Theoretical Analysis on Heat and Mass Transfer in a Direct Evaporative Cooler

Available online at www.ijiere.com International Journal of Innovative and Emerging Research in Engineering e-issn: 2394 3343 p-issn: 2394-5494 Theoretical Analysis on Heat and Mass Transfer in a Direct Evaporative Cooler Rasika D Deshmukh a, Samir Jdeshmukh b,dipak A Warke c a P.G Student,Mechanical Engineering Department, P.R.M.I.T.& R,Badnera, Dist. Amravati, India b Mechanical Engineering Department, P.R.M.I.T.& R,Badnera, Dist. Amravati, India c Mechanical Engineering Department, J.T.Mahajan College Of Engineering,Faizpur, Dist. Jalgaon, India ABSTRACT: This paper presents 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. The heat and mass transfer between air and water film in the direct evaporative cooler is theoretically analyzed in present paper. The experimental study is based on weather data from Maharashtra (Amravati), India. The performance of the evaporative cooler is evaluated using the output temperature, saturation efficiency, and heat transfer coefficient. The output temperature of the air varies between 24.44 C and 33 C for different velocities of air. Keywords- Evaporative cooling, Mathematical Formulation, Theoretical Analysis, direct evaporative cooling,heat and mass transfer I. INTRODUCTION Evaporate cooling operates using induced processes of heat and mass transfer, where water and air are the working fluids. It consists, specifically, in water evaporation, induced by the passage of an air flow, thus decreasing the air temperature. When water evaporates into the air to be cooled, simultaneously humidifying it, that is called direct evaporative cooling (DEC) and the thermal process is the adiabatic saturation. The main characteristic of this process is the fact that it is more efficient when the temperatures are higher, that means, when more cooling is necessary for thermal comfort. It has the additional attractiveness of low energy consumption and easy maintenance. Due to use total airflow renewal, it eliminates the recirculation flow and proliferation of fungi and bacteria, a constant problem in conventional air conditioning systems. Due to its characteristics the evaporative cooling system is more efficient in places, where the climate is hot and dry but it can also be used under other climatic conditions. Many studies have dealt with the performance of direct evaporative cooling. In India, Kulkarni and Rajput [1] made a theoretical performance analysis of direct evaporative cooling. Different materials were considered in the analysis; rigid cellulose, high density polythene, aspen fiber and corrugated paper material. The results of the analysis showed that the aspen fiber material had the highest efficiency of 87.5%, while the rigid cellulose material had the lowest efficiency at 77.5%. The outlet temperature and cooling capacity varied between 28.8 C and 26.5 C and 1348 KJ/h and 56686 KJ/h for the two materials, respectively. Camargoa, CarlolEbinumab, Silveira[2] presents, initially, a mathematical model for a direct evaporative cooling air conditioning system that is obtained by writing the energy conservation equation for an elementary control volume and analyzing the heat and mass transfer between the humid air and the water. The resulting equation allows to determinate the DEC(Direct Evaporative cooler) effectiveness and compares it with the experimental results. J. M. Wuab, X. Huang b, H. Zhang [3] analyzed theoretically the heat and mass transfer between air and water film in the direct evaporative cooler. The analysis shows that the frontal air velocity and pad thickness of the pad module are two key influencing factors to the cooling efficiency of a direct evaporative cooler. Baredar, Khare, Chaturvedi, M. M. Sahu [4] experimentally investigated the Cooling performance of indirect/direct evaporative cooling system. For this purpose, a two-stage evaporative cooling experimental setup consisting of an indirect evaporative cooling stage(iec) followed by a direct evaporative cooling stage (DEC) was designed, constructed and tested. Mohammed Ahmed,Abaas, Mohammed Ahmed, Mohd Ismail [5] evaluate performance of three types of evaporative cooling pads for greenhouses (celdek pads, straw pads and sliced wood pads), as compared to the conditions outside the greenhouses (control), for pads. The results obtained for the temperature at 8 am showed that there was no significant difference (.5) inside the greenhouses, while a high significant difference between the conditions inside and outside of the greenhouses was found. A. Fouda, Z. Melikyan [6] discussed the heat and mass transfer, process in direct evaporative cooler. A simplified mathematical model is developed to describe the heat and mass transfer between air and water in a direct evaporative cooler. Manuwa1 &Odey[7] were carried out investigation into local materials as cooling pads, and shapes for constructing evaporative coolers. Materials investigated include jute, latex foam, charcoal and 152

wood shavings. Shapes of cooling systems considered were of hexagonal and square cross-sections. Abbouda, and. Almuhanna[8] proposed and analyzed proposed and analysed to get higher cooling efficiency in hot and arid environments such as Saudi Arabia. The obtained results also revealed that, the overall effectiveness of the combining cooling system was more than 1%. Abdulrahman Th. Mohammad, Sohif Bin Mat, M.Y. Sulaimana, K. Sopian, Al-abidi[9] Works presents an experimental investigation on the performance of a direct evaporative cooler in hot and humid regions. The experimental study is based on weather data from Kuala Lumpur, Malaysia. The output temperature of the air varies between 27.5 C and 29.4 C, while the cooling capacity is between 1.384 kw and 5.358 kw. Shrivastava, Dr. Deshmukh, M. V. Rawlani[1] investigates the performance analysis for a new sustainable application to reuse an Coconut Coir fiber, in evaporative cooling pads. The coconut coir fibre pad was analyzed and compared with those of a commercial Aspen wood (wood wool) pad. Haruna, Akintunji, Momoh, Tikau[11] attempt to theoretically analyse the performance of direct evaporative cooler in hot and dry climate with Kano being the study area. The performance of the cooler was determined at different air velocities at a saturation effectiveness of 5% to 9%. The determined parameters are the leaving air temperature, relative humidity, cooling capacity and the water consumption rates. II. DIRECT EVAPORATIVE COOLING The principle underlying direct evaporative cooling is the conversion of sensible heat to latent heat. Non-saturated air is cooled by heat and mass transfer increases by forcing the movement of air through an enlarged liquid water surface area for evaporation by utilizing blowers or fans. Some of the sensible heat of the air is transferred to the water and becomes latent heat by evaporating some of the water. The latent heat follows the water vapour and diffuses into the air[15]. Fig. 1 shows a schematic direct evaporative cooling system, where water is running in a loop and the makeup water entering the sump to replace evaporated water must be at the same adiabatic saturation temperature of the incoming air. In a DEC, the heat and mass transferred between air and water decreases the air-dry bulb temperature (DBT) and increases its humidity, keeping the enthalpy constant (adiabatic cooling) in an ideal process. The minimum temperature that can be reached is the thermodynamic wet bulb temperature (TWBT) of the incoming air. The effectiveness of this system is defined as the rate between the real decrease of the DBT and the maximum theoretical decrease that the DBT could have if the cooling were 1% efficient and the outlet air were saturated. Practically, wet porous materials or pads provide a large water surface in which the air moisture contact is achieved and the pad is wetted by dripping water onto the upper edge of vertically mounted pads. Fig. 1.Direct evaporative cooling (DEC). III. MATHEMATICAL FORMULATIONS In the study of the psychometric process dry air is considered as a single gas characterized by an average molecular mass equal to 28.9645. In this work the humid air is considered as a mixture of two gases: the dry air and water vapour. Considering the flow of humid air close to a wet surface, according to Fig. (2), the heat transfer will occur if the surface temperature Tsis different from the draft temperature T. If the absolute humidity (concentration) of the air close the surface wsis different from the humidity of the draft w a mass transfer will also occur. The elementary sensible heat is δq s= h cda(ts- T) (1) Where hcis the convective heat transfer coefficient, A is the area of the heat transfer surface, Tsis the surface temperature and T is the bulk temperature. 153

Fig. 2. Schematic direct evaporative cooler The hccoefficient is determined from the Nusselt number (Nu) expressed as a function of the Reynolds number (Re) and Prandtl number (Pr). In a similar way the rate of water vapour transfer dm Vbetween the draft and the air close to the surface will dm v= h mρ ada (ws - w) (2) wherehmis the mass transfer coefficient by convection and ρa is the density of the water. By analysis of the interface air-liquid, the latent heat δq Lis determined by the energy conservation law. δq L = δq- δq s = h Lvsdm v (3) whereδqis the flow of total heat and h LVSis the specific enthalpy of vaporization of the water at surface temperature. Rearranging (1), (2) and (3), the total differential heat flow is δq = [h c (T s - T) + ρ ah Lvsh m (w s - w) ]da (4) Equation (4) indicates that the total heat transfer is the result of a combination of a portion originating from temperature difference and other portion originating from the difference of the absolute humidity's. The total heat is caused by two potentials and these potentials can be combined by the Lewis relationship so that the total heat flow will be expressed by a single potential that is the enthalpy difference between the air close to the wet surface and the air free current. Using the specific enthalpy of the mixture as the sum of the individual enthalpies [16] gives h s- h = (h sa- h a ) (w sh vs - wh v ) (5) whereh vsis the vapour enthalpy at surface temperature, h as is the enthalpy of the leaving air, ha is the air enthalpy and h vis the vapour enthalpy. With the hypothesis that air and vapor are perfect gases it follows that h s- h =c pu (Ts- T) + h vs (w s- w) (6) where the humid specific heat is c pu= c pa+ wc pv. (7) Cpa is the constant pressure specific heat of the air and Cpv is the constant pressure specific heat of the vapour. In the standard environmental conditions Cpa = 1,6 kj/kg K and Cpv = 1,85 kj/kg K. Therefore Ts T = (hs h) hvs (ws w) cpu (8) Combining (4) and (8) gives hc da (ws w) δq = [(hs h) + (hlvs RLe hvs)](9) cpu RLe wherer Leis the Lewis relationship, a dimensionless number expressed a RLe = hc hm cpu (1) In the above deduction the density of the humid air was approximated by the density of the dry air. Taking the Lewis relationship as being unitary, gives ( h Lvs - h vs ) h Ls. It is also verified that the term (w - ws) h Ls is usually negligible in the presence of difference of the specific enthalpies (hs- h), so that only the first term inside brackets is significant. In the same way, the total heat flow is caused by the difference of specific enthalpies of the air and of the saturated air close to the wet surface and is given hc da δq = (hs h) (11) cpu The sensible heat transferred is δq s= m ac pudt (12) wherem a is the air mass flow. Therefore by combining (12) with (1) gives hcda (Ts - T) = ma cpudt (13) which can be integrated, resulting in A hc ma cpu da dt (Ts T) T2 T1 = 154

The integration yields 1 T₁ T₂ = exp ( hc A ) (14) T₁ Ts ma cpu The effectiveness of a direct evaporative cooling equipment is defined as ℇ = T₁ T₂ (15) T₁ Ts Then ℇ = 1 exp ( hc A ) (16) ma cpu Analysing the (15) it is verified that an effectiveness of 1% corresponds to air leaving the equipment at the wet bulb temperature of entrance. This requires a combination of large area of heat transfer and a high heat transfer coefficient and low mass flow. It is also observed that the effectiveness is constant if the mass flow is constant since it controls directly and indirectly the value of the parameters on the (16). IV. THEORETICAL ANALYSIS OF DIRECT EVAPORATIVE COOLER The equipment utilizes an evaporative pad with 75 71 7.62 cm 3, and provides about 37 m 2 of evaporative surface area per cubic metre of media [12], providing a wetted area equal to 14.8 m 2 in the pad. Dowdy and Karabash [13] presents a correlation to determinate the convective heat transfer co-efficient in a rigid cellulose evaporative media: Nu =.1 ( le l ).12 Re.8 Pr.33 (17) where le is defined by le = θ (18) A This parameter is called characteristic length and is used to calculate the Reynolds (Re) and Nusselt (Nu) numbers. The following air properties are used: ρ=1.128kg/m 3 ; k=.2756w/m ; Pr=.699; Cpu=15 J/kg andv= 16.96 1-6 m 2 /s. Table I. The resulting convective heat transfer coefficient for several air velocities calculated from (17). v(m/s) m(kg/s) Re hc(w/m 2 ) 1.66.98 264.41 52.56 2.5 1.48 398.22 72.98 5 2.961 796.44 127.8 9 5.32 1433.59 23.46 Table II. The outlet dry air which calculated theoretically using (15) and (16) when velocity of air is 1.66m/s. Inlet Dry air T₁ Inlet wet air Ts Relative Humidity outlet dry 31 19 32 24.44 35 19 21 26.26 4 2.8 17 29.51 41 22.8 2 31.6 Table III. The outlet dry air which calculated theoretically using (15) and (16) when velocity of air is 2.5m/s. Inlet Dry air T₁ Inlet wet air Ts Relative Humidity outlet dry 31 19 32 24.8 35 19 21 26.74 4 2.8 17 3 41 22.8 2 31.6 Table IV. The outlet dry air which calculated theoretically using (15) and (16) when velocity of air is 5 m/s. Inlet Dry Inlet wet Relative outlet dry Humidity air T₁ air Ts 31 19 32 25.37 35 19 21 27.5 155

Outlet Temp of Air Effectiveness Effectiveness International Journal of Innovative and Emerging Research in Engineering 4 2.8 17 31 41 22.8 2 32.47 Table V. The outlet dry air which calculated theoretically using (15) and (16) when velocity of air is 9 m/s. Inlet Dry bulb temp of air T₁ Inlet wet bulb temp of air Ts Relative Humidity.6.5.4.3.2.1 outlet dry 31 19 32 25.86 35 19 21 28.1 4 2.8 17 31.73 41 22.8 2 33 2 4 6 8 1 Air Velocity Fig. 3. Air velocity Effectiveness The evaporative cooler provides air flow variation by the of fan rotation. Fig. 3 presents a variation of the cooling effectiveness as a function of air speed..6.5.4.3.2.1 5 1 15 2 Reynolds Number Fig.4. Reynolds number Effectiveness Fig. 4 shows the comparison between the effectiveness calculated from (15), with data obtained from the tests, and from (16) as function of the Reynolds number. 35 3 25 2 15 1 5 31 35 4 41 Inlet Temp Fig. 5. Inlet Temp Outlet Temp of Air v=1.66m/s v=2.5m/s Fig. 5 shows the comparison between inlet and outlet temp of air at different velocity of air. V. DISCUSSION AND CONCLUDING REMARKS This paper presents, initially, a mathematical formulation for a direct evaporative cooling air conditioning system that is obtained by writing the energy conservation equation for an elementary control volume and analyzing the heat and mass transfer between the humid air and the water. The resulting equation allows to determinate the DEC effectiveness v=5m/s v=9m/s 156

and compares it with the experimental results, according to Fig. 4 which the curve concerning to (16) was determined using the mass air flow and the convective heat transfer coefficient obtained from the (17). Using (15) and (16) the effectiveness and outlet temperature of air is calculated theoretically, which will be the possible values of temperature after experimentation. Fig. 3 presents the effectiveness as a function of air speed across the evaporative pad. It can be seen that higher speed decreases the contact time between the air and the wet surface, reducing the effectiveness. Also as the speed increases the mass flow rate and heat transfer coefficient increases but effectiveness decreases. Fig. 5 shows the velocity of air is also the function of outlet air temperature, as speed increases the temperature drop decreases, reducing the heat transfer rate. It is possible to obtain the maximum temperature difference up to 1.4 for relative humidity 17 velocity 1.66 m/s and minimum temperature difference up to 5.14 for relative humidity 32 velocity 9 m/s. So it can be conclude that the optimum frontal velocity of the pad module should be in a range between 1.66 to 2.5 m/s for the needed supply air volume. This recommended value can be used to decide the frontal area of a direct evaporative cooler. Too low velocity will result in a large frontal area of the pad module, and an increase of size and primary investment of the direct evaporative cooler. It concludes that evaporative cooling systems have a very large potential to propitiate thermal comfort and can still be used as an alternative to conventional systems in many tropical regions, saving energy and protecting the environment. REFERENCES [1] Kulkarni,R. K. and Rajput, S. P.S., 211 "Comparative performance of evaporative cooling pads of alternative materials". IJAEST.; Vol.1, pp. 239-244. [2] Camargo, J. R.,Ebinumab,C. D., Silveira,J. L., 25 "Experimental performance of a direct evaporative cooler operating during summer in a Brazilian City"International Journal of Refrigeration 28, pp.1124 1132. [3] Wua,J.M., Huang,X., Zhang,H., 29,"Theoretical analysis on heat and mass transfer in a direct evaporative cooler.", Applied Thermal Engineering 29.,pp.98 98. [4] Baredar P., Khare, H., Chaturvedi, B.,Sahu, M.M.,21, "Analysis of Indirect-Direct Evaporative Cooling System." BLB-International Journal of Science & Technology Vol.1, No. 2, pp. 243-248. (ISSN 976-374) [5] Egbal Mohammed Ahmed, Osama Abaas, Mohammed Ahmed, MohdRodzi Ismail, 211,"Performance evaluation of three different types of local evaporative cooling pads in greenhouses in Sudan." Saudi Journal of Biological Sciences 18, pp. 45 51. [6] Fouda, A. Melikyan,Z., 211, "A simplified model for analysis of heat and mass transfer in a direct evaporative cooler" Applied Thermal Engineering 31.,pp. 932-936. [7] Manuwa, S. I. &Odey, S. O., 212, "Evaluation of Pads and Geometrical Shapes for Constructing Evaporative Cooling System'', Modern Applied Science; Vol. 6, No. 6; ISSN 1913-1844. [8] Abbouda, S. K. and Almuhanna, S. K.,212, "Improvement of Evaporative Cooling System Efficiency in Greenhouses." International Journal LatestTrends Agr.Food Sci. Vol-2, No. 2. [9] Abdulrahman Th. Mohammad, Sohif Bin Mat, M.Y. Sulaimana, K. Sopian, Abduljalil A. Al-abidi, 213, "Experimental Performance of a Direct Evaporative Cooler Operating in Kuala Lumpur.", International Journal of Thermal & Environmental Engineering Vol. 6, No. 1., pp. 15-2. [1] Shrivastava1, K.,Deshmukh, D.,Rawlan, M.V., 214, "Experimental Analysis of Coconut Coir Pad Evaporative Cooler" International Journal of Innovative Research in Science, Engineering and Technology, Vol. 3, Issue 1. [11] Ibrahim U. Haruna, Lateef L. Akintunji, Bello S. Momoh, Muhammad I. Tikau, 214, "Theoretical Performance Analysis Of Direct [12] Evaporative Cooler In Hot And Dry Climates.", International Journalof Scientific &Technology Research Volume 3, Issue 4,ISSN2277-8616. KUUL PADS, Available In www.kullpads.com; 23. [13] Dowdy,J.A. and Karabash, N.S., 1987, "Experimental Determination of Heat And Mass Transfer Coefficients In Rigid Impregnated Cellulose Evaporative media."ashare Trans 93 (Part 2), pp. 382-395. [14] Cities Weather Data Retrieved From Www.Myforecast.Com [15] Watt,J.R. and Brown, W.K., 1997, "Evaporative air conditioning handbook", 3rd ed., The Fairmont Press, Lilburn, GA, pp. 57. [16] Moreira, J.R.S., 1999, "Fundamentos e Aplicac o es da Psicrometria" RPA Editorial Ltda, Sa o Paulo. 157