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A water droplet of radius R=1mm at ambient conditions (27 degree C and 1 atm) is

ID: 1842378 • Letter: A

Question

A water droplet of radius R=1mm at ambient conditions (27 degree C and 1 atm) is used to cool a computer chip's hot spot as shown by the adjacent sketch. The chip is continuously generating 50W of power. Contact surface effects produce a semi-spherical droplet shape. If we assume uniform volume heating of the droplet by the chip, approximate the time it takes for the droplet to fully vaporize. Why is this an approximation? How would you make the calculation more accurate besides accounting for non-uniform heating?

Explanation / Answer

Rate of evaporation:

W = 4R2Ddn/dR.

D is the diffusivity of the droplet.

The power is given as , 50w i.e. 50 J/s.

Heat transfer through convection can be calculated as:

Q = hcA dT.

A is the contact surface area while hc is the convective heat transfer coefficient.

dT is the temperature difference.

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