A liquid droplet radiator (LDR) is used to liberate heat fromthe UT Space StationnamedDOLLYPARTON(Droplets OfLiquidLeaveYielding Particles Alleviating Radiation To OverwhelmingNothingness). The LDR works in the following way. Waste heatgenerated from daily operation of the space stationistransferred toan oil bath. The bath is ejected into space in droplet formeffectively radiating energy into deep space.The droplets arerecollected after travelling a distance (L)through spaceandreintroduced to the oil bath.

The average ejected droplet temperature is Ti = 550 [K] and thedroplet velocity is v = 0.05 [m/s]. The oil has a density of

p =1000 kg/m^3 ,a specific heat capacity of cp= 2000 J/kg/K andan emissivity of E= 0.92.The average droplet diameter is 500 [\um].Deep space can be thought of as surroundings with zero temperature(Tsurr= 0 [K]). The LDR is shielded from solar radiation.

The distance between the ejector and collector can be adjustedto optimize the temperature of the droplet when it is recollected.Ideally, the temperature should be Tf = 300 [K] because this is themean temperature of the station interior. A lower temperature wouldliberate more energy making the system more efficient butcomplications with freezing could occur operating below 300 [K].What ejector–collector separation (L) will yield a dropletrecollection temperature of Tf = 300 [K]?

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What is the total internal energy lost per droplet to space?