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A spherical water drop is suspended from a fine thread in still, dry air. Show: (a) That the Sherwood number for mass transfer from the surface of the drop into the surroundings has a value of 2 if...

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A spherical water drop is suspended from a fine thread in still, dry air. Show:
(a) That the Sherwood number for mass transfer from the surface of the drop into the surroundings has a value of 2 if the characteristic length is the diameter of the drop. If the initial drop diameter is 1 mm, the air temperature is 38oC, the drop temperature is 14.4oC, and the pressure is 1 atm, calculate:
(b) The initial mass of the drop in grams.
(c) The initial rate of evaporation in grams per second.
(d) The time in seconds for the drop diameter to be reduced to 0.2 mm.
(e) The initial rate of heat transfer to the drop. If the Nusselt number is also 2, is the rate of heat transfer sufficient to supply the heat of vaporization and sensible heat of the evaporated water? If not, what will happen?
Answered Same DayDec 31, 2021

Solution

Robert answered on Dec 31 2021
64 Votes
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notified on: Mar 15, 2017 03:18 AM
Title
A spherical water drop is suspended from a fine thread
Description
A spherical water drop is suspended from a fine thread in still, dry air. Show:
(a) That the Sherwood number for mass transfer from the surface of the drop into the
su
oundings has a value of 2 if the characteristic length is the diameter of the drop. If the initial
drop diameter is 1 mm, the air temperature is 38oC, the drop temperature is 14.4oC, and the
pressure is 1 atm, calculate:
(b) The initial mass of the drop in grams.
(c) The initial rate of evaporation in grams per second.
(d) The time in seconds for the drop diameter to be reduced to 0.2 mm.
(e) The initial rate of heat transfer to the drop. If the Nusselt number is also 2, is the rate of heat
transfer sufficient to supply the heat of vaporization and sensible heat of the evaporated water? If
not, what will happen?
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Answer Text
part a
Sherwwod no = k / D /L= k * L /D
[ Here , k = mass transfer coefficient , D = diffusivity ( m2 /s ) . L = d =
diameter = 1 mm = 1/1000 =0.001 m= L ]
Sh = k*L /D
2 = k* 0.001 /Dab ...
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