The velocity boundary layer
u
s =
y y =0
u/u = u* = 0.99
Free stream
u
y
(x)
Cf
s
2
u 2
Velocity boundary layer
x
Fig. 3.2 The development of velocity boundary layer on a flat
plate.
1
The thermal boundary layer
Ts T
= T* = 0.99
Ts T
T
u
T
t(x)
x
T
y y
Performing indexes for fin design
fin effectiveness
T
Tb
Ac,b
q = hAc,b b
T
Tb
qf
f =
hA c,b b
f 2
qf
1
Performing indexes for fin design fin effectiveness
Fin effectiveness versus P/Ac
100
90
80
Fin effectiveness
70
60
50
hP
kP
kP
f =
tanhmL =
tanh
L
A general conduction analysis
1
A general conduction analysis
qx = qx+dx + dqconv
q x +dx
dq x
= qx +
dx
dx
( x ) dT k
q x +dx = kAc
dx
d 2 T 1 dA c dT 1 h dA s
( T T ) = 0
+
2
dx
A c dx dx A c k dx
d
( x ) dT dx
Ac
dx
dx
2
Fins of uniform cross-sectio
Conduction with thermal energy generation:
The plane wall
T(x)
Ts,1
q
Ts,2
T,2, h2
T,1, h1
+L
-L
x
Fig 2.7 Conduction in a plane wall with
internal heat generation.
1
Conduction with thermal energy generation:
The plane wall
d 2T q
+ =0
2
dx
k
T(x)
Ts,1
q
The composite wall
1
LA
LB
LC
1
Rt = h A + k A + k A + k A + h A
1
A
B
C
4
x
T, 1
Ts, 1
T2
Ts, 4
Hot fluid
T, 1, h1
T3
A
T, 1
qx
1
h 1A
Cold fluid
T, 4, h4
Ts, 1
B
T2
LA
kAA
C
T3
LB
kBA
T, 4
Ts, 4
LC
kCA
qx =
T ,1 T ,4
R
t
q x UA( T ,1 T ,4 ) = UAT
T, 4
Example 10.4
x
A
hydrogen
B
plastic
D AB = 8 m 2 s
8.7 10
=3 kmol m 3
SAB 1.5 10
bar
Hydrogen
CA,2
pA,2 = 1 bar
Hydrogen
CA,1
pA,1 = 3 bar
CA,s2
CA,s1
Temperature = 25C
0.3mm
Determine the mass diffusive flux of hydrogen
1
Example 10.4
x
A
hydrogen
B
2 Boundary conditions
T T T
T
= cp
k
+ k
y + z k z + q
x x y
t
Ts
T, h
Constant surface
temperature
T(0, t)
T(x, t)
T(x, t)
Convection
surface condition
x
x
q
s
T(x, t)
x
Constant surface
heat flux
T(x, t)
x
Insulated surface
1
Example 1.2
Air: T,
9.5.1 Evaporation and sublimation
Raoults law
Gas phase with
species A
x
NA , x
pA(0)
xA(0)
Liquid or solid concentrated in
species A
p A ( 0 ) = x A ( 0 ) p A,sat
For water vapor
xA(0) = 1
pA(0) = pA,sat
Figure 10.3 Evaporation or sublimation of
species
The heat diffusion equation
qz+dz
qy+dy
dz
Eg
qx
Steady state conditions
0 internal heat generation
qx+dx
E st
qy
dy
dx
E in + 0 Eout = 0
qz
Fig 1.8 Differential control volume for a heat diffusion analysis
2 T 2 T 2 T q 1 T
+ 2+ 2+ =
2
x
y
z
k t
2T 2T
Mass transfer in nonstationary media
(
NA = CD AB x A + x A NA + NB
For equimolecular
counterdiffusion
NA = CD AB x A
When NB = 0
NA,x =
CD AB dx A
( 1 x A ) dx
)
NA = N
B
Ficks Law
Stefans Law
1
Mass transfer in nonstationary media
(
NA = CD AB x A + x
The heat diffusion equation
A current
carrying rod
Cladding
Air
Cooling fluid
Fig 1.6 What is the temperature distribution within the rod?
Wall
Insulator
Heater
Fig 1.7 How does the temperature
distribution in the wall change with time?
1
The heat diffusi
Mass transfer in nonstationary media
Absolute mass flux of A in a mixture of A and B
A = A v A
n
Absolute mass flux of B in a mixture of A and B
nB = B v B
Absolute mass flux of a mixture
v = n = nA + n = A v A + B v B
B
Mass average velocity for the mi
CHPR2432
Heat and Mass Transfer
Prof. Hui Tong Chua
E-mail id.: [email protected]
Tel no.: 6488 1828
Room: 2.06 Eng-Civil&Mech
1
Introduction to Conduction
2
Introduction to Conduction
T
q x = kA
x
When x 0
dT
q x = kA
dx
Fouriers Law
3
Introduction
Equimolecular counterdiffusion
Vapor A + B
1 mol of A
1 mol of B
Liquid A + B
Latent heat of A = Latent heat of B
1
Equimolecular counterdiffusion
*
dC A
jA = D AB
dx
dCT x A
dCT x B
=
dx
dx
*
dC B
jB = DBA
dx
or
d A M A
d B M B
=
dx
dx
dx A
dx B
=
dx
dx
Chapter 9 Diffusion Mass Transfer
Driving force concentration difference
High concentration High temperature
Low temperature
Low concentration
Distance
1
Chapter 9 Diffusion Mass Transfer
Gas
df o e a R
t
Liquid
Solid
2
Chapter 9 Diffusion Mass Transfer
Adapted from FP Incropera, DP De Witt, Introduction to Heat Transfer, 2002, John
Wiley & Sons.
Chapter 8 Radiation exchange between surfaces
We have so far been discussing processes that occur at a single surface. Now, we
shall consider radiative exchange
1
q i = ( Ebi J i )
(1 i )
i Ai
The reradiating surface
AR, TR, R
qR = 0
A1, T1, 1
1 R
R AR
A2, T2, 2
JR = EbR
1
A 1 F1R
q1
1 1
1 A 1
1
A 2 F2 R
q1R
J1
1 2
2A2
qR2
1
A 1 F12
J2
1
-q2
J1 J R
J J2
R
=0
( 1 A1F1R ) ( 1 A 2F2R )
The reradiating surface
AR, TR
Adapted from FP Incropera, DP De Witt, Introduction to Heat Transfer, 2002, John
Wiley & Sons.
Chapter 7 Radiation: Processes and Properties
7.1 Fundamental concepts
Radiation involves the transport of thermal energy by electromagnetic waves.
Consider a s
8.3.1 Net radiation exchange at a surface
1
q i = ( Ebi J i )
(1 i )
i Ai
qi = Ai(Ji-Gi)
Ji = i Ebi + (1 - i)Gi = i Ebi + (1 - i)Gi
qi = Ai(Ei - [1 - i] Gi)
J i i Ebi
Gi =
1 i
qi = Ai(Ei - i Gi)
1
8.3.2 Radiation exchange between surfaces
N
A i G i = Fji
Adapted from FP Incropera, DP De Witt, Introduction to Heat Transfer, 2002, John
Wiley & Sons.
Chapter 6 Transient conduction
6.1 The lumped capacitance method
A hot metal forging is suddenly quenched in a liquid bath. Can we predict how does the
temperat
8.2 Blackbody radiation exchange
qij = (AiJi) Fij
qji = (Aj Ebj) Fji
qij = (Ai Ebi) Fij
ni
nj
Ji = Ebi
Jj = Ebj
N
(
q i = A i Fij Ti4 Tj4
j =1
Ai, Ti
)
Aj, Tj
qij = qij - qji = Ai Fij Ebi - Aj Fji Ebj
Figure 8.6 Radiation heat transfer between two
blackbo
Adapted from FP Incropera, DP De Witt, Introduction to Heat Transfer, 2002, John
Wiley & Sons.
Chapter 5 Internal flow
For internal flow applications, in addition to ascertaining whether the flow is laminar or
turbulent, we have to be cognizant of the exi
Chapter 8 Radiation exchange between surfaces
dA
8.1 View factor
j
nj
j
dAi
ni
R
Aj, Tj
i
Fij =
Ai, Ti
q i j
AiJ i
8.1.1 View factor relations
TN
Ti
N
F
T1
j =1
ij
T2
Figure 8.2 Radiation exchange
within an enclosure.
=1 , 1 i N
8.1.1 View factor relation
Adapted from FP Incropera, DP De Witt, Introduction to Heat Transfer, 2002, John
Wiley & Sons.
Chapter 4 External flow
4.1 The flat plate in parallel flow
u, T
Ts
y
Laminar
Turbulent
x
Fig. 5.1 The flat plate in parallel flow.
4.1.1 Laminar flow
In the la
Adapted from FP Incropera, DP De Witt, Introduction to Heat Transfer, 2002, John
Wiley & Sons and Incropera, DeWitt, Bergman, Lavine, Fundamentals of Heat and Mass
Transfer, 6th ed., 2007, John Wiley & Sons.
Chapter 3 Introduction to convection
3.1 A basi
Blackbody Radiation
Diffuse emission
Isothermal surface
For a prescribed temperature and wavelength,
no surface can emit more energy than a blackbody.
The Planck distribution
E ,b ( , T ) =
C1
5 [ exp( C 2 T ) 1]
2
C1 = 2hc o = 3.742 108 W m 4 m 2
C2 = h
Adapted from FP Incropera, DP De Witt, Introduction to Heat Transfer, 2002, John
Wiley & Sons.
Chapter 2 One-dimensional, steady-state conduction
2.1 The plane wall
Let us consider the situation when a plane wall separates two streams of fluids as shown
i
Adapted from FP Incropera, DP De Witt, Introduction to Heat Transfer, 2002, John
Wiley & Sons.
Chapter 1 Introduction to Conduction
1.1 The conduction rate equation
Consider a cylindrical rod of say, aluminum, which is insulated on its lateral surface as