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CUKUROVA UNIVERSITY
Faculty of Engineering & Architecture Department of Mechanical Engineering
THE EXPERIMENT OF LAMINAR VISCOUS FLOW HEAT TRANSFER UNIT
Name : Erhan Ekici
Number : 2010257017
Group No : 3
Due Date : 11/12/2014
Instructor : RESEARCHER GOKHAN TUCCAR
LAMINAR VISCOUS FLOW HEAT TRANSFER UNIT
Results and calculations
Determination of mass flow rate of oil:
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Core tube Outer tube
Material copper Copper
Outer diameter (domm) 12,7 15,9
Inner diameter (dimm) 11,3 14,4
Effective length (L mm) 910 910
Dimensions of tubes
oiloil
oil
t
Vm .
= skg/03805,085,07,6
3,0 where
Voil: volume of oil collected in the glass measuring tank.
t: time to collect oil in glass measuring tank.
oil: density of oil at mean temperature (T1+T2)/2 from graphic of properties of shell thermia oil B.
oil=0.85 kg/l w=0.996 kg/l
Simple energy account for a heat exchanger:
)( 21
..
TTcmQ poiloiloil = 03805,0 *1,92*2.3=0,168kj/s
)( 56
..
TTcmQ pwww = 1*0,132*1=0,132 kj/s where
oilQ.
: rate of heat transferred from oil.
wQ. : rate of heat transferred to cold water.
cpoil: specific heat of oil at mean temperature (T1+T2)/2 .
cpw: specific heat of water at mean temperature (T5+T6)/2.
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Determination of surface heat transfer coefficients on both the oil and water sides and of the
overall heat transfer coefficient:
toi
oilot
TA
Qh
ln
.
= 148
09,35*0323,0
/168,0
skj (W/m2C0)
wt
oil
twTA
Qh
ln0
.
= 47298,0*0363,0
/168,0
skj (W/m2C0)
wm
oil
TA
Qu
0ln
.
= 1352,36*0343,0
168,0 (W/m2C0) where
hot: Surface heat transfer coefficient between oil and tube.
htw: Surface heat transfer coefficient between tube and water.
u: Overall heat transfer coefficient.
Ai: Internal heat transfer surface area of the inner tube. Ai= 0.0323 m2
Ao: outer heat transfer surface area of the inner tube. Ao= 0.0363 m2
Am: Logarithmic heat transfer surface area of the inner tube.
)(i
o
iom
A
A
Ln
AAA
toT ln : Logarithmic mean temperature difference between oil and tube.
42
31
4231
ln
TT
TTLn
TTTTto =
C
Ln
009,35
1,1752
193,54
1,1752193,54
wtT ln : Logarithmic mean temperature difference between tube and water.
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64
53
6453ln
TT
TTLn
TTTTwt
=
C
Ln
098,0
5.161,17
5,1719
5,161,175,1719
woT ln : Logarithmic overall mean temperature difference between oil andwater.
)(
)(
62
51
6251ln
TT
TTLn
TTTTT wo
=
C
Ln
02,36
5.1652
5,173,54
5.16525,173,54
Mean velocity of Oil (Uoil) and Water (Uw):
ioil
oiloil
A
mU
*
.
= 4476,0
0001,0*85,0*1000
03805,0 (m/s)
506,100002,0*996,0*1000
03,0
*
.
ww
w
wA
mU
(m/s) where;
Ai: Flow cross-sectional area of the oil passed in the inner tube.
Aw: flow cross-sectional area of the water passed between inner and outer tubes.
Ai= 0.0001 m2 Aw=0.00002 m
2
Calculation of nusselt numbers and z*
What does nusselt number represents ?: For forced convection of a single-phase fluid with
moderatetemperature differences, the heat flux is nearly proportional to the temperature difference T=Tw
Tf(Tw: temperature of the wall, T f: temperature of the fluid).This was discovered by Newton who then
inferred that q T. Thus arrive at Newtonslaw of cooling.
q = h ( TwTf) where h is the heat transfer coefficient with units of W / m20C
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But h is dimensional and thus its value depends on the unit used. The traditional dimensionless
form of h is theNusselt Number.Nu, which may be defined as the ratio of convection heat transfer to fluid
conduction heat transfer under the same conditions. Lets consider a fluid of width L and temperaturedifference ( TwTf). Assuming that the layer is moving so that the convection occurs, the heat flux would
be,
q = h (TwTf)
If on the other hand, the layer were stagnant, the heat flux would be entirely due to the fluid
conduction through the layer.
q = k (TwTf) / L
We define the nusselt numberas the ratio of these two
k
Lh
q
qN
conduction
convectionu
*
A nusselt number of order unity would indicate a sluggish motion little more effective than pure
fluid conduction; for example, laminar flow in a long pipe. A large nusselt number means very efficient
convection; for example, turbulent pipe flow yield Nuof order 100 to 1000.
Another number that is called Prandtl number used in our calculations to determine z * and
theoritical Nusselt number. The Prandtl number is another dimensionless number representing the ratio of
momentum transport in a flow. Reynolds number is another one giving the characteritics of flow. f it is
greater than 2300 the flow is called as turbulant. Numbers less than this indicates a laminar flow.
Experimental Nusselt number can be calculated using equation below;
oil
ito
uek
dhN
* = 84,121302,0
0113,0*148
oil
ioil
v
du *Re =
6^10*14
0113,0*4476,0
= 27.361
oilidLz
PrRe**
* = 001486.0
150*27.361*0113,0910,0
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The theoritical Nusselt number can be calculated using equation below:
11,03
1
*
8
1
*4
3*
PrPr*0861,0
*5,341*
0704,01657,32
w
utz
zz
N
= 27,3800
150*
001486.0
0861,0
)3*5,341(*5,1
0704,01657,3
11,031
81
where
Nue: Experimental Nusselt number.
Nut: TheoriticalNusselt number.
koil: Thermal conductivity of oil at arithmetic mean temperature (T1+T2)/2, from table 5 koil = 0,1302
W/m0C.
oil: Kinematics viscosity of oil at arithmetic mean temperature (T1+T2)/2, from table 2 oil=14*10-6m2/s.
Proil: Prandtl number of oil at (T1+T2)/2, from table 1 Proil= 150
Prw: Prandtl number at wall temperature (T3+T4)/2, from table 1 Prw= 800.
All values calculated from above equations and recorded values are given below in the tables.
For Water Flow Rate is Constant
con-current flowExperiments T1 T2 T3 T4 T5 T6 Voil t mwater
1 54,5 52,1 19,9 19,3 16,1 18,7 0,2 4,89 18
For Water & Oil Flow Rate is Constant
counter-current
flow
1 54,3 52 19 17,1 17,5 16,5 0,3 6,7 30
2 55,5 52,1 18,6 17 17,3 16,5 0,3 11,5 30
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3 56,6 52,3 18,4 16,9 17,2 16,5 0,3 16,6 30
4 57,7 54,1 22,6 17,7 19,6 16,5 0,3 11,4 10
5 58,2 54,5 19,8 17,1 17,9 16,4 0,3 11,4 20
6 58,7 54,9 17,9 16,7 16,8 16,4 0,3 11,4 45
Table 1: Values recorded during experiment
m oil Q oil h o-t u oil Re z Nu e Nu t Exp. No:
0,03805 168 148 0,4476 361,27 1,486/
10-3
12,84 3,271
DISCUSSION
a)
Experimental value of Nusselt Number is greater than the theoretical value. It can caused
experiment conditions. For example; relative errors, precision of measurement, calibration of
instrument
b) Con-current flow: The hot and cold fluid enter at the same end of the heat exchanger flow
through in the same direction and leave together at the other end.
Counter-current flow: The hot and cold fluids enter in the opposite ends of the heat exchanger flow
through in the opposite direction and leave together at the other end
c) These differences are depend on the water and oil mass flow rate, specific heats of oil and water,
entering and leaving temperatures of oil and water. Because of these, we can say that the volumes
of oil and water collected in the glass measuring tank, time to collect oil in the glass measuring
tank and density of the oil at mean temperature from graphic are important for changing the rate of
heat transfer.
d)Shell and tube, plate, plate and shell, platefin, pillow plate.
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e)Shell and tube, plate, plate and shell, platefin, pillow plate, adiabatic, fluid heat exchanger regenerative
heat exchanger , dynamic scraped surface , phases change .
f)Regenerative heat exchanger is a type of heat exchanger where heat from the hot fluid is
intermittently stored in a thermal storage medium before it is transferred to the cold fluid.
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