Lecture 4 Heat Transfer Concepts

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ABE 303 – Lecture 4 Heat Transfer Concepts
HEAT TRANSFER MECHANISMS
Heat Conduction – Composite Cylindrical wall Example 4 : A 4mm plastic coating (k=0.26 W/mK) is sprayed onto the pipe in the previous example. The outside of the coating is now at 20oC. What is the heat flow?
2 L k r2 ln r1
r1
1 2
Q
r2
( UA )m
r2 ln r1 1 UA m 2 L k
ABE 303 – Lecture 4 Heat Transfer Concepts 9
HEAT TRANSFER MECHANISMS
Heat Conduction – Cylindrical wall Example 3 : Calculate the heat flow through the wall of a stainless steel pipe (0.04m ID, 0.05m OD, 16m long, k=15 W/mK) if the inner wall is at 80oC and the outer wall at 20oC.
ABE 303 – Lecture 4 Heat Transfer Concepts
2
1 2
1
Fluid 1
HEAT TRANSFER MECHANISMS
s1
s2
Fluid 2
s3
Q
2
Solid 1 (k1,x1) x1 x2
Solid 2 (k2,x2)
Q UA ( 1 2 )
HEAT TRANSFER MECHANISMS
s1
Fourier’s Law
s2
Heat transferred by conduction
Fluid 2
Heat transferred by motion of the fluid molecules and macroscopic movement of the fluid CONVECTION (h1)
HEAT TRANSFER MECHANISMS
Natural CONVECTION Forced
1
Fluid
2
Surface
Q h A ( 1 2 )
Q
Heat Convection Coefficient
ABE 303 – Lecture 4 Heat Transfer Concepts
CONVECTION ON EITHER SIDE OF A CYLINDRICAL WALL
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HEAT TRANSFER MECHANISMS
CONVECTION h (W/m2K) Liquids Natural Convection Force Convection Phase Change 1-200 200-10,000 1000-20,000 Gases 0.10 -10 (Buoyancy driven) 10-200 (pump/Fans) (Boiling/Condensing)
s3
Q
k1 x1
k2
x2
2
1 2
1 / UA
Heat transferred by motion of the fluid molecules and macroscopic movement of the fluid CONVECTION (h2)
Q UA ( 1 2 )
ABE 303 – Lecture 4 Heat Transfer Concepts
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HEAT TRANSFER MECHANISMS
Heat Conduction – Composite Spherical walls
i
1
r1 r2 k1
2
Q UAm ( 1 2 )
k2
ABE 303 – Lecture 4 Heat Transfer Concepts
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HEAT TRANSFER MECHANISMS
CONVECTION - CONDUCTION
Fluid 1 Fluid 2
Q UA ( 1 2 )
1
Solid Wall
h1
k1 x1
h2 2
ABE 303 – Lecture 4 Heat Transfer Concepts
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HEAT TRANSFER MECHANISMS
Heat Conduction – Cylindrical Wall
Q UAm ( 1 2 )
2 L k ( 1 2 ) r ln 2 r1
Newton cooling/heating Law
Newton cooling/heating Law
U function( k1 , k2 , h1 , h2 , x1 , x2 )
ABE 303 – Lecture 4 Heat Transfer Concepts 4
HEAT TRANSFER MECHANISMS
ABE 303 – Lecture 4 Heat Transfer Concepts
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HEAT TRANSFER MECHANISMS
Heat Conduction – Composite Cylindrical wall
Q UAm ( 1 2 )
i
1
r1 r2 k1
2
k2
Q
1 1 x1 1 U h1 k1 h2
For n-wall layers
xn 1 1 1 x1 x2 ...... U h1 k1 k 2 k n h2
ABE 303 – Lecture 4 Heat Transfer Concepts 17
HEAT TRANSFER MECHANISMS
r3
r3 r2 ln ln 1 1 r1 r2 k2 UA m 2 L k1
For n-layers

rn 1 r3 r2 ln ln ln rn 1 r1 r2 1 ....... k2 kn UA m 2 L k1
r3
rn 1 rn 1 r2 r1 r3 r2 1 ....... UA 4 k r r k r r k r r m 2 3 2 n n 1 n 1 12
ABE 303 – Lecture 4 Heat Transfer Concepts 14
Solid 2 (k2,x2)
Driving Force Q UA ( 1 2 ) 1 / UA Resistance
Q : Heat transfer rate (Watts) 1 2 : Temperature difference U : Overall Heat Transfer Coefficient (W/m2K) A : Area (m2)
x
1 d U k
m m2 K Units of 1/U are : W W mK
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ABE 303 – Lecture 4 Heat Transfer Concepts
HEAT TRANSFER MECHANISMS
Heat Conduction Example 1 : A cold store wall is 0.05 m thick cork (k = 0.043 W/mK). The inside wall temperature is -18oC, and the outside wall is at 23oC. The wall area is 100 m2. Calculate the rate of heat and what it would be if the cork were replaced by 0.05m polystyrene (k = 0.028 W/mK).
2
Material 1
k1 x1 Q
k2 x2
Q
3
1 x1 x2 U k1 k 2
ABE 303 – Lecture 4 Heat Transfer Concepts 7
HEAT TRANSFER MECHANISMS
Heat Conduction – Composite Flat Slab Example 2 : For the cold store in Example 1 polystyrene is added to the cork rather than substituted for it. Calculate the heat transfer rate Q, and the temperature at the junction between the two layers.
ABE 303 – Lecture 4 Heat Transfer Concepts
6
HEAT TRANSFER MECHANISMS
Heat Conduction – Composite Flat Slab
1
Material 2
Q UA( 1 3 )
Q 1 x1 x2 k1 k 2 A ( 1 3 )
ABE 303 – Lecture 4 Heat Transfer Concepts
1
1
Fluid 1 convection
HEAT TRANSFER MECHANISMS
s1
s2
cid 2
s3
Q
convection
2
Solid 1 (k1,x1) x1 x2
1 2
1 / UA
• How could we calculate U ? • What properties are involved for the calculation of U ?
ABE 303 – Lecture 4 Heat Transfer Concepts 3
1
Fluid 1
HEAT TRANSFER MECHANISMS
Learning Objectives To gain an understanding of the different mechanisms for heat transfer and find out the effect that the thermophysical properties have on heat transfer operations • Conduction – Fourier Law • Convection – Newton cooling/heating law • Mixed heat modes • Other modes of heat transfer e.g. radiation will be covered in a heat and transfer mass transfer course next semester
ABE 303 – Lecture 4 Heat Transfer Concepts
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HEAT TRANSFER MECHANISMS
Heat Conduction – Spherical walls
Q UAm ( 1 2 )
1 r1
r2
2
r2 r1 1 UA m 4 k r1r2
Heat Conduction (Fourier’s Law)
d Q kA dx
For steady state Q = constant By integration of the Fourier’s Law
1
k
2
d
Q kA
By comparing with
1 2
d Q UA( 1 2 )