08 lecture heat transfer
TRANSCRIPT
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MEL301 : Heat and Mass Transfer
by
Dr. Himanshu Tyagi
IIT Ropar 13-Oct-2014 (Mon)
Chapter 8Internal Forced Convection
Instructions for this chapter:a) Students must try to read this chapter from the textbook &
b) try out the various solved examples
before coming to class
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Circular vs. Non-circular
2Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.
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Average Velocity & Temperature
3Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.
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Average Velocity & Temperature
4Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.
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Average Velocity & Temperature
5Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.
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Q. How do we know if the flow is Laminar orTurbulent?
6Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.
Usually,
Re < 2300 Laminar
Re > 10,000 Turbulent
Q. Can Laminar flow occur ateven Re = 100,000 ??
Q. How is Re for non-circular pipes/ducts
defined?
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Hydraulic Diameter
7Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.
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Entrance Region (Hydrodynamic)
8Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.
Hydrodynamically fully developed:
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Entrance Region (Thermal)
9Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.
Q. Is the fluid being cooled or heated by the
surface?
Thermally fully developed:
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fxand hx
10Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.
Hydrodynamically fully developed:
Thermally fully developed:
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Entry Length (Lhand Lt)
11Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.
For laminar flow:
For turbulent flow:
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Nu (turbulent flows)
12Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.
Note (for laminar):
NuT ~ 3.66
NuH ~ 4.36
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13/2813Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.
Constant Surface Heat Flux Constant Surface TemperatureVs.
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Constant Surface Heat Flux
14Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.
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Constant Surface Temperature
15Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.
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NTU (Number of Transfer Units)
16Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.
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17Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.
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Laminar Flow in Tubes
18Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.
Q. What is the fully developed profile in laminar flows in
tubes?Q. Why is it parabolic in shape?
Q. What is the pressure drop in laminar flow in tubes?
Q. How does the stress vary (with r and x)?
Q. How does Tvary (with r and x)?
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Derivation of Parabolic Velocity Profile
19Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.
By substituting
We get
B.C.s ?
Finally, we obtain
the parabolic
velocity profile
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Average Velocity
20Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.
Lets substitute the
following expression to
Vavgterm
We get:
Which also shows that
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Pressure Drop
21Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.
From previous page, we
already have
By rearranging we can
easily write:
If length is doubled, Palso doubles
If mass flow rate is doubled, Palso
doubles
If Ris halved, Pincreases by 4 times!!
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Pumping Power
22Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.
PVWpump
Pumping
power is
given by:
is the volumetric flow rateV
4
2D
VAVV avgcavg
PSince,
28 avgpump LVW
42
216
8D
VL
2
4
144V
D
L
If Dis halved, pumping power increases by
16 times!!
We get,
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Temperature Profile
23Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.
Q. How does Tvary (with r and x)?
By substituting
We get
Next by
substituting
&
We get
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Temperature Profile
24Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.
Case A: Constant Surface Heat Flux
Q. How to solve this to get T(r)?
We already have:
Hence, we get
B.C.s ??
Finally T(r)is solved!!
Also, we can
calculate the mean
temperature Tm
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Temperature Profile
25Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.
Case A: Constant Surface Heat Flux
Q. Does this expression look
familiar?
Repeating a similar exercise
for constant surface
temperature gives us:
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Laminar Flow in
Non-circular
Tubes
26Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.
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Laminar Flow in Entrance Region
27Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.
Q. Can we apply Nu = 4.36 and Nu = 3.66 in the entrance
region?
Q. If not, what relations can be applied?
Q. Will Nu be same/higher/lower in the entrance region
(compared to the fully developed region)?
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Comparing Laminar & Turbulent Flows (in Entrance Region)
Laminar flowTurbulent flow