powerpoint presentation · title: powerpoint presentation author: sophia created date: 12/16/2019...
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HW #4 /Tutorial # 4
WRF Chapter 18; WWWR Chapter 19
ID Chapter 6
• Tutorial # 4
• WWWR #19.1,19.4.
• ID # 6.33. 6.37.
• To be discussed on Feb.
9, 2021.
• By either volunteer or
class list.
• Correction
• Question WWWR # 19.19
1/ 2 1/ 4 1/ 4
1/ 2 1/ 4 1/ 4
3.94Pr (Pr 0.954)
0.508Pr (Pr 0.954) ;
x
x x x x
Grx
kNu Gr h Nu
x
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Convective Heat Transfer
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Fundamental Considerations In
Convective Heat Transfer
• Two main classifications of convective heat
transfer
• These have to do with the driving force causing
fluid to flow
Natural or free convection
Fluid motion results from heat transfer
Fluid heated/ cooled -> density change/ buoyancy effect ->
natural circulation in which affected fluid moves of its own
accord past the solid surface
- fluid it replaces is similarly affected by the energy transfer -
process is repeated
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Forced convection
Fluid circulation is produced by external agency (fan or pump)
Analytical Methods
(a) Dimensional Analysis
(b) Analogy between Energy and Momentum Exchange
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Significant Parameters In
Convective Heat Transfer
A. Both have same dimensions L2/t; thus their ratio must be
dimensionless
B. This ratio, that of molecular diffusivity of momentum to the
molecular diffusivity of heat, is designed the Prandtl number
Pr =n
a
mcp
k
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Prandtl number
•observed to be a combination of fluid properties;
•thus Pr itself may be thought of as a property.
•Primarily a function of temperature
s
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A ratio of conductive thermal resistance to the convective thermal
resistance of the fluid
Nusselt numberNu hL
k
Where the thermal conductivity of the fluid as opposed to that of the
solid, which was the case in the evaluation of the Biot modulus.
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Dimensional Analysis of
Convective Energy Transfer
Forced Convection
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Dimensional
Analysis for
Forced Convection
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Natural Convection
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Dimensional
Analysis for
Natural Convection
Courtesy Contribution
by ChBE Year
Representative, 2004.
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Energy and Momentum Transfer
Analogies
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The Colburn analogy expression is
St Pr 2/3 = Cf
2(19-37)
8)
9)
s
oner
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Example 1
Water at 50o
F enters a heat-exchanger tube having an inside diameter of 1 in and a length of 10
ft. The water flows at 20 gal/min. For a constant wall temperature of 210o
F estimate the
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Film temperature = (water mean bulk temperature + pipe wall temperature)/2
Mean bulk temperature of water = (inlet + outlet)/2
=(90+210)/2 = 150 = (50+130)/2
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Second iteration is required since if |TL – 130| >
3o
F?