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 b
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
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
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 ge
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
One-dimensional steady-state conduction
x
qx
T, 1
Ts, 1
Cold fluid
T, 2, h2
Ts, 2
Hot fluid
T, 2
T, 1, h1
L
T, 1
qx
Ts, 1
1
h 1A
Ts, 2
L
kA
T, 2
1
h 2A
Figure 2.1 Steady-state heat transfer through a
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 di
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
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
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 an
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
Mas
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
distri
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
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
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
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
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 si
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
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 o
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
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
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 l
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
wit
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 fl
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
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 [ ex
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
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,