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The Diffusion Handbook: Applied Solutions for Engineers
CITATION
Thambynayagam, R.K. Michael
.
The Diffusion Handbook: Applied Solutions for Engineers
.
US
: McGraw-Hill Professional, 2011.
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The Diffusion Handbook: Applied Solutions for Engineers
Authors:
R.K. Michael Thambynayagam
Published:
April 2011
eISBN:
9780071751858 0071751858
|
ISBN:
9780071751841
Open eBook
Book Description
Table of Contents
Contents
Preface
1 Preliminaries
1.1 Introduction
1.2 Nomenclature, symbols and iconic illustrations
1.3 Mathematical operations of special functions
1.4 The diffusion mode of transference of heat, mass and pressure
2 Integral transforms and their inversion formulae
2.1 Laplace transform
2.2 Fourier transforms
2.3 Finite Fourier transforms
2.4 Hankel and Weber transforms
2.5 Finite Hankel transforms
3 Infinite and semi-infinite continua. p (x, t) is a function of x and t only
3.1
3.2
3.3
3.4
4 Bounded continuum. p (x, t) is a function of x and t only
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
5 Infinite and semi-infinite (quadrant) continua. p(x, y, t) is a function of x, y and t only
5.1
5.2
5.3
5.4
5.5
5.6
5.7
6 Infinite and semi-infinite lamellae. p(x, y, t) is a function of x, y and t only
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
6.10
6.11
6.12
6.13
6.14
6.15
6.16
6.17
6.18
6.19
6.20
6.21
6.22
6.23
6.24
6.25
6.26
6.27
6.28
6.29
6.30
6.31
6.32
6.33
6.34
6.35
6.36
6.37
6.38
7 Rectangle. p(x, y, t) is a function of x, y and t only
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
7.10
7.11
7.12
7.13
7.14
7.15
7.16
7.17
7.18
7.19
7.20
7.21
7.22
7.23
7.24
7.25
7.26
7.27
7.28
7.29
7.30
7.31
7.32
7.33
7.34
7.35
7.36
7.37
7.38
7.39
7.40
7.41
7.42
7.43
7.44
7.45
7.46
7.47
7.48
7.49
7.50
7.51
8 Infinite and semi-infinite (octant) continua. p(x, y, z, t) is a function of x, y, z and t only
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9
8.10
8.11
9 Quadrant layer: infinite and semi-infinite continua. p(x, y, z, t) is a function of x, y, z and t only
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9.9
9.10
9.11
9.12
9.13
9.14
9.15
10 Octant layer. Infinite and semi-infinite continua. p(x, y, z, t) is a function of x, y, z and t only
10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
10.9
10.10
10.11
10.12
10.13
10.14
10.15
10.16
10.17
10.18
10.19
11 Cuboid. p(x, y, z, t) is a function of x, y, z and t only
11.1
11.2
11.3
11.4
11.5
11.6
11.7
11.8
11.9
11.10
12 Infinite and semi-infinite cylindrical continua. p(r, t) is a function of r and t only
12.1
12.2
12.3
12.4
13 Bounded cylindrical continua. p(r, t) is a function of r and t only
13.1
13.2
13.3
13.4
13.5
13.6
13.7
13.8
13.9
13.10
13.11
13.12
13.13
13.14
13.15
13.16
13.17
13.18
13.19
14 Infinite and semi-infinite cylindrical continua. p(r, θ, t) is cyclic around the cylinder with a period 2π. p(r, θ, t) is a function of r, θ and t
14.1
14.2
14.3
14.4
15 Bounded cylindrical continuum. p(r, θ, t) is cyclic around the cylinder with a period 2π. p(r, θ, t) is a function of r, θ and t
15.1
15.2
15.3
15.4
15.5
15.6
15.7
15.8
15.9
15.10
15.11
15.12
15.13
16 Wedge-shaped infinite and semi-infinite continua. The range of the θ variable is a portion of the circle; that is, 0 ≤ θ ≤ υ, where υ < 2π. p(r, θ, t) and the intial and boundary conditions are functions of r, θ and t
16.1
16.2
16.3
16.4
16.5
16.6
16.7
16.8
16.9
16.10
16.11
16.12
16.13
16.14
16.15
16.16
16.17
16.18
16.19
16.20
16.21
16.22
16.23
16.24
16.25
16.26
16.27
16.28
16.29
16.30
16.31
16.32
16.33
16.34
16.35
16.36
17 Wedge-shaped bounded continuum. The range of θ is a portion of the circle; that is, 0 ≤ θ ≤ υ, where υ < 2π. p(r, θ, t) is a function of r, θ and t
17.1
17.2
17.3
17.4
17.5
17.6
17.7
17.8
17.9
17.10
17.11
17.12
17.13
17.14
17.15
17.16
17.17
17.18
17.19
17.20
17.21
17.22
17.23
17.24
17.25
17.26
17.27
17.28
17.29
17.30
17.31
17.32
17.33
17.34
17.35
17.36
17.37
17.38
17.39
17.40
17.41
17.42
17.43
17.44
17.45
17.46
17.47
17.48
17.49
17.50
17.51
17.52
17.53
17.54
17.55
17.56
17.57
17.58
17.59
17.60
17.61
17.62
17.63
17.64
17.65
17.66
17.67
17.68
17.69
17.70
17.71
17.72
17.73
17.74
17.75
17.76
17.77
17.78
17.79
17.80
17.81
17.82
17.83
17.84
17.85
17.86
17.87
17.88
17.89
17.90
17.91
17.92
17.93
17.94
17.95
17.96
17.97
17.98
17.99
17.100
17.101
17.102
17.103
17.104
17.105
17.106
17.107
17.108
18 Infinite and semi-infinite cylindrical continua. The continuum is also either infinite or semi-infinite in z. p(r, z, t) is a function of r, z and t
18.1
18.2
18.3
18.4
18.5
18.6
18.7
18.8
18.9
18.10
18.11
18.12
18.13
18.14
18.15
18.16
19 Infinite and semi-infinite cylindrical continua bounded by the planes z = 0 and z = d. p(r, z, t) is a function of r, z and t
19.1
19.2
19.3
19.4
19.5
19.6
19.7
19.8
19.9
19.10
19.11
19.12
19.13
19.14
19.15
19.16
19.17
19.18
19.19
19.20
19.21
19.22
19.23
19.24
19.25
19.26
19.27
19.28
19.29
19.30
19.31
19.32
19.33
19.34
19.35
19.36
20 Bounded cylindrical continuum. The independent variable z is either infinite or semi-infinite. p(r, z, t) is a function of r, z and t
20.1
20.2
20.3
20.4
20.5
20.6
20.7
20.8
20.9
20.10
20.11
20.12
20.13
20.14
20.15
20.16
20.17
20.18
20.19
20.20
20.21
20.22
20.23
20.24
20.25
20.26
20.27
20.28
20.29
20.30
20.31
20.32
20.33
20.34
20.35
20.36
20.37
20.38
20.39
20.40
20.41
20.42
20.43
20.44
20.45
20.46
20.47
20.48
21 Bounded cylindrical continuum. The continuum is also bounded by the planes z = 0 and z = d. p(r, z, t) is a function of r, z and t
21.1
21.2
21.3
21.4
21.5
21.6
21.7
21.8
21.9
21.10
21.11
21.12
21.13
21.14
21.15
21.16
21.17
21.18
21.19
21.20
21.21
21.22
21.23
21.24
21.25
21.26
21.27
21.28
21.29
21.30
21.31
21.32
21.33
21.34
21.35
21.36
21.37
21.38
21.39
21.40
21.41
21.42
21.43
21.44
21.45
21.46
21.47
21.48
21.49
21.50
21.51
21.52
21.53
21.54
21.55
21.56
21.57
21.58
21.59
21.60
21.61
21.62
21.63
21.64
21.65
21.66
21.67
21.68
21.69
21.70
21.71
21.72
21.73
21.74
21.75
21.76
21.77
21.78
21.79
21.80
21.81
21.82
21.83
21.84
21.85
21.86
21.87
21.88
21.89
21.90
21.91
21.92
21.93
21.94
21.95
21.96
21.97
21.98
21.99
21.100
21.101
21.102
21.103
21.104
21.105
21.106
21.107
21.108
22 Infinite and semi-infinite cylindrical continua. p (r, θ, z, t) is cyclic around the cylinder with a period 2π. p (r, θ, z, t) is a function of r, θ, z and t
22.1
22.2
22.3
22.4
22.5
22.6
22.7
22.8
22.9
22.10
22.11
22.12
22.13
22.14
22.15
22.16
23 Infinite and semi-infinite cylindrical continua bounded by the planes z = 0 and z = d. p (r, θ, z, t) is cyclic around the cylinder with a period 2π. p (r, θ, z, t) is a function of r, θ, z and t
23.1
23.2
23.3
23.4
23.5
23.6
23.7
23.8
23.9
23.10
23.11
23.12
23.13
23.14
23.15
23.16
23.17
23.18
23.19
23.20
23.21
23.22
23.23
23.24
23.25
23.26
23.27
23.28
23.29
23.30
23.31
23.32
23.33
23.34
23.35
23.36
24 Bounded cylindrical continuum. The independent variable z is either infinite or semi-infinite. p(r, θ, z, t) is cyclic around the cylinder with a period 2π. p(r, θ, z, t) is a function of r, θ, z and t
24.1
24.2
24.3
24.4
24.5
24.6
24.7
24.8
24.9
24.10
24.11
24.12
24.13
24.14
24.15
24.16
24.17
24.18
24.19
24.20
24.21
24.22
24.23
24.24
24.25
24.26
24.27
24.28
24.29
24.30
24.31
24.32
24.33
24.34
24.35
24.36
24.37
24.38
24.39
24.40
24.41
24.42
24.43
24.44
24.45
24.46
24.47
24.48
25 The continuum is also bounded by the planes z = 0 and z = d. p(r, θ, z, t) is cyclic around the cylinder with a period 2π. p(r, θ, z, t) is a function of r, θ, z and t
25.1
25.2
25.3
25.4
25.5
25.6
25.7
25.8
25.9
25.10
25.11
25.12
25.13
25.14
25.15
25.16
25.17
25.18
25.19
25.20
25.21
25.22
25.23
25.24
25.25
25.26
25.27
25.28
25.29
25.30
25.31
25.32
25.33
25.34
25.35
25.36
25.37
25.38
25.39
25.40
25.41
25.42
25.43
25.44
25.45
25.46
25.47
25.48
25.49
25.50
25.51
25.52
25.53
25.54
25.55
25.56
25.57
25.58
25.59
25.60
25.61
25.62
25.63
25.64
25.65
25.66
25.67
25.68
25.69
25.70
25.71
25.72
25.73
25.74
25.75
25.76
25.77
25.78
25.79
25.80
25.81
25.82
25.83
25.84
25.85
25.86
25.87
25.88
25.89
25.90
25.91
25.92
25.93
25.94
25.95
25.96
25.97
25.98
25.99
25.100
25.101
25.102
25.103
25.104
25.105
25.106
25.107
25.108
26 Wedge-shaped infinite and semi-infinite continua. The range of the variable θ is a portion of the circle; that is, 0 ≤ θ ≤ υ, where υ < 2π. p(r, θ, z, t) is a function of r, θ, z and t
26.1
26.2
26.3
26.4
26.5
26.6
26.7
26.8
26.9
26.10
26.11
26.12
26.13
26.14
26.15
26.16
26.17
26.18
26.19
26.20
26.21
26.22
26.23
26.24
27 Wedge-shaped infinite and semi-infinite continua bounded by the planes z = 0 and z = d. The range of the variable θ is a portion of the circle; that is, 0 ≤ θ ≤ υ, where υ < 2π. p(r, θ, z, t) is a function of r, θ, z and t
27.1
27.2
27.3
27.4
27.5
27.6
27.7
27.8
27.9
27.10
27.11
27.12
27.13
27.14
27.15
27.16
27.17
27.18
27.19
27.20
27.21
27.22
27.23
27.24
27.25
27.26
27.27
27.28
27.29
27.30
27.31
27.32
27.33
27.34
27.35
27.36
27.37
27.38
27.39
27.40
27.41
27.42
27.43
27.44
28 Wedge-shaped bounded continuum. The independent variable z is either infinite or semi-infinite. The range of the variable θ is a portion of the circle; that is, 0 ≤ θ ≤ υ, where υ < 2π. p(r, θ, z, t) is a function of r, θ, z and t
28.1
28.2
28.3
28.4
28.5
28.6
28.7
28.8
28.9
28.10
28.11
28.12
28.13
28.14
28.15
28.16
28.17
28.18
28.19
28.20
28.21
28.22
28.23
28.24
28.25
28.26
28.27
28.28
28.29
28.30
28.31
28.32
28.33
28.34
28.35
28.36
28.37
28.38
28.39
28.40
28.41
28.42
28.43
28.44
28.45
28.46
28.47
28.48
28.49
28.50
28.51
28.52
28.53
28.54
28.55
28.56
29 Wedge. The range of the variable θ is a portion of the circle; that is, 0 ≤ θ ≤ υ, where υ < 2π. The independent variable z is bounded by the planes z=0 and z=d. p(r, θ, z, t) is a function of r, θ, z and t
29.1
29.2
29.3
29.4
29.5
29.6
29.7
29.8
29.9
29.10
29.11
29.12
29.13
29.14
29.15
29.16
29.17
29.18
29.19
29.20
29.21
29.22
29.23
29.24
29.25
29.26
29.27
29.28
29.29
29.30
29.31
29.32
29.33
29.34
29.35
29.36
29.37
29.38
29.39
29.40
29.41
29.42
29.43
29.44
29.45
29.46
29.47
29.48
29.49
29.50
29.51
29.52
29.53
29.54
29.55
29.56
29.57
29.58
29.59
29.60
29.61
29.62
29.63
29.64
29.65
29.66
29.67
29.68
29.69
29.70
29.71
29.72
29.73
29.74
29.75
29.76
29.77
29.78
29.79
29.80
29.81
29.82
29.83
29.84
29.85
29.86
29.87
29.88
29.89
29.90
29.91
29.92
29.93
29.94
29.95
29.96
29.97
29.98
29.99
29.100
29.101
29.102
29.103
29.104
29.105
29.106
29.107
29.108
29.109
29.110
29.111
29.112
29.113
29.114
29.115
29.116
Appendix A: A supplement to Chapter 8
Appendix B: A supplement to Chapter 9
Appendix C: A supplement to Chapter 10
Appendix D: A supplement to Chapter 11
Appendix E: A table of integrals
Appendix F: General properties and a table of Laplace transforms
Appendix G: Series
Bibliography
Author Index
A
B
C
D
E
F
G
H
J
K
L
M
N
O
P
R
S
T
W
Subject Index
A
B
C
D
E
F
G
H
I
K
L
M
N
O
P
Q
R
S
T
U
V
W
