Energy-efficient indirect evaporative cooler design framework: An experimental and numerical study

earlier available correlation is based on simple airflow between parallel plates assumption and does not incorporate the effect of the evaporative potential of the system resulting in under/over-estimation of the heat transfer characteristics. The results showed that the proposed system achieved a temperature drop of 20 ◦ C, a cooling capacity of around 180 W, and an overall heat transfer coefficient of up to 30 W/m 2 K. Moreover, the study presents an experiment-regression-based heat transfer coefficient correlation that satisfactorily captures the effect of outdoor air temperature and airflow rate ratio which are critical in the design of evaporative coolers. The proposed correlation showed a high ( ± 5%) with experimental data thus making it suitable for the future design of IEC systems over assorted operating scenarios.


Introduction
Comfort cooling is now perceived as a social imperative and is believed to improve the working efficiency of humans and technology [1]. Therefore, its demand is increasing exponentially due to various drivers including the warming planet, population growth, urbanization, and high-income growth (refer to Fig. 1) [2]. The cumulative impact of these drivers is triggering the air conditioning demand. So based on the business-as-usual scenario of 2018, the global air conditioners (ACs) are predicted to ramp up to 5.6 billion in 2050 with room ACs (mini split + packaged) alone exceeding 4.5 billion [2]. It implies that around 10 AC units will be sold every second in the next 30 years and particularly the developing regions will face a fivefold increased demand for room air conditioners [3]. The more serious concerns with piling AC units are energy consumption and emissions [4,5]. A threefold increase in global AC-related energy is expected by 2050, aggregating the total demand to 7700 terawatt-hours (TWh) from 2300 TWh in 2017 [6,7]. Similarly, AC CO 2 emissions have tripled to 1600 million metric tons since 1990 [8] and are expected to cross 167 gigatons of CO 2 equivalent by 2050 [9].
The cooling market is captured by vapor compression technology which is responsible for high energy consumption and emissions [10,11]. So a water-based cooling solution is required to minimize energy consumption and emissions.
Evaporative cooling has emerged as the only viable solution because of significantly low energy consumption, water-based operation, and benign emissions [12,13]. However, the conventional direct evaporative coolers (using Aspen, Khus fibers cellulose paper sheets, etc.) have limited applications due to high humidity (100%) issues in the supply air [14][15][16]. While an advanced idea of indirect evaporative cooling (IEC) resolves the issue of high humidity and has the potential to outperform conventional vapor compression systems sustainably [17]. It uses water as a refrigerant and evaporative potential of air and provides humiditycontrolled cooling [18,19]. These systems handle latent and sensible  cooling loads separately thus offering individual process optimization without any rigid operational limitations [20]. Therefore, these can achieve a COP ranging from > 30 (for only cooling) and 10-12 for overall systems (including the dehumidification process) [21]. Therefore, these systems can be employed for various applications [22,23] like human comfort [24], artifacts preservation [25], animal comfort [26], agricultural product storage [27], and energy recovery for vapor compression systems [28][29][30]. Above all, the current carbon neutrality demand is favoring sustainable solutions as recommended by Dai et al. [31]. Keeping in view the extensive applications and advantages, significant research is conducted to investigate and improve IEC system performance [32][33][34]. However, the commercial-scale deployment of The flow between isothermal parallel plates Where b/e = aspect ratio Used for dry channel only and standard rectangular dry channel with constant surface flux. [22,51] Where b/e = 0.066 is the aspect ratio (minimum/ maximum) For a laminar, hydrodynamically, and thermally fully developed flow in a rectangular duct that is exposed to a uniform wall temperature     these systems is subject to addressing certain design limitations [35]. These include heat transfer improvement, effective water management, operational reliability, and heat transfer wall development [36]. This is because, in the typical IEC systems, these issues have been reported to be the major design challenges for commercial scale realization. Particularly, the water showering inside the heat exchanger complicates the wall development with multi-layers, lowers heat transfer, increases maintenance issues, and obstructs water management. The current study investigates a novel IEC system that addresses the design challenges in conventional IEC systems through the rearrangement and retrofitting of new components in the system. Particularly, the study is focused on the development of heat transfer coefficient correlation for the proposed system for accurate heat transfer modeling of the system. This is because the earlier studies on IEC use typical heat exchanger correlations for the calculation of heat transfer coefficients in dry and wet channels. These are based on the concept of airflow between parallel plates and the effect of evaporation and outdoor air temperature variations is not properly captured in these calculations. Therefore, these correlations under/over-estimate the heat transfer area requirement misleading the cooling capacity which is critical for large-scale systems. A robust experimental-based heat transfer coefficient correlation development is conducted for the IEC systems which was missing earlier. For this purpose, a critical review of existing heat transfer correlations is conducted first. It comprehensively summarized the mathematical formulation, operational conditions, assumptions, applicability ranges, reported values, and characteristics under different operational conditions. This is followed by the design and development of an experimental test rig based on the proposed operational configuration. Then a detailed experimental investigation of the system performance under assorted outdoor air temperature and working air flow rate conditions. The experimental data is then used to calculate the overall heat transfer coefficient. Then the theoretical model is applied to estimate the local dry and wet channel heat transfer coefficients. Finally, the experimental data is used to formulate heat transfer coefficient correlation using regression. The proposed correlations showed good agreement (±5%) with the experimental data and can be used for commercial scale design of IEC systems.

Flat plates
One of the important and frequently adopted formulae was developed by Ranz and Marshall [37] in 1952 (C-1). They proposed a model to calculate the heat transfer from water droplets due to evaporation in terms of Reynolds number, and Prandtl number with constants as given below. It has been used extensively used in recent studies [38][39][40][41][42][43][44].
Lin et al. [45] developed correlations for the calculation of Nu for dry and wet channels and also Sherwood number (Sh) by studying the heat and mass transfer process for a dewpoint indirect evaporative cooler. They reported the average convection heat and mass transfer coefficients as 26.8 to 29.9 W/m 2 ⋅K, and 0.025 to 0.027 m/s, and the Nu for the dry and wet side as 8.67 to 9.95, 8.68 to 9.21 and 8.17 to 8.67.
Wan et al. [46] developed heat and mass transfer correlations for IEC with condensation in the dry channel. The study used the orthogonal test method and experimentally validated the CFD model based on COMSOL as given below Another correlation was developed by Dowdy and Karabash [47] for direct evaporative coolers with the surface covered by a rigid cellulose media saturated with water. The correlation is modified in terms of Re, Pr, characteristics length, and evaporation surface thickness and is used for IEC applications [22,[47][48][49][50][51][52].
In addition to the above-mentioned formulations, some standard correlations have also been used for the heat transfer study of IEC systems. A summary of these correlations is presented in Table 1.

Enhanced surfaces
Besides plain surface geometry, enhanced surfaces with patterns, fins, and protrusions have also been used in IECs for higher heat transfer rates. Therefore, formulations have also been developed to estimate the heat transfer characteristics of these surfaces. For instance, Antonellis et al. [72] developed the heat transfer correlation (for Aluminum alloy plates with surface dimples based on the concepts of enhanced surface heat transfer [73,74]. They showed that the most influential parameters affecting heat transfer include dimples height, pitch, size, and placement. They developed the correlation in terms of Re and Pr with constants.
Where the values for constants were calculated by minimizing the error in dry bulb effectiveness and the results obtained from simulation and experiments. A summary of these correlations is presented in Table 2.

Ranges and characteristics of earlier IEC heat transfer coefficients
The above heat transfer review shows that a variety of correlations for Nusselt number/heat transfer coefficient are reported for different operating scenarios. However, the actual quantitative values for Nu/h are seldom reported because most of the earlier studies report IEC performance in terms of cooling capacity, coefficient of performance, or efficiencies. However, the heat transfer coefficients are of paramount significance for IEC as these govern the heat transfer process and control the area footprints and economics of the system. A higher heat transfer coefficient results in a lower heat transfer area and reduced capital cost requirements. A comprehensive summary of the reported values for Nusselt number, local, and overall heat transfer coefficients alongside the geometric and process parameters are presented in Table 3. It shows that in most of the studies, the heat transfer coefficient is calculated using constant surface temperature or constant surface heat flux approach-based correlations. Therefore, the value for Nu varies between 7 and 8 for constant heat flux and 4-5 for constant surface temperature cases thus calculating the heat transfer coefficient 20-30 W/m 2 K. However, it is also important to mention that the heat transfer coefficient values increase considerably under special working conditions of systems. For instance, under condensation in the dry channel conditions, the heat transfer coefficient is reported to vary between 180-200 W/ m 2 K. Similarly, under direct-indirect hybrid system operation conditions, the overall heat transfer coefficient is reported to vary between 100-400 W/m 2 K. Likewise, the heat transfer coefficient for porous ceramic tubular-based IEC system is reported up to 80 W/m 2 K.
A detailed investigation of heat transfer coefficient characteristics against important geometric and process parameters has been rarely conducted. Lin et al. [45] conducted an experiment and CFD-based investigation of heat transfer coefficients. For local temperature measurements, the IEC generic cell was equipped with 8 pairs of temperature sensors in dry and wet channels along the heat exchanger length. The local heat transfer coefficients for dry (h d ) and wet (h w ) channels were reported to be ranging between 25 and 30.3 W/m 2 K as shown in Fig. A1  (a). The experimentation also showed minor irregular fluctuations in the heat transfer coefficients along the heat exchanger length. A similar trend for different outdoor air velocities (Fig. A1 (b)) and outdoor air humidity (Fig. A1 (c)) is also reported with small irregular variations in the heat transfer coefficient for dry and wet channels. The study also concluded that the heat transfer coefficients calculated using constant surface temperature and constant heat flux correlations resulted in an underestimation of the values. This is because the values calculated from experimentation were higher than the theoretically calculated values because of better heat transfer characteristics of the naturally formed boundary condition than the conventionally considered boundary conditions.  Similarly. Wan et al. [46] also investigated the characteristics of dry and wet side heat transfer coefficients for a counter-flow IEC. They reported that (refer to

Heat transfer coefficient correlation development
The methodology adopted here involves extending the existing dry channel heat transfer coefficient correlations by incorporating the effect of outdoor air temperature and the airflow rate ratio. In this regard, the wet side heat transfer coefficient is calculated using the Ranz and Marshall [37] correlation (refer to Eq. (1) which is reported to be one of the most accurate correlations for estimating heat transfer from water droplets as discussed above. While, for the dry side, three commonly used correlations (summarized as C1, C2, and C3 in Table 4) are selected for comparison with the current experimental findings and the development of a new correlation.

Theoretical model
The dimensionless terms in the above correlations including the Reynolds, Prandtl, and Nusselt numbers can adequately capture the effect of geometric parameters and flow velocity to estimate the heat transfer in the channels. However, large variations in the outdoor air temperature and the airflow rate ratio can boost the heat transfer significantly which is not fully incorporated in the traditional correlations. Therefore, these correlations are revisited to capture these additional effects in the correlation.
The most important parameter for calculating the overall heat transfer coefficient is the total heat transferred or cooling capacity which is calculated using temperature drop (ΔT) across outdoor air, flow rate (ṁ), and the specific heat (c p ) as given below [52].
Using log mean temperature difference (ΔT LMTD ), heat transfer area (A), and cooling capacity (Q OA ) the overall heat transfer coefficient is calculated as [44 91].

U =Q
A ΔT LMTD (10) Where the overall heat transfer coefficient is given as the convection heat transfer coefficients (h OA , h WA ), and the conduction heat transfer through the wall is given as [92].
The wall resistance in the above equation is negligible because of the very small wall thickness (0.025 mm) and high thermal conductivity of Aluminum (i.e., 235 W/(m.K)). Therefore, the experimentation is focused on capturing the overall heat transfer coefficient. Then the experimental outdoor air heat transfer coefficient is calculated using the above equation. The correlation is then presented in the standard form of the Nusselt number which is given as:

Experimentation
The experimental system considered in the study consists of an innovative indirect evaporative cooler as shown in Fig. 2. The two major parts of the system include an air humidification (H) section and a sensible heat exchanger (SHX). The purpose of the humidification section is to supply working air to the heat exchanger at wet bulb temperature and 100% relative humidity. For this purpose, the hightemperature outdoor air is passed through the humidifier where it is cooled and humidified through continuous water mist showering (1-3). The fine mist boosts the air-water interaction mechanism in the humidifier thus producing cold humid air with additional mist particle carryover (3). The humidifier consists of a water sump, mist nozzles, a water pump, and a supplementary water supply through a floatcontrolled valve to the water sump. While the heat exchanger consists of alternative airflow channels dedicated to dry and working air streams. The dry air is taken as hot outdoor air in the dry channels which is sensibly cooled to the supply air temperature (1)(2). While the heat from the dry channel is extracted by the working air stream in the wet channel (3)(4). The mist particles in the working air are evaporated during the heat transfer process. Therefore, the mode of heat transfer in the working air channels includes both sensible and latent heat transfer. The cold dry air is supplied to the room (2) and the hot humid working air is rejected by the environment (4). The operational scheme of the system is presented on the psychrometric chart in Fig. 3.
The geometric specification of the system is summarized in Table 5. The system is fully instrumented to capture all required data including dry bulb temperature, wet bulb temperature, and velocity as presented in Table 6. For dry bulb temperature, the OMEGA thermistor probe with an accuracy of ± 0.15 • C is used. While for wet bulb temperature, the customized wet bulb measuring station is used which involves a thermistor + Felt + Test tube. The dry and wet bulb temperature measurements are made at the dry channel inlet, dry channel outlet, humidifier inlet, humidifier outlet, wet channel inlet, wet channel outlet, and water sump. All the thermistors are connected to Agilent Benchlink Data Logger for real-time data monitoring and recording. For air flow rate measurement, hot-wire anemometer Testo 405i with an accuracy of ± 0.03 m/s is used at dry and wet channel outlets. The experimentation involved system operation at assorted outdoor air and working air conditions to record the supply air temperature. For this purpose, the outdoor air and working temperature varied between 27 and 50 • C, and the airflow rate ratio was from 50% to 200%. It covers the whole range of outdoor air temperatures to appropriately incorporate the effect. Since last decade the peak temperature during summer is  Table 4 as C1 [45], C2 [58], C3 [42].
> 45 • C in most parts of GCC and Asia which are the biggest markets of the cooling industry. Moreover, most of the earlier IEC systems are tested in labs and onsite testing is seldom seen so they are limited to < 42 • C. So, to enhance the applicability of the current study and correlation over a wider range the temperature. Moreover, the evaporative cooling system performance is influenced by the outdoor air temperature, flow velocity, and airflow rate ratio. For each data set the experimental procedure is the same as the system is first operated to achieve the required outdoor air temperature at the dry channel inlet and the humidifier inlet. Then the water showering in the humidifier starts to achieve the wet bulb temperature at the wet channel inlet. Once the system temperatures achieve a steady state trend the data is used for subsequent calculations like cooling capacity, efficiency, coefficient of performance, and the heat transfer coefficient.
Meanwhile, it is worth mentioning that the data in this study is presented against dry bulb temperature because of the extensive application of evaporative cooling systems for dry and hot climates. Though in IEC systems the supply air humidity is constant as that of the inlet,  under extremely high outdoor humidity conditions the outdoor air needs to be dehumidified. This is because the evaporative system performance drops under humid conditions and the thermal comfort is not achieved with high humidity supply air. In such cases, the IEC system is integrated with a dehumidifier (desiccant wheel, microwave, membrane-based, etc.). This integration increases the energy consumption of the system; however, the overall COP is still higher than MVC systems. It is also important to mention that the dehumidification technologies are well established and have been extensively used for domestic and industrial air treatment. However, the scope of this study is only limited to IEC sections.

Results and discussion
The most important parameters that govern the heat transfer coefficient in the heat exchanger are cooling capacity and log mean temperature difference (LMTD). A comprehensive summary of the parameters used in the experimental data is presented in Table 7. The uncertainty study is conducted at 45 • C using the accuracy of the sensors and anemometer. The maximum uncertainty in the estimation of different parameters is as follows: cooling capacity ± 2.13, log mean temperature difference ± 0.314, and overall heat transfer coefficient ± 1.71. An energy balance diagram of the heat exchanger as presented in  It is important to note that the cooling in the dry channel is produced by rejecting heat to the wet channel. The heat in the wet channel is transferred in sensible and latent forms. However, latent heat has a major share in the wet channel because of evaporation. However, an increase in the working air temperature shows sensible heat transfer as well. The contribution of sensible and latent heat transfer is presented in Table 7.
The effect of outdoor air temperature and airflow rate ratio on the cooling capacity calculated experimentally is presented in Fig. 5. It shows that the cooling capacity is significantly influenced by outdoor air temperature as well as the airflow rate ratio. For instance, a maximum cooling capacity of 178 W is achieved at an AFR of 200% and an outdoor air temperature of 50 • C. While the minimum cooling capacity of 178 W is achieved at an AFR of 50% and an outdoor air temperature of 25 • C. This is because at higher outdoor air temperatures the temperature differential across dry and wet channels is considerably high. The working air always enters at the wet bulb temperature which boosts the heat transfer process and cooling capacity at higher outdoor air temperatures. Similarly, at higher air flow rate ratios, the mist carry-over in the working air channels is increased which enhances the evaporation and increases the latent heat extraction. Overall, the higher temperature and higher air flow rate ratio increase the heat transfer rate. Meanwhile, Fig. 6 shows that the maximum LMTD is obtained at higher outdoor temperatures and lower air flow rate ratios. This is because at higher AFR the latent heat transfer dominates, and the temperature rise in the working air outlet stream becomes smaller. The corresponding overall heat transfer coefficient values at different outdoor air temperatures and AFR are presented in Fig. 7.
The trends for experimental overall heat transfer coefficients calculated using cooling capacity and log mean temperature difference are presented in Fig. 8. Fig. 8(a) presents the overall heat transfer coefficient at different outdoor air conditions for an air flow rate ratio of 50%. It is observed that the U value increased by 11% from 11.2 W/m 2 K to 12.5 W/m 2 K when the outdoor air temperature increased from 25 • C to 50 • C. Meanwhile, for AFR of 100% as shown in Fig. 8 Fig. 8(c)) and for 200% (refer to Fig. 8(d)) by 55% from 20.1 W/m 2 K to 31.6 W/m 2 K for the outdoor air temperature varying from 25 • C to 50 • C. It is worth mentioning that the conventional IEC system water flows inside the wet channel and the heat transfer coefficient is majorly governed by the flow rate of air and water. The effect of these parameters is incorporated in terms of Reynold number and Pr number. In the proposed cooler, fine water droplets are only carried with mist and evaporation takes place in the wet channel from these water mist particles. The variation in outdoor air temperature enhances the temperature differential across the air streams in dry and wet channels. It enhances the rate of orthogonal heat transfer between the channels. This increase in heat transfer with outdoor air temperature can be seen in the cooling capacity which is then used to calculate the heat transfer coefficient experimentally. Without incorporating the effect of outdoor air temperature, the heat transfer coefficient gives poor estimation which is only sufficient for lower operating temperature where the effect is insignificant.
Overall, the heat transfer coefficient is influenced by outdoor air temperatures and airflow rate ratio. The variations are significantly enhanced at higher values of temperature and airflow rate ratio. These variations are because higher outdoor air temperature increases temperature differential and a higher air flow rate ratio boosts evaporation which in turn enhances the heat transfer.
The above analysis shows that the heat transfer coefficient is strongly influenced by outdoor air temperature and airflow rate ratio. Therefore, the correlations calculating the local heat transfer coefficients are required to incorporate the effect of these parameters. Meanwhile, the traditional heat transfer coefficient correlations in literature for dry channels are based on simple airflow between parallel plates with major reliance on Re and Pr numbers as shown in Table 4. These can adequately incorporate the effect of geometric parameters, flow parameters, and thermophysical properties in the respective channel. However, the effect of heat transfer enhancement due to variations in outdoor air temperature and evaporation (in wet channels) is not covered. Therefore, the values of dry side local heat transfer coefficients calculated using traditional correlations (presented in Table 4 as C1, C2, C3) from literature remain insensitive to the outdoor air temperature and airflow rate ratio as shown in Fig. 9. It shows that the h OA values calculated using these correlations remain almost constant at 22-23 W/ m 2 K for all outdoor air temperatures and airflow rate ratios. On the other hand, the experimental values show significant variations from 16 to 57 W/m 2 K against T OA and AFR. It implies that the effect of outdoor air temperature and airflow rate ratio is not properly captured in traditional correlations. This is because the effect of temperature in these correlations only occurs in Re and Pr numbers due to thermophysical properties like density (ρ), viscosity (μ), thermal conductivity (k), specific heat (C p ), etc. Meanwhile, it is important to emphasize that these properties are a weak function of temperature with benign variation over temperature ranging from 25 to 50 • C as shown in Fig. 10. Therefore, traditional correlation does not incorporate these effects and necessitates the development of new correlations addressing these limitations.
A correlation based on new experimental measurements incorporating the additional effects of air flow rate ratio (AFR) and outdoor air temperature (T OA ) is proposed for the calculation of the heat transfer coefficient. The correlation is formulated in terms of key parameters including Reynold number (Re), Prandtl number (Pr) air flow rate ratio (AFR), and outdoor air temperature (T OA (K)) normalized by reference temperature T ref (K) as given below.
A regression with these parameters against the experimental results is conducted as presented in Fig. 11. It shows a good agreement with R 2 = 0.99 between experimental and calculated (from the proposed correlation) values. A slightly higher discrepancy between experimental and correlation values is observed at lower (i.e., 25 • C) outdoor air temperatures. This is because the system cooling capacity is significantly decreased than the designed value at this temperature. Moreover, the IEC systems are not generally operated in this temperature range because of being in the ASHRAE comfortable zone. Therefore, the proposed correlation can be used with acceptable accuracy for IEC operation at as high as 50 • C temperature. The correlation plot for the proposed formulation showing dependency on different parameters is presented in Fig. 12. It shows that the most influential parameters are air flow rate ratio with a significance level of 0.87, followed by outdoor air temperature with 0.23, and then Prandtl number with 0.23 and Reynold number with 0.037. It affirms the dependency of correlation on the newly added terms. Fig. 13 and Fig. 14 show a comparison of the outdoor air heat transfer coefficient calculated using the proposed correlation and measured experimentally. It shows that the proposed correlation can effectively capture the effect of outdoor air temperature and airflow rate ratio. Therefore, the calculated values occur within ± 5% of the experimental values. Particularly, at higher outdoor air temperatures and higher air flow rate ratios where the effects are dominant, the accuracy of the correlation is higher. Moreover, the earlier studies in the literature are only limited to a maximum outdoor air temperature of 42 • C. While the current study incorporates the outdoor air temperature of as high as 50 • C which makes the proposed correlation suitable for IEC system design under harsh climatic conditions.

Conclusion
Indirect evaporative cooling technology is a sustainable alternative to conventional cooling systems in hot dry climatic areas. A novel indirect evaporative cooler addressing major limitations in the earlier systems is proposed and developed in this study. The study is particularly focused on the development of a dry channel heat transfer coefficient for the large-scale expansion of these systems. This is because the conventional correlations are observed to be insensitive to these parameters and give a poor prediction of the heat transfer coeffects. Predominantly, at higher values of outdoor air temperature and working air flow rate the conventional correlations become inapplicable and mislead the calculations. The major findings of this study are summarized below.
• The proposed system achieved a temperature drop up to 25 • C, and a cooling capacity of 178 W. The system showed higher performance under higher outdoor air temperatures because of a larger temperature differential across channels. • The dry side heat transfer was calculated using conventional correlation hover around 22-23 W/m 2 K for the outdoor air temperatures varying between 25 and 50 • C and air flow rate ratios of 50% to 200%. • The experimental and proposed correlation heat transfer coefficient value varied from 16 to 57 W/m 2 K when the outdoor air temperature increased from 25 to 50 • C and the air flow rate ratio increased from 50 to 200%. • The most influential parameters in indirect evaporative cooler design are observed to be Reynold number, Prandtl number, air flow rate ratio, and outdoor air temperature under hot dry climates. • The newly developed heat transfer correlation properly incorporates the effect of outdoor air temperature ranging from 25 to 50 • C and air flow rate ratio ranging from 50 to 200% with an accuracy of ± 5% with the experiment.
Overall, the conventional correlations underpredict the heat transfer coefficient values and are unable to track the effect of outdoor air temperature and airflow rate ratio. So, the new terms are introduced in the proposed correlation that captures the effect of temperature and airflow rate ratio. Moreover, the high experimental accuracy makes the proposed correlation viable for the future design of IEC systems over assorted operating scenarios.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability
Data will be made available on request.