INTRODUCTION TO HEAT TRANSFER

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INTRODUCTION TO HEAT TRANSFER (ME 411) Summer
2003 Lecture Number III Ali R. Mazaheri Course
webpage www.clarkson.edu/mazahear/MAIN/ME411 De
partment of Mechanical and Aeronautical
Engineering Clarkson University
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Heat Source Systems
1D Conduction with heat generation

• PLANE WALL

Boundary Conditions
General solution
where
3
The temperature distribution is then become
To determine the centerline temperature we have

1
4
2. Cylinder with Heat Source
R
Boundary Conditions
(Continuous temperature distribution)
General solution
where
5
The temperature distribution is then become
To determine the centerline temperature we have
T
T0

1
r
r0
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3. Hollow Cylinder with Heat Source
ro
ri
Boundary Conditions
General solution
where
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Heat Source with Convection
1D Convection with heat generation
Find temperature at the center of the wire, T0.
d3mm
Tw
r
I200A
L1m
, h4000 W/m2 oC
where
Tw215 oC
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We know that
Where
T0231.6 oC
Temperature at the center of the wire..
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Conduction-Convection Systems (Fins)
tltltL
1D heat transfer
qconv.
Energy balance
qcond.
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Changing variable
Physical situation
Case1 Fin is very long, that is
Case2 Fin is of finite length, that is
Case3 Fin is insulated at the end, that is
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CASE 1
(Fin is very long)
Boundary conditions
General solution
where
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CASE 2
(Fin is of finite length)
Boundary conditions
General solution
where
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CASE 3
(Fin is insulated at the end)
Boundary conditions
General solution
where
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Heat loss from fins
All the heat loss must be conduct into the fin
basement.
Case 1(fin is very long)
Case 2(fin is of finite length)
Case 3(fin is insulated at the end)
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Fin Efficiency
Definition
For the case 3 we have
and
P(2z2t)
Azt
where
Assume zgtgtt
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Types of fins
Radial fin
Circular-rod fin
Rectangular fin
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Evaluation the fin efficiency for different fins
types.
Rectangular fins
Triangular fins
Circumferential fins
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Heat transfer from the finned surfaces
Total heat transfer
Consider following definitions
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Heat transfer from the original surface
Fin efficiency
Total heat transfer from the surface with fins
Assume

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Overall surface efficiency
Definition
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Thermal contact resistance
q
A
B
T1
T2A
T2B
T3
Thermal contact resistance
Rc
RA
RB
T1
T3
hc Contact coefficient