.8023 -11.35

34.5 30 25 1.4 0.958 0.8975 -6.31

34.5 30 25 1.5 1.018 0.9963 -2.13

34.5 30 25.5 1.3 1.016 0.9631 -5.2

34.5 30 25.5 1.4 1.083 1.0774 -0.51

34.5 30 25.5 1.5 1.161 1.196 3.0234.5 30 26 1.3 1.161 1.1521 -0.77

34.5 30 26 1.4 1.249 1.2888 3.19

34.5 30 26 1.5 1.354 1.4307 5.66

35 29 25 1.3 1.817 1.8658 2.68

35 29 25 1.4 2.033 2.0872 2.67

35 29 25 1.5 2.312 2.3169 0.21

35 29 25.5 1.3 2.162 2.2398 3.6

35 29 25.5 1.4 2.465 2.5056 1.65

35 29 25.5 1.5 2.87 2.7814 -3.09

35 29 26 1.3 2.668 2.6793 0.42

35 29 26 1.4 3.12 2.9973 -3.93

35 29 26 1.5 3.758 3.3271 -11.47

35 29.5 25 1.3 1.345 1.3074 -2.8



35 29.5 25 1.4 1.463 1.4626 -0.03

35 29.5 25 1.5 1.607 1.6235 1.03


NTUregression

% Error

35 29.5 25.5 1.4 1.706 1.7557 2.9235 29.5 25.5 1.5 1.902 1.949 2.47

35 29.5 26 1.3 1.83 1.8774 2.59

35 29.5 26 1.4 2.048 2.1002 2.55

35 29.5 26 1.5 2.329 2.3314 0.1

35 30 25 1.3 1.021 0.9216 -9.74

35 30 25 1.4 1.089 1.031 -5.33

35 30 25 1.5 1.167 1.1445 -1.93

35 30 25.5 1.3 1.148 1.1064 -3.63

35 30 25.5 1.4 1.234 1.2377 0.3

35 30 25.5 1.5 1.336 1.3739 2.84

35 30 26 1.3 1.316 1.3234 0.56

35 30 26 1.4 1.429 1.4805 3.635 30 26 1.5 1.565 1.6434 5.01

35.5 29 25 1.3 2.009 2.139 6.47

35.5 29 25 1.4 2.27 2.3929 5.41

35.5 29 25 1.5 2.613 2.6563 1.66

35.5 29 25.5 1.3 2.395 2.5678 7.22

35.5 29 25.5 1.4 2.76 2.8726 4.08

35.5 29 25.5 1.5 3.259 3.1888 -2.16

35.5 29 26 1.3 2.96 3.0717 3.77

35.5 29 26 1.4 3.505 3.4362 -1.96

35.5 29 26 1.5 4.291 3.8144 -11.11

35.5 29.5 25 1.3 1.493 1.4989 0.39

35.5 29.5 25 1.4 1.639 1.6768 2.335.5 29.5 25 1.5 1.818 1.8613 2.38

35.5 29.5 25.5 1.3 1.723 1.7993 4.43

35.5 29.5 25.5 1.4 1.916 2.0129 5.06

35.5 29.5 25.5 1.5 2.16 2.2344 3.45

35.5 29.5 26 1.3 2.04 2.1524 5.51

35.5 29.5 26 1.4 2.308 2.4078 4.33

35.5 29.5 26 1.5 2.658 2.6728 0.56

35.5 30 25 1.3 1.14 1.0566 -7.32

35.5 30 25 1.4 1.224 1.182 -3.43

35.5 30 25 1.5 1.324 1.3121 -0.9

35.5 30 25.5 1.3 1.284 1.2684 -1.2235.5 30 25.5 1.4 1.392 1.4189 1.93

35.5 30 25.5 1.5 1.521 1.5751 3.56

35.5 30 26 1.3 1.475 1.5173 2.86

35.5 30 26 1.4 1.616 1.6973 5.03

35.5 30 26 1.5 1.789 1.8841 5.32









CHAPTER FIVE

5. CONCLUSION

Merkerl’s theory was used to obtain theoretical correlation for predicting the

NTU of cross-flow cooling towers in the form of power equation,

NTU = a0. tw1a1.tw2

a2.twba3(L/G)a4

Where the coefficients a0, a0, a0 and a0 are summarized in table 5.1.

Table 5.1 Coefficients of NTU Correlation

L/G a0 a1 a2 a3 a4 Maximum error

0.5 - 0.7 6.800115

5.403319

-10.30583

2.785535

0.48952

-4.5%

0.7 - 0.9 6.661408

3.968963

-8.62258

2.638664

0.398717

-5.3%

0.9 - 1.1 7.26992

4.627645

-9.36951

2.502056

0.517805

-6.4%

1.1 - 1.3 8.420994

4.314386

-9.97400

3.167216

0.714365

-8.1%

1.3 - 1.5 9.458658

4.383413

-11.2752

4.164945

0.832753

-11.5%



REFERENCES

1.W.F.Stoecker & J.W.Jones, Refrigeration and Air Conditioning Second Edition,McGraw-Hill

2.Dickey, J. B., Evaporative Cooling Towers, Marley Cooling Towers Co., 1978.

3. ASHRAE, “Cooling Towers,” in ASHRAE Handbook—HVAC Systems and Equipment, New York: ASHRAE, 2004.

4. Wistrom, G., “Cold Weather Operation of Crossflow Cooling Towers,” Plant Engineering, September 8, 1975.

5. Lipták, B. G. (ed.), “Cooling Towers: Their Design and Application,” in Environmental Engineer’s Handbook, Lewis Publishers, 1997.

6.Optimal Design of Cooling Towers, Heat and Mass Transfer - Modeling andSimulation, Prof. Md Monwar Hossain (Ed.), ISBN: 978-953-307-604-1, InTech,Available from: http://www.intechopen.com/books/heat-andmass-transfer-modeling-and-simulation/optimal-design-of-cooling-towers

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