1.Introduction

The energy demands all over the world have become on of the most emerging problems at the way of developing the economies and achieve the welfare for the people. There are three branches of the energy consumption Industry, Transportation, Architecture which Architecture is using around 20- 40 percent of the total amount of energy. Among the architecture application Heat, ventilation and air conditioning (HVAC) take around half the energy which means that it is almost taking one quarter of the whole amount of energy.

Conventional, the cooling system is mechanical vapor compression system which depends on several mechanical parts to achieve the target of air conditioning like compressor, evaporator, condenser and expansion valve. The working fluid is usually refrigerant like R22 or R134. Due to the wonderful cooling effect of this method it have improved and continued for long time however it needs a lot of power to operate its mechanical parts in addition to the emissions of chlorofluorocarbon (CFC) which make this process unsustainable and environmentally unfriendly. The evaporative cooling is one of the alternative air conditioning sources which aim to avoid the drawbacks of the conventional method of cooling. To evaporate water the required heat is absorbed from whatever surface the water comes in contact with. This could be an object, from the air itself or from a wet cooling pad. As heat is removed from an object the temperature of that object or space is decreased. For example, in case of water as it evaporates into vapor it cools both the impinging on saturated air and the remaining water which provided the necessary sensible heat. The amount of heat required to evaporate one gallon (4.547 liters) is about 8700 B.T.U (1 B.T.U = 1055.06 Joules). So it can be seen that through evaporative cooling tremendous amount of heat can be removed from the air

having contact with evaporative cooling surface. There are two basic types of conventional evaporative coolers. Direct evaporative cooler (DEC) and indirect evaporative cooler (IEC). Fig (1.1)

Basically direct evaporative cooling system, dry outside air is blown over water-saturated medium made of porous ceramics and cooled by evaporation. The method introduces moisture to the air until the air stream is close to saturation. So the air temperature falls while its moisture contents increases. As a result energy contained in the exit remains unchanged and its wet bulb temperature kept the same. Fig (1.2)

Many applications are depending on the direct evaporative cooling. Drip or misting systems are one of the older evaporative cooling methods around. In this type a low pressure mist or drip is sprayed directly on a body. As moisture evaporates from the surface of the body, heat is absorbed and therefore it becomes cool. This method was commonly used on animals. As water drips sprayed on the animal skin evaporate, heat is absorbed. The animal therefore enjoys cooling. Drip evaporative cooling method was constructed with simple materials and used for the preservation of fruits and vegetables .It consists of a simple low cost cavity wall evaporative cooler constructed from bricks.

Fig.1.1 Evaporative cooling

The primary idea of the indirect evaporative coolers is cooling by decreasing air sensible heat without changing its humidity, which is a distinctive advantage over DEC systems. A common IEC unit comprises of a heat exchanger small fan, pump, water tank, and water distribution lines. Indirect evaporative coolers are classified into: Wet-bulb temperature IEC systems and Subwet-bulb temperature ICE systems.

Fig .1.2. Types of evaporative coolers

2. Literature Review

A lot of researches and modification have been done on the field of the evaporative cooling. These researches covered all the parts of and components of the evaporative cooling process.

2.1. Historical Review

Evaporative cooling was used around one thousand years ago by the ancient Egyptian people. At that time, porous pots and ponds covered with a wet cloth were often used to preserve food against hot weather and some water chutes were also integrated into walls to keep the inside space cool due to the evaporation of water when air flowed through. [1]

In India evaporation even helped make ice. Shallow beds in the earth, filled with a foot (30.5 cm) of straw insulation, supported shallow earthen pans on top. On still, frosty nights, even when the air fell no lower than 43F (6.1 C), ice formed, sometimes 1.5 in. (3.8 cm) thick.

Old homes and buildings in Iran are frequently cooled by evaporation; rooms are partially underground to escape solar heat and contain pools of running water with ventilating towers opening above them to catch wind and divert it across the water surfaces below. Reservoirs for drinking water are similarly cooled. Both ancient Persians and some American Indians topped tents with felt, which was then kept wet to provide cooling.

Leonardo da Vinci made the first mechanical air cooler, to cool the boudoir of his patron's wife. It was a hollow water wheel through which air was drawn by rising and falling water in its chambers as they revolved successively into and out of a stream. Water entering the wheel splashed through the air, cooling and cleansing it and forcing it through wooden valves out the hollow axle and into the boudoir.

Air washers and textile mill evaporative cooling were invented between 1900 and 1930. The term "air conditioning" was first used by engineer Stuart W. Cramer of Charlotte,N.C., in a 1906. In 1899, John Zellweger of St. Louis invented air washer fan whose blades and casing kept wet to remove all the dust and lint. After one year Robert Thomas invented the Acme washer which conducts air through falling stream of water. This was the introduction to the first modern air washer which made by Dr. Willis H. Carrier the founder of carrier company later. His invention were spray chambers featuring multiple pressure-type spray nozzles and eliminator plates, which allowed air to pass through them but confined the cleansing mist and spray. While cleaning the air it was also cooling and humidifying the air. It was used widely at the textile industry. The cooling power wasn’t understood or formulated but latter by trial and error adequate conditions was achieved by

increasing the water flow and the number of nozzles. To foster understanding, 67 pages of Department of agriculture psychrometric tables were adapted into the first psychrometric charts. Carrier questioned the charts and in 1911 presented his famous "Rational Psychrometric Formulas," which created accurate bases for evaporative cooling and for all air conditioning.

The first mechanical direct evaporative cooler appeared about 1932 when householders began to assist their window-hung wet cloths with electric fans. Burlap was used as the cloth material which was covering wood frame and dripping water over the cloth and mount it outside the window and by means of automobile fan the air was conducted through the frame to the room to get cold air. Soon excelsior pads replaced burlap. It was first called "wet-boxes," then they became known as "desert coolers" and then as "drip coolers."

For a long time the evaporative coolers wasn’t studied or analyzed and there was no literature for it. The reasons may be because this method was very old and it was found before the scientific era and the technological development in addition to the nature of the environments which used this method like the far desert places which wasn’t have a lot of habitants which resulted the lack of studying and developing of this cooling method. Consequently, this industry has far outstripped its related technical literature. In 1958, when at least 1,250,000 coolers were sold, the 1272-page Guide of the American Society of Heating and Air Conditioning Engineers devoted half a page to them, without tables or data. Only in 1961, following three years of a million plus cooler sales, did the Guide add a full chapter.

In 1963 Dr. Watt introduced the first serious analysis for direct and indirect evaporative cooling by his book “evaporative air conditioning Handbook”. This book was an attempt to understand the nature of the process of evaporative cooling although the limited number of the companies and research concerning about this field. This book was followed with another edition in 1986 after the development of this field. [2]

2.2. Terminology

Most of the evaporative cooling terminology are derived from the psychometric chart which is describing all the conditions which occurs during the air conditioning process fig.2.1

Fig.2.1 Psychometric chartsDry Bulb Temperature (DBT): The Dry Bulb Temperature refers to the ambient air temperature measured using a normal thermometer freely exposed to the air but shielded from radiation and

moisture. It is called "Dry Bulb" because the air temperature is indicated by a thermometer not affected by the moisture of the air. The dry bulb temperature is an indicator of heat content of the air. As the DB temperature increases, the capacity of moisture the airspace will hold also increases. The dry bulb temperature is usually given in degrees Celsius (ºC) or degrees Fahrenheit (ºF). The SI unit is Kelvin (K). Zero Kelvin equals to -273oC.

Wet Bulb Temperature: The Wet Bulb temperature is the temperature measured by using a thermometer whose glass bulb is covered by a wet wick/cloth. The wet bulb temperature is indicator of moisture content of air. Wet bulb temperature is very useful in evaporating cooling processes as the difference between the dry bulb and wet bulb temperature is a measure of the cooling efficiency. At 100% relative humidity, the wet bulb temperature equals dry bulb temperature.

Humidity: The term humidity describes the quantity of water vapor in air. If the air holds 50% of its capacity, the humidity would be 50%. If the humidity is low, then the capacity to hold more water is higher, and a greater amount of evaporation takes place. It can be expressed as an absolute, specific or a relative value.

Specific humidity or (humidity ratio) is the ratio between the actual mass of water vapor present in moist air - to the mass of the dry air. The humidity ratio is very useful in evaporative cooling because it provides the measure of the amount of moisture absorbed by the air stream and is useful in determining the spray water requirements. Specific Humidity is normally expressed in grains of water vapor /lb of dry air and may also be expressed in the units of pounds of water vapor/lb of dry air or grams of water vapor /kg of dry air.

Relative humidity: Relative Humidity or RH is the actual amount of moisture in the air compared to the total or maximum moisture the air can hold at a given temperature. When air has 50 percent relative humidity (RH), we say it is 50 percent saturated (the terms are numerically so close that we use them interchangeably). Obviously, as air approaches 100 percent saturation, it can take on less and less water until at 100 percent RH, the air cannot hold more water. Relative humidity is determined by comparing the "wet-bulb" and "dry-bulb" temperature readings. Dry bulb and wet bulb temperatures are taken simultaneously and then plotted on a psychrometric chart. Relative humidity is determined by the value at the intersection of two temperature lines.

Dew point: The Dew Point is the temperature at which water vapor starts to condense out of the air and becomes completely saturated. Above this temperature the moisture will stay in the air. The dew point temperature is an indicator of the actual amount of moisture in air.The dew-point temperature is expressed in degrees and like humidity ratio; it represents an absolute measure of the moisture in the air at a constant pressure. If the dew-point temperature is close to the air temperature, the relative humidity is high, and if the dew point is well below the air temperature, the relative humidity is low.

Sensible Heat: The heat used to change the temperature of the air. Sensible heat will always cause a change in the temperature of the substance.

Latent heat: Latent heat is the heat energy involved in the phase change of water. The heat will only change the structure or phase of the material without change to temperature.

Wet Bulb Depression (WBD): The difference between the dry bulb and wet bulb temperatures.Example: If dry bulb is 100ºF and the wet bulb is 70ºF; the web bulb depression is [100 - 70 = 30ºF]. At 100% cooling efficiency, the temperature drop across the evaporative cooler would be equal to the Wet Bulb Depression.

Saturation or Cooling Efficiency (SE or CE): The difference between the entering and exit dry-bulb temperatures over the wet-bulb depression.

Air Changes per hour (ACH): Air change is the number of times the air within a space is replaced during a specified period such as hour or minute. It is usually expressed in changes per hour or per minute.

British Thermal Units (BTU): A British thermal unit, or BTU, is a unit used to measure heat.

Face Velocity (FV): Expressed in feet per minute (FPM), it is the ratio of air flow divided by face area of the cooling media.

2.3. Direct Evaporative cooler

The Direct Evaporative cooling (Adiabatic Cooling) is the process where the air is cooled by the effect of the evaporation of water. When the air passes through wetted medium the water content of the medium will start to evaporate by converting the sensible heat of the air to latent heat for evaporation Fig (1-b). The wet bulb temperature is a measure of the potential of the cooling process of adiabatic cooling. By definition, the adiabatic process means that no heat addition or extraction from the system so all the heat needed for the evaporation of water is supported by the air which leads to decrease at the dry bulb temperature. Humidity is vital factor which affects the ability of the process to achieve the comfort condition. At humid regions the ability of the adiabatic cooling process to achieve the targeted comfort conditions is limited to the wet bulb temperature which is little high at humid weather. The representation of this process in the psychometric chart is showing that the line between the first and second point is on constant wet bulb temperature which is almost constant enthalpy process Fig (1-b) The combination of the adiabatic coolers with other systems to overcome these drawbacks is the only solution in order to get reliable and efficient system can be operated under any conditions.

Dzivama, (2000) [3] did a study on the forms of evaporative cooling process. There are two forms of in which the evaporative cooling principle can be applied. The difference is based on the means of providing the air movements across/through the moist materials .These are the passive and non-passive forms. The passive form of evaporative cooling relies on the natural wind velocity, to provide the means of air movement across/through the moist surface to effect evaporation. This form can be constructed on the farm, for short term on farm storage while the non- passive form uses a fan to provide air movement.

Fig 1. Direct Evaporative cooler. (a) Configuration of the process.

(b) Flow of the process in the psychometric chart

2.4.Indirect evaporative cooler

The Indirect Evaporative coolers decreasing the air temperature without affect the moisture content of the air. It depends on two air streams both of them are separated from the other. The heat transfer is taking place by means of heat exchanger. The heat exchangers have one wetted channel and the other one is dry. The wetted channel air is cooled by the principal of adiabatic cooling so certain heat and mass transfer is happening at this channel which is usually called working air. However, the primary air is losing the heat across the separating media which is allowing heat transfer between the two sides Fig (2-a). The cooling of the primary air stream is taking place unadibatically. The representation of this process shows that the humidity ratio of the primary air will stay the same along the process and the dry bulb temperature will approach the dry bulb temperature while the enthalpy of the air will change also. Fig (2-b)

Fig 2. Indirect Evaporative cooler. (a) Configuration of the process

(b) Flow of the process in the psychometric chart

2.5. Recent development

In 1961 Baker and Shryock [4] have analyzed the cross-flow cooling tower using finite difference method. The used merkel equation [5] sacrificed the accuracy in deducing the resultant heat transfer between the bulk water and the air stream by ignoring the temperature difference and the water evaporation effect.

In 1968, Donald pescod [6] developed heat exchanger to provide heat recovery and increase the cooling efficiency by cooling the air but without adding any moisture to the working air.

Eskra (1980) [7] presented a two stage system associating a direct and an indirect evaporative cooling in order to increase the system’s efficiency. Construction of various evaporative systems was done by Rusten, (1985) [8] using available materials as absorbent (pads). Materials used include canvas, jute curtains and hourdis clay blocks. Also a mechanical fan was introduced to some of the coolers constructed. He did an extensive research in the construction of different evaporative cooling

systems using locally available absorbent materials such as canvas, jute curtains, etc. Mechanical fans were used in some of the designs which drew air through a continuously wetted pad. The continuous wetting of the pad was achieved by placing elevated water basins on the fabric material, which absorbed the water gradually and eventually got saturated. He described the functionality of a hourdis clay block coolers which was constructed by two researchers.

Liesen and Pedersen [9] presented five configurations of evaporative cooling for energy analysis through BLAST software (Building Loads Analysis and System Thermodynamics). Mathews et al, provided a model of integrated simulation of building conditioning using evaporative coolers. This paper was aiming to design an efficient simulation of the combination of building and evaporative cooling systems using program EASY. It was simulated the regenerative evaporative cooling to the building and the results shown that it can be achieve thermal comfort in more than 80 % of southafrican houses.

Luigi Schibuola [10] presented a case study for a regenerative air conditioning to increase the efficiency of the cooling system using the waste air by passing it in adiabatic air saturation system which will increase the ability of cooling the working air to temperatures lower than the dry bulb temperature and reduce the amount of used water in addition to increasing the efficiency of the system.

Halasz [11] presented a general dimensionless mathematical model to describe all evaporative cooling devices used today (cooling water towers, evaporative condensers of fluid, air washes, dehumidification coils and others)

Camargo and Travelho [12] worked on a research where a thermal balance study for direct and indirect cooling systems is developed. Then Camargo and Ebinuma [13] presented the principles of operation for direct and indirect evaporative cooling systems and the mathematical development of the equations of thermal exchanges. it was allowing for the determination of heat transfer convection coefficients for primary and secondary air flow the basic principles of the evaporative cooling process for human thermal comfort, the principles of operation for the direct evaporative cooling system and the mathematical development of the equations of thermal exchanges, allowing the determination of the effectiveness of saturation. It also presented the results of experimental tests in a direct evaporative cooler that take place in the Air Conditioning Laboratory and the experimental results are used to determinate the convective heat transfer coefficient and to compare with the mathematical model.

After that they have presented three ways to determine the most efficient operating of the evaporative cooling systems according to the temperature condition and the humidity of the region. The first method was using the feasibility indexes which depend on watt (1963 pp. 54). The second method was the cooling process vector which depended on the comfort areas on the psychometric chart and it depended on the ASHRAE comfort zones. The third and last method was nomographic and templates and it is like modification for the method used by watt 1963.

Dai and Sumathy [14] theoretically investigated a cross flow direct evaporative cooler, in which wet durable honeycomb paper constituted as the packing material, and the air channels formed by alternate layers of two kinds of papers with different wave angles were regarded as parallel plate channels with constant spacing. Air flows across the falling water film through the channels, being cooled and humidified. The governing equations for the falling film and moist air are solved by integration. Obviously the effects of the wave angles of the packing paper on the heat and mass transfer enhancements are neglected.

Ghasem Heidarinejad [15] introduced general approach to evaporative cooling devices, modeling of a cross flow two stage evaporative cooler has been presented. The indirect stage is well described by the numerical solution of energy and mass balance equations while the direct stage effectiveness is determined by an analytical simple equation which is suitable for cellulose paper pads. Two stage evaporative cooler could provide comfort conditions in some major cities of Iran where direct cooling system is unable to meet comfort requirements.

Ghasem et al [16] made also hybrid system which uses the underground precooling as a tool to increase the performance of the evaporative cooling system. The research simulated the results using CFD to find the effectiveness of using ground coupled circuit (GCC) prior to the DEC to achieve effectiveness higher than unity.

J.M. Wu and X. Huang [17] made Numerical investigation on the heat and mass transfer in a direct evaporative cooler. The models and methods are validated by comparing the numerical results with those of experiment for the same evaporative cooler. The influences of the inlet frontal air velocity pad thickness; inlet air dry-bulb and wet-bulb temperatures on the cooling efficiency of the evaporative cooler are calculated and analyzed.

Chenguang Sheng et al [18], did research about three parameters which were tested for their impact on efficiency and other crucial system properties: the velocity of the frontal air, the temperature of the frontal air, and the temperature of the inlet water. By conducting multiple tests for each parameter using incremental velocities/temperatures and by plotting these increments against efficiency, it was possible to determine the effect of each parameter on efficiency. An empirical correlation between frontal air velocity and cooling efficiency within a certain velocity range was established and compared with theoretical calculation. It was determined that lower velocities, lower cooling water temperatures.

S. Elmetenani et al,[19] made investigation about the using of DEC in Algerian environment and the result shown that the temperature depression is 18.8 C at the desert side of the country which represent two third of the country. Therefore the energy consumption is very low the system can be operated by solar photovoltaic panels.

American society of heating, Refrigerating and air conditioning engineers (ASHRAE) is four volume publications. The four volumes are Fundamentals, Refrigeration, HVAC Applications, and HVAC Systems and Equipment.[20] [21]

3.1. Applications

The applications of evaporative cooling include several fields like residential buildings, agricultural, commercial and industrial applications (power plants, mills and foundries). There are many general applications for the evaporative cooling systems like cooling, Humidification, dehumidification and air cleaning.

3.1.1.Cooling

Evaporative cooling is used in almost all climates. The wet-bulb temperature of the entering airstream limits direct evaporative cooling. The wet-bulb temperature of the secondary airstream limits indirect evaporative cooling.

Direct evaporative cooling is generally used in spot cooling applications like kitchens, laundries, agricultures and industrial applications. It depends on removing the sensible heat of the air steam from the air stream to be latent heat at the water. It is applicable in almost all the temperature conditions which have lower relative humidity. Consequently, when the direct evaporative cooling is not able to achieve the air conditioning target the indirect evaporative cooling is combined with it in order to achieve the comfort condition. The wet bulb temperature of the air stream limits direct evaporative cooling and the wet bulb temperature of the secondary air limits the indirect evaporative cooling. When the air is cooled to wet bulb temperature the effectiveness is 100%. The psychometric chart can show us the difference between the cooling of the direct evaporative coolers and the indirect evaporative cooler.

(Fig 3.1) Direct/indirect evaporative cooling

3.1.2. Humidification

Using direct evaporative cooling the air can be humidified using three ways

1. Recirculated water2. Preheating the air and treating with recirculated water3. Heating the circulated water

1. Recirculated water

This method depends on saturating the air stream by means of water spray powered by pump. This process is almost completely adiabatic except the small power used to operate the pump rod.

The effectiveness of these methods depends on the air velocity and the area of explosion between the air and the wetting media.

2. Preheating the air and treating with recirculated water

By heating the inlet air both wet and dry bulb temperature are increased. the ability of the air to accept more water content increases also because the humidity ratio is decreasing. The process is achieved by heating to the required wet bulb temperature and then adiabatically cooling the air dry bulb temperature to the required temperature and humidity ratio. There are two ways to the control the process which are bypassing the inlet air arrounf the weting media or modify the number of the spraying nozzles.

3. Heating water

By heating the water the effectiveness of the evaporative cooling is increased. the dry temperature of the air stream will be increased also which will allow for more humidification effect like the preheating of the air stream. The controlling methods are similler also to the previous method.

3.1.3.Dehumidification and cooling

Direct evaporative coolers may be used to cool and dehumidify air. Using cold water which has temperature lower than the wet bulb temperature of the air will cause both the air wet and dry bulb temperature. If the water temperature is maintained lower than the wet bulb temperature of the air so the air will start to lose humidity and after that this air can be used as dehumidifier.

3.2. Indirect evaporative cooler applications

There are five applications for indirect evaporative cooling in the residential and industrial field which will be discussed in more details.

3.2.1. Heat pipe air to air H.E.

The heat pipe air-to-air heat exchanger uses a direct water spray from a recirculation sump on the wet side of the heat pipe tubes (Scofield and Taylor 1986)[22]. When either room return or outdoor air passes over the wet surface, outdoor air entering the building is dry-cooled and produces an approach to the wet side wet-bulb temperature in the range of 60 to 80% IEE for equal mass flow rates on both sides of the heat exchanger. The IEE is a function of heat exchanger surface

area, face velocity, and completeness of wetting achieved for the wet-side heat exchanger surface. Face velocities on the wet side are usually selected in the range of 2 to 2.3 m/s. (fig 3.2)

(Fig 3.2) Heat pipe air to air heat exchanger

3.2.2.Cross flow plate air to air H.E.

A cross flow plate type air-to-air indirect evaporative cooling heat exchanger (Yellott and Gamero 1984) [23]. In this configuration, outdoor air is supplied for both wet- and dry-side flows through the heat exchanger. Recirculation water from the sump below the heat exchanger is sprayed downward through the vertical wet-side air path, counter flow to the air which moves vertically up through the heat exchanger. The approach to the ambient wet bulb is a function of heat exchanger surface area and the effectiveness of the water spray system at completely wetting the wet-side surface of the air-to-air heat exchanger. (Fig 3.4)

(Fig 3.4) cross flow air to air heat exchanger

3.2.3.The heat wheal and run around coil

The heat wheel (Fig 3.5) and the run-around coil (Fig 3.6) both use a direct evaporative cooling component on the cold side to enhance the dry-cooling effect on the makeup air side. The heat wheel (sensible transfer), when sized for 2.5 m/s face velocity with equal mass flows on both sides, has an IEE around 60 to 70%. The run-around coil system at the same conditions produces an IEE of 35 to 50%. The adiabatic cooling component is usually selected for an effectiveness of 85 to 95%. Water coil freeze protection is required in cold climates for the run-around coil loop.

(Fig 3.5) the heat wheel

(Fig 3.6) the run around energy recovery

3.2.4.Cooling tower

A cooling tower to coil indirect evaporative cooling system with IEE in the range of 50 to 75% (Colvin 1995)[24]. This system is sometimes referred as a water-side economizer. The cooling tower is selected for a close approach to the ambient wet-bulb temperature, with sump water from the tower then pumped to precooling coils in an air-handling unit. Provision for water filtration to remove solids from sump water is needed, and water coils may need to be cleanable. Freeze protection of the water coil loop is required in cold climates. No winter heat recovery is available with this design. (Fig 3.7)

Common applications include cooling the circulating water used in oil refineries, petrochemical and other chemical plants, thermal power stations and HVAC systems for cooling buildings. The

classification is based on the type of air induction into the tower: the main types of cooling towers are natural draft and induced draft cooling towers.

(Fig 3.7) cooling tower

4. Computational model

Psychometrics uses thermodynamic properties to analyze conditions and processes involving moist air. Dry air is atmospheric air with all water vapor and contaminants removed. Its composition is relatively constant, but small variations in the amounts of individual components occur with time, geographic location, and altitude. The relative molecular mass of air is 28.966 and the universal gas constant is 8314.472. The gas constant for dry air using the current Mohr and Taylor [25] value for the universal gas constant is

Rda = 8314.472

28.966 = 287.1 Jkg·K

Moist air is a binary (two-component) mixture of dry air and water vapor. The amount of water vapor varies from zero (dry air) to a maximum that depends on temperature and pressure. Saturation is a state of neutral equilibrium between moist air and the condensed water phase. The molecular mass of water is 18.0152 and the gas constant of water vapor is

Rwv = 8314.47218.0152 = 461.5

Jkg·K

The temperature and barometric pressure of atmospheric air vary considerably with altitude as well as with local geographic and weather conditions. The standard atmosphere gives a standard of reference for estimating properties at various altitudes. Pressure values may be calculated from the formula of .

P= 14.696 (1 – 6.8754 · 10-6 Z)5.2559

WhereZ = altitude, Mp = barometric pressure, Pa

The saturation pressure over liquid water for the temperature range of 0 to 200 °C is given by [26]

Ln pws = c1

T + C2 + C3 T + C4 T2 + C5 T3 + C6 ln T

WhereC1 = -1.044 039 7 E+04C2 = -1.129 465 0 E+01C3 = -2.702 235 5 E-02C4 = 1.289 036 0 E-05C5 = -2.478 068 1 E-09C6 = 6.545 967 3 E+00

T is the temperature in 0KPws is saturated vapor pressure Kpa

The principle of psychometric hygrometry is that the humidity is calculated by the dry-and-wet bulb equation according to dry-bulb and wet-bulb temperatures (Zelin et al.)[27]. Then the relative humidity can be calculated by the dry and wet bulb temperature using the formula:

Ø = ew−(A ∙ P ∙∆T )

ed x 100

WhereØ = The relative humidity ew = The saturation vapor pressure in the wet-bulb temperature

ed = The saturation vapor pressure in the dry-bulb temperature

A = The measuring humidity coefficient P = The mean atmospheric pressure t = The difference between the dry-bulb temperature and the wet-bulb temperatureΔ

Here we can use buck formula to calculate the saturation vapor pressure because it is simpler than the formula of coff in 1965[28]:

E= 6.112 · e17.502· t240.97+t

A is the conversion factor which can be calculated by empirical formula of (Butler and García-Suárez,)[29]:

A=0.00066 (1+ 0.00115 · Tw)

We can find that the method of calculating the relative humidity have s mall errors value which is suitable for industrial calculations with high accuracy and here are some recorded values and the error recorded between the theoretical and linear smooth value

Dry bulb temperature 0C

Wet bulb temperature 0C

Formula values % Ls values % Relative error %

20 15 58.8 58 1.4

36 21 25.1 24.2 3.6

45 29 30.7 30 2.3

58 44 45 44.8 0.4

60 58 90.4 90 0.6

72 62 62.4 61.8 0.9

The actual vapor pressure can be calculated by the equation

Ø = pwpws

%

Where pw is the vapor pressure

The humidity ratio can also be expressed with the partial pressure of water vapor and air by the equation [30]

W= 0.622 pw

p−pws kg(water )

kg(air)

The Enthalpy of moist air can be expressed as: [31]

h = ha + W hw

Whereh = specific enthalpy of moist air (kJ/kg)ha = specific enthalpy of dry air (kJ/kg)W = humidity ratio (kg/kg)hw = specific enthalpy of water vapor (kJ/kg)

It can be rewritten in this form

h = Cpa · t + W (hw + Cpw· t) kJ/kg

h = 1.01 · t + W (2502+1.84 · t) kJ/kg

The specific heat of moist air can be driven from the enthalpy law

Cp = (1.0029 +5.4 · 10 -5 · T) + W (1.856 + 2· 10 -4 · T) KJKg· K

Specific volume is defined as the total volume of dry air and water vapor mixture per kg of dry air and water vapor

ⱱ = V

ma+mw m

3

kg

ⱱ = V

ma(1+w) =V a

1+W

ⱱ = Ra·TP ·

1+W ·RwRa

1+w m

3

kg

Where:

ⱱ = specific volume of moist air

Va = specific volume of moist air per mass unit of dry air (m3/kg)

ma = mass of dry air (kg)

mw = mass of water vapor (kg)

p = pressure in the humid air (Pa)

T = temperature of the moist air (K)

The dew point temperature is found by the regression analysis to relate the dew point temperature to the partial water vapor pressure .the temperature range is divided in the ranges to give accurate results. The three equations are[30]

Tdp = 5.994 + 12.41 · + 0.4273 · α α2 (223 ⋜ T ⋜ 273) 0KTdp = 6.983 + 14.38 · + 1.079 · α α2 (273 ⋜ T ⋜ 323) 0KTdp = 13.80 + 9.478 · + 1.991 · α α2 (323 ⋜ T ⋜ 383) 0KWhere α = ln ( pw )

References

[1] Watt J.R. 1986; “Evaporative Air Conditioning Handbook”, Editorial Chapman & Hall, New York.

[2] Watt, J, R. 1963“Evaporative air conditioning”, New York, the industrial press. 300p.

[3] Dzivama A.U. 2000. “Performance evaluation of an active cooling system for the storage of fruits and vegetables”. Ph.D. Thesis, Department of Agricultural Engineering, University of Ibadan, Ibadan.

[4] D.R. BAKER, H.A. SHRYOCK. 1961. “A comprehensive approach to the analysis of cooling tower performance”. ASME Transactions, Journal of Heat Transfer (August):339.

[5] F. Merkel, “Verdunstungskuehlung,” VDI Forschungsarbeiten No. 275, Berlin, 1925

[6] Pescod, D., 1968, “Unit air cooler using plastic heat exchanger with evaporatively cooled plates”, Australian Refrigeration, Air Conditioning and Heating, Vol. 22, No. 9, pp. 22-26.

[7] Eskra, N., 1980, “Indirect/direct evaporative cooling systems”, ASHRAE Journal, may, 1980, pp. 21-25;

[8] Eric Rusten (1985). “Understanding Evaporative Cooling”. Volunteers in Technical Assistance (Vita), 1600 Wilson Boulevard, Suite500 Arlington, Virginia 22209 USA.

[9] Liesen, R. J., Pedersen, C. O., 1991, “Development and demonstration of an evaporative cooler simulation model for blast energy analysis computer program”, ASHRAE Transactions, Vol. 97, Part 2, pp. 866-873.

[10] Luigi Schibuola, Experimental analysis of a condenser heat recovery ill an air conditioning plant, Energy 24(1999) 273-283.

[11] Halasz, B., 1998, “A general mathematical model of evaporative cooling devices”, Rev. Gén. Therm., FR, Vol. 37, pp. 245-255, Elsevier, Paris.

[12] Cardoso, S., Camargo, J. R., Travelho, J. S., 1999.” Introdução à utilização do resfriamento evaporativo para condicionamento de ar automotivo, XV Brazilian Congress of Mechanical Engineering, COBEM99, Águas de Lindóia, SP.

[13] J.R. Camargo, C.D. Ebinuma, A mathematical model for direct and indirect evaporative cooling air conditioning systems, Proceedings of the 9th Brazilian congress of thermal engineering and sciences, 2002 [ENCIT, UFPB, Joa˜o Pessoa, PB, paper CIT02-0855].

[14] Y.J. Dai, K. Sumathy, Theoretical study on a cross-flow direct evaporative cooler using honeycomb paper as packing material, Applied thermal engineering, Elsevier, Amsterdam, 2002. p. 1417–1430.

[15] Ghassem Heidarinejad, Mojtaba Bozorgmehr, Shahram Delfani, and Jafar Esmaeelian “Experimental investigation of two stage indirect/direct evaporative cooling system in various climatic conditions” Building and Environment 44. 2010. 2073-2079

[16] Heidarinejad Ghassem et al. “Performance analysis of a ground-assisted direct evaporative cooling air conditioner”. Building and Environment, 45, 2421-2429, 2010

[17] J.M. Wu, X. Huang, H. Zhang, Theoretical analysis on heat and mass transfer in a direct evaporative cooler, Applied Thermal Engineering 29 (2009) 980–984.

[18] C. Sheng and A. G. Agwu Nnanna, 2012, “Empirical Correlation of Cooling Efficiency and Transport Phenomena of Direct Evaporative Cooler”, Applied Thermal Engineering, Vol. 40. pp. 48 - 55.

[19] S. Elmetenani et al., “Investigation of an evaporative air cooler using solar energy under Algerian climate,” Energy Procedia, vol. 6, pp. 573-582, 2011.

[20] American Society of Heating, Refrigerating and Air-Conditioning Engineers. 2009 “ASHRAE Handbook Fundamentals.” Atlanta, GA: American Society of Heating, Refrigeration and Air-Conditioning Engineers, 2009.

[21] American Society of Heating, Refrigerating and Air-Conditioning Engineers. 2011 .”ASHRAE Handbook heating, ventilating, and air-conditioning applications”. Atlanta, GA: American Society of Heating, Refrigeration and Air-Conditioning Engineers, 2011. ISBN 978-1-936504-07-7

[22] Scofield, M. and J.R. Taylor. 1986. “A heat pipe economy cycle”. ASHRAE Journal 28(10)35-40.

[23] Yellott, J.I. and J. Gamero. 1984. “Indirect evaporative air coolers for hot, dry climates”. ASHRAE Transactions 90(1B):139-147.

[24] Colvin, T.D. 1995. “Office tower reduces operating costs with two-stage evaporative cooling system”. ASHRAE Journal 37(3):23-24.

[25] Mohr, P.J., and P.N. Taylor. 2005. CODATA recommended values of the fundamental physical constants: 2002. Reviews of Modern Physics 77:1-107.

[26] Wexler, Arnold and Gr eenspan, Lewis, Vap or pressure equation for water in the range 0 to 100 °C, J. Res. Nat. Bur. Stand. (U.S.), 75A, Phys. and Chern., No. 3, 213- 230 (1971) .

[27] Zelin, Y., L. Xiangbai, L. Jianchun and T. Yali, 2010. Design of intelligent psychrometric humidity sensor. Process Automat. Instrument., 2(2010): 16-20, (In Chinese).

[28] Buck, A.L., 1981. New equations for computing vapor pressure and enhancement factor. J. Appl. Meteorol., 20(12): 1527-1532.

[29] Butler, C.J. and García-Suárez, 2012. Relative humidity at armagh observatory 1838-2008. Int. J. Climatol., 32(2012): 657-668.

[30] American Society of Heating, Refrigerating and Air-Conditioning Engineers. 2013 “ASHRAE Handbook Fundamentals.” Atlanta, GA: American Society of Heating, Refrigeration and Air-Conditioning Engineers, 2015. 1.12 P. ISBN: 1-936504-45-6.

[31] R. K. Rajput. 2007 “thermal engineering (3rd Edition)”. New Delhi , LAXMI PUBLICATIONS (P) LTD, 2015 422 p. ISBN: 978-0-7637-8272-6.