Question

Snow Making The newer style snowmaking guns use high pressure nozzles used to atomize water into drops and large fans to blow the water droplets out onto the ski hill. See the illustration below The water droplets that are formed are typically on the order of D 2mm and the fan can produce a breeze with a velocity of 10m/s. If the outside air temperature is T 10 C and the water droplets are atomized at an initial temperature of T 10 C we want to know how long it will take for the droplets to begin freezing. To make life easier we won't worry about phase change to start, but will determine the time it takes for the surface of the water drop to reach T,-0 C Air: T.-10°C U 10m/s T10°C Water Drop2mm es Air k 0.026 W/m K Water k 0.569 W/mK c,-4.2kJ/kgk p-1000kg/m Pr 12.99 c,-1.00kJ/kgK Pr 0707 v-v 1 5.89% 10-6m2 /s What is the Reynolds number of the flow? b) What is the Nusselt number? c) What is the heat transfer coefficient? yacen d) You can assume that the water in the droplet does not move and so the heat transfer in the droplet is purely conductive. Can the droplet be considered lumped system? Justify your answer e, How long will it take for the outer surface of the water droplet to reach T, =0,C and begin to freeze?

Answer 1

Given dala blu il 2 0.026 w Pr 12.9 10 2¥10 以 Re 238.6

2 The Coyrelaicup Yo ts -0.3 2S.0q4 い016 N 61 h D Nu h矢2*10 0. 026 22.61 2

By 3 k Bị 2 0.0861 lumped approach Šaprlad Ti -To- 0 (-10) lo --l0) 3 23 oY 고e, 2.15- 0.643 o.429 t