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Unformatted text preview: PTFE 3210
Spring 2007 Q . #4 . ,
“a Name \/ 1. Write the rate equation (Fick’s law) for molar diffusion of species A in a binary mixture of A and B
measured relative to coordinates that move with the average velocity of the mixture and deﬁne all
terms used in your expression. .... gig—m w ( 10 points) .71, * (kmol/s ' m2) is the diffusive molar ﬂux of species A measured relative to coordinates that
move with the average velocity of the mixture. C is the total molar concentration.
DAB is the binary diffusion coefﬁcient or mass diffusivity.
7V— is the dc] operator. XA is the molar fraction of species A. 2. Write the rate equation (Fiek’s law) for molar diffusion (Fick’s law) of species A in a binary mixture of A and B measured relative to stationary coordinates. Deﬁne all terms. (10
points)
in
 n m, _ ”— * u " n
72A —— pDABVmA +mAIrzA +143 I
cm...» W Wm...“
ABSOLUTE contribution due to contribution due to
FLUX difﬁision that is motion of A with
. motion of A relative to massaverage motion
Relative to massaverage motion of mixture
the ﬁxed of mixture
coordmate
system EA" (kgm/s ‘ m2) is the diffusive mass ﬂux of species A measured relative to stationary coordinates.
17,3 “ (kgm/s ‘ m2) is the diffusive mass flux of species B measured relative to stationary coordinates. p is the total mass concentration.
DAB is the binary diffusion coefficient or mass difﬁxsivity.
“V7 is the dei operator. mA is the mass fraction of species A. 3. Saturated water vapor leaves a steam turbine at a ﬂow rate of 1.5 kg/s and a pressure of 0.51
bar. The vapor is to be completely condensed to saturated liquid in a shell and tube heat
exchanger with one shell pass and two tube passes. City water is used as the mid ﬂuid. The
water is to enter the thin wall tubes at 17°C and is to leave at 57°C. Assuming that an overaﬂ
heat transfer coefﬁcient of 2000 W/m2 ' K, determine the required heat transfer surface area and water 00%; to eompleteiy condense the vapor. “W Assume the properties of the water and steam are as follows: Saturated water: Cp = 4178 J/kg ' K, p = 1000 kg/m3 and u v: 3.43 x 104 N ‘ s/mz. Saturated steam at 0.51 bar: Tsat = 355 K, hfg = 2304 Iii/kg and k "—“ 0.0233 W/ m ' K.
(30 points) TWA”: K 4. Forced air at a temperame of 25°C and a velocity of 10 m/s is used to cool electronics
elements on a circuit board. One such element is a chip, 4 mm by 4 mm, located 120 mm
from the leading edge of the board. Experiments have revealed that the convective heat
transfer from the board is correlated by the foilowing expression“. Nux = 0.04Rex°‘85 Prm i
L: 120 mm Estimate the surface temperature of the chip if it is dissipating 30 row.
(25 points) Assume that steady state conditions exist and the power dissipated by the chip is lost by
convection across the upper surface only. The properties of the air are as follows: Cp = 1.0
kJ/icg  K, p a 1.10 kg/m3, a =1.s4 x 105 N  s/m2, v = 1.67 x 10'5 1112/3, k 2 0.0269 W/ m
K, and Pr = 0.703. Wait“ (£2016? 20:37 4—
PROBLEM w KNOWN: Expression for the local heat transfer coefﬁcient of air at prescribed velocity and
temperature ﬂowing over electronic elements on a circuit board and heat dissipation rate for a 4 x 4
mm chip iocated 120m from the ieading edge. FIND: Surface temperatIne of the chip surface, TS. SCHEMATIC:
Appropria‘f'e Correla ﬂan : Wan—25°C 3‘4"” Nux=ao+Remerm
“"9 V=10m/s Chip
I Board
L>x L=120mm ASSUMPTIONS: (1) Steady—state conditions, (2) Power dissipated within chip is lost by convection
across the upper surface only, (3) Chip surface is isothermal, (4) The average heat transfer coefﬁcient
for the chip surface is equivalent to the local value at x = L. PROPERTIES: Table A4, Air (assume TS ﬂ 45°C, Tf= (45 + 25)/2 = 35°C = 308K, latm): v m 16.69 x 10”6m2/s, k = 26.9 x 10"3 W/ran, Pr : 0.703. ANALYSIS: From an e waaﬁnYee on the chip {see above),
 ,., '7' T ~— ﬁm team to » MW I s in) a) Newton’s law of cooling for the upper chip surface can be written as
T5 3 Too 'i" ciconv / h Achip (2) where Achip = £2. Assume that the average heat transfer coefﬁcient (5) over the chip surface is equivalent to the local coefﬁcient evaluated at x = L. That is, Hemp z hx (L) where the local
coefﬁcient can be evaluated none the special correlation for this situation, 0.85
Nux =Wmhﬁ" =0.04[X§] Fri/3
V and substituting numerical values with x m L, ﬁnd 0.85
hme.04—IE[—V——£] Pr1/3
L v 0.85
hx =0_04[W] (0_703)“3 2107 w/m3 .K_
0120m 16.69x10” m /s
The surface temperature of the chip is from Eq. (2), T5 = 25"c+3c><10'3 W/107 Vii/1112oiii><(0.00tﬁirn)2 a 425°C. < COMMENTS: (1) Note that the estimated value for Tf used to evaluate the air properties was
reasonable. (2) Alternatively, we couid have evaluated hemp by performing the integration of the local value, h(x). 5. Helium gas at 25°C and 4 bars is contained in a very long glass cylinder of 100~mm inside
diameter and 5~mm thickness. What is the rate of mass loss per unit length of cylinder? Assume: (1) Steady«state conditions, (2) Onedimensional radial diffusion through cylinder
wall, (3) Negligible end losses, (4) Stationary medium, (5) Uniform total molar concentration,
and (6) Negligible helium concentration outside cylinder. PROPERTIES: For He~Si02 (298 K): DAB = 0.4 x 10‘” 1112/5; and He—SiOZ (298 K): s = 0.45
x 10'3 kneel/ms ' bar; For helium Cp = 5.2 lei/kg ' K; v 3 L2 X104 mZ/s, and k “—” 0.15 W/ In ' K.
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 Spring '11
 Dr.Carr
 Heat, Heat Transfer, heat transfer coefficient, Fick, total molar concentration

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