# Cooling Performance of Fresh and Aged Automatic Transmission Fluids for Hybrid Electric Vehicles
###### Abstract
Hybrid powertrain for a passenger car composed of an internal combustion engine and an electrified transmission with two electric motors inside the planetary gearbox. therefore the lubricant chemistry must be improved by using new base oils and additives at different concentrations. As for any other heat transfer fluid (HTF) or coolant, the thermophysical properties (density, viscosity, heat capacity, and thermal conductivity) of the ATFs are necessary to determine its heat transfer performance. The ATFs must demonstrate high heat transfer performance and low pumping power, low fluid volume, and low heat losses or low temperature drop [13]. Thus, fluids with high densities, thermal conductivities, and heat capacities, in addition to low viscosities, are preferred when selecting ATFs. Nevertheless, materials usually demonstrate good values for some properties but poor ones for others, so finding criteria for comparing and selecting possible candidate fluids is mandatory. In this case, it is useful to use a figure of merit (FOM), which is a numerical quantity based on one or more characteristics of a system or device and represents a measure of efficiency or effectiveness. The Mouromtseff number (Mo) is a dimensionless FOM that can be used to quantify the heat transfer performance of the ATFs [1,14] and this is defined as:  
\[\text{Mo}=\rho^{a}.k^{b}.C_{p}^{c}.\mu^{d} \tag{1}\]  
where \(a\), \(b\), \(c\), and \(d\) are constants which are dependent on the heat transfer mode and represent the sensitivity to the different thermophysical properties [15]. The Mouromtseff number for forced convection is calculated as:  
\[\text{Mo}=\frac{\rho^{0.8}.k^{0.6}.C_{p}^{0.4}}{\mu^{0.4}} \tag{2}\]  
In addition, some other FOMs (Equations (3)-(5)) can be used to compare HTFs considering the abovementioned pumping power, fluid volume, and heat losses or temperature drop [13]. \[\text{FOM}_{pumping}=\frac{\mu^{0.2}}{\rho^{2}.C_{p}^{2.8}} \tag{3}\]  
\[\text{FOM}_{volume}=\frac{\mu^{0.1}}{\rho^{0.84}.C_{p}^{1.16}} \tag{4}\]  
\[\text{FOM}_{heat\ losses}=\text{FOM}_{temp\ drop}=\frac{\rho^{0.34}.k^{0.6}.C _{p}^{0.06}}{\mu^{0.44}} \tag{5}\]  
The \(a\), \(b\), \(c\), and \(d\) sensitivity numbers indicate how much each property affects the FOMs. Higher Mo is preferred for better heat transfer performance, while for better efficiency and economics, lower \(\text{FOM}_{pumping}\) is preferable. Conversely, lower \(\text{FOM}_{volume}\) is preferable to require less coolant volume for the same heat transfer performance under the same pumping power; meanwhile, lower \(\text{FOM}_{heat\ losses}\) or \(\text{FOM}_{temp\ drop}\) is preferable because less insulation is required for preventing heat loss. Considering the abovementioned FOMs, higher density, thermal conductivity, and heat capacity lead to higher heat transfer performance and lower pumping power and coolant volume, but they also increase the heat loss and temperature loss. Conversely, low viscosity improves the heat transfer performance, and reduces pumping power and coolant volume, but worsens the heat loss and temperature drop. When selecting an ATF, which also plays the role of coolant of the EM, not only the abovementioned FOMs are to be considered for the fresh candidate ATF samples, but also the potential evolution of the FOMs over time and at operation temperatures of the EM. It is very important to study how the changes over time in the composition and degree of oxidation influence the thermophysical properties of ATFs and the impact of these changes on the heat transfer/cooling performance and efficiency of the ATFs. Numerous studies have investigated the changes in viscosity, friction reduction, thermogravimetry, and electrical conductivity of fresh and aged/used ATFs [16; 17; 18; 19; 20], but none of these have studied the cooling performance of these ATFs through properties of figures of merit, except in the case of thermal conductivity.