# Evaporative Mist Cooling as Heat Dissipation Technique: Experimental Assessment and Modelling
## 3 Natural Cooling Technique Modelling
### Proposed Simplified Model  
The detailed model for a single droplet described in Section 3.1 calls for information on the nozzle (droplet distribution depending on the initial radius for a given nozzle, mass fraction, etc.) which is difficult to glean from system manufacturers' catalogues. That raises a need for a simplified nozzle characterization model based on the theoretical fundamentals of the detailed model but in which the input data are readily found on manufacturers' datasheets. The aim is to enhance model applicability to the design and assessment of such solutions. The simplified characterization model for evaporative mist cooling is based on energy exchange efficiency (Equation (5)), a widely used indicator of evaporative cooling system performance, as mentioned earlier. An \(\varepsilon\)-NTU relationship equivalent to that used in evaporative cooling towers can be found for sprayers, where the process taking place can be likened to developments in such towers. In the NTU method (number of transfer units method) [44], the effectiveness is the ratio of the actual heat transfer rate to the maximum possible heat transfer rate and the NTU is related with the value of the heat transfer capacity of the exchanger. If NTU is high, the more closely the exchanger tends to its thermodynamic limit value. This method is commonly used for the characterization of evaporative cooling equipment [49; 50; 51]. The functional relationship associated with an exchanger is represented in efficiency calculations as term \(A\), which depends on system operating variables. Efficiency can be calculated from Equation (7):  
\[\varepsilon=1-e^{-NTU}=1-e^{-A} \tag{7}\]  
where coefficient \(A\) is found from the system operating variables with a significant impact on cooling efficiency, measurable or furnished by manufacturers. On those grounds, the following parameters were applied to find parameter \(A\):  
* Factors depending on actual experimental conditions: outdoor temperature, absolute humidity, and initial droplet temperature. * Factors with a role in evaporative cooling system operation: droplet launch height, working pressure, and droplet diameter. In short, the simplified model proposed is linked to the treatment of the phenomenon as a heat dissipation system. So, determining the mathematical dependence of this parameter with the operating parameters of the system, Equations (1) to (4) have been implemented in Matlab [52]. These equations have been solved in a coupled way for thousands of combinations of boundary conditions. In this way, the mathematical formulation of parameter A that appears in Equation (7) is proposed. This formulation will be calibrated using experimental data, so it can be assumed that it is an instrumental step in the proposed methodology. As noted earlier, the simplified characterization model is designed for nozzles, not single droplets. Nozzles launch droplets of different sizes, creating a mist with water particles of varying radii. Most nozzles spray droplets with a wide range of diameters, normally summarized via statistical analysis of the results of trials conducted with sophisticated measuring instruments, including laser analyzers and imaging systems. Further to that information, the droplets are classified on the grounds of a statistical distribution based on spraying pressure (see the paper by [PERSON] et al. [53]). The diameter that qualifies nozzles for given rated working conditions is VMD or mean volumetric diameter, defined as the volume-median droplet diameter (the diameter for which half the total water content is contained in droplets larger and a half in droplets smaller than the median volume). Defined in standards and specific references such as [54; 55], that widely used parameter is deemed to be the characteristic jet diameter. After entering the parameters into the simplified model, the effect of each of the aforementioned variables on evaporative cooling efficiency was analyzed.