J.V. BECK, DEPT . OF MECH. EN G., MI CH. STATE UNIV. 1990
LIST OF NUMBERS IN CARSLAW AND JAEGER (1959 Edition) using the numbering
system for heat conduction found in our book
"Heat Conduction Using Green's Functions", Chapter 2.
NO. TYPE BOOK Pg EQ# COMMENTS
1 X00T- C&J 53 1 For conditions on f(x), see p.54, C&J
2 X00T- C&J 54 2 Same as no. 1 which is preferred.
3 X00T5 C&J 54 3 F(x)=V, -a<x<a; F(x)=0, abs(x)>a
4 X00T5 C&J 54 4 F(x)=0, -a<x<a; F(x)=V, abs(x)>a
5 X00T2 C&J 54 5 F(x)=0, abs(x)>a; F(x)=V(a-x)/a, see C&J
6 X20B0T- C&J 56 6
7 X10BOT- C&J 59 1
8 X10B0T- C&J 59 2 Same as C&J, p.59,(1), which is preffered
9 X10B0T1 C&J 59 3
10 X10B1T0 C&J 60 10
11 X00T5 C&J 61 12 F(x)=0, x<0 ;T=V, x>0
12 X10B0T2 C&J 61 13 F(x)=V+kx
13 X10B0T5 C&J 62 14 F(x)=V, 0<x<d;T=0 x>0
14 X10B0T5 C&J 62 15 F(x)=V, a<x<b;T=0, 0<x<a, x>b
15 X10B-T0 C&J 63 1
16 X10B5T0 C&J 63 2,3 f(t)=V0, 0<t<ta; f(t)=V1, t>ta
17 X10B2T0 C&J 63 4,5 f(t)=kt, two expressions
18 X10B3T0 C&J 63 6,7 f(t)=sqrt(kt)
19 X10B3T0 C&J 63 8 f(t)=sqrt(t**n)
20 X10B4T0 C&J 64 9 f(t)=exp(nt)
21 X10B6T0 C&J 64 1,2 f(t)=a cos(wt-e)
22 X10B6T C&J 65 8 f(t)=a cos(wt-e), steady st. periodic
23 X20B6T C&J 67 14 f(t)=a cos(wt-e)
24 X10B6T C&J 68 18 f(t)=a0+a1 cos(wte1), st. st. periodic
25 X10B5T C&J 68 20 steady state periodic
26 X30B0T1 C&J 71 1
27 X30B1T0 C&J 72 5
28 X30B-T0 C&J 74 1
29 X30B5T0 C&J 74 2,3 f(t)=a, 0<t<V;f(t)=b, t>ta
30 X30B6T0 C&J 74 4 f(t)=sin(wt+e)
31 X20B1T0 C&J 75 6,7 Two forms of solution
32 X20B-T0 C&J 76 9
33 X20B5T0 C&J 76 10 f(t)=q0, 0<t<ta;f(t)=0, t>ta
34 X20B3T0 C&J 76 12 f(t)=a sqrt(kt), 0<t<ta; f(t)=0, t>ta
35 X20B6T0 C&J 76 13 f(t)=sin(wt+e)
36 X20B3T0 C&J 77 16 f(t)=q0 sqrt(t**n), n=-1,0,1..
37 X10B0T(1,2)G1 C&J 79 2 F(x)=a+bx
38 X10B0T(1,2)Gx4 C&J 79 3 F(x)=a+bx, g(x)=a exp(-nx)
39 X10B0T(1,2)Gx5 C&J 79 4,5 F(x)=a+bx; g(x)=a, 0<x<L<B
40 X20B0T0Gx5 C&J 80 9,10 g(x)=a, 0<x<L; g(x)=0, x>L
41 X10B0T0Gt4 C&J 80 12 g(x)=a exp(-kt)
42 X20B0T2Gx4 C&J 80 13 F(x)=a+bx, g(x)=a exp(-bx)
43 X0T1CX0T0 C&J 88 5,6 Composite, F(x)=V, x>0; F(x)=0,X>0
44 X0T0C2X0T0 C&J 88 9,10 Composite, heat flux at x=0
45 X0T1C3X0T0 C&J 89 12 Composite, resistance at x=0
46 X11B00T- C&J 94 4,5 0<x<L
47 X11B00T1 C&J 96 6 0<x<L
48 X11B00T2 C&J 96 7 F(x)=kx, 0<x<L
49 X11B00T1 C&J 97 8,9 #NAME?
49 X21B00T1 C&J 97 8,9 0<x<L
50 X11B00T2 C&J 97 14,15 F(x)=V(L-abs(x))/L, -L<x<L
51 X21B00T2 C&J 97 14,15 F(x)=V(L-x)/L, 0<x<L
52 X11B00T3 C&J 98 16,17 F(x)=V(L**2-X**2)/L**2, -L<x<L
52 X21B00T3 C&J 98 16,17 0<x<L
53 X11B00T6 C&J 99 18 F(x)=V cos(x/2L), -L<x<L
54 X21B00T6 C&J 99 18 F(x)=V cos(x/2L), 0<x<L
55 X11B11T- C&J 100 1 T(0,t)=T1, T(L,t)=T2
56 X11B11T0 C&J 100 2 -L<x<L
57 X21B01T0 C&J 100 2 0<x<L
58 X11B11T0 C&J 100 4 -1<x<1 Dimensionless
59 X21B01T0 C&J 100 4 0<x<1 Dimensionless
60 X21B01T- C&J 101 5
61 X22B00T- C&J 101 6
62 X11B--T- C&J 104 2
63 X21B0-T- C&J 104 3
64 X11B22T0 C&J 104 4 T(-L,t)=T(L,t)=kt, -L<x<L
65 X21B02T0 C&J 104 4 T(L,t)=kt, 0<x<L
66 X11B66T0 C&J 104 5 T(-L,t)=T(L,t)=V(1-exp(-bt))
67 X21B06T0 C&J 104 5 T(L,T)=V(1exp(bt)) 0<x<L
68 X11B44T0 C&J 105 6 T(-L,t)=T(L,t)=V exp(bt) -L<x<L
69 X21B04T0 C&J 105 6 T(L,t)=V exp(bt) 0<x<L
70 X11B66T0 C&J 105 1 T(\L\,T)=sin(wt+e)
71 X21B06T0 C&J 105 1 T(L,t)=sin(wt+e)
72 X11B06T0 C&J 105 5,6 T(L,t)=sin(wt+e) 0<x<L
73 X11B05T C&J 108 15,17 Steady periodic
74 X21B05T C&J 109 20,21 Steady periodic
75 X22B01T0 C&J 112 3,4 Two forms, 0<x<L
76 X12B01T0 C&J 113 5,6 Two forms, 0<x<L
77 X22B03T0 C&J 113 7 T(L,t)=q0 sqrt(t**m), m=-1,0,1,..
78 X12B03T0 C&J 114 8 T(L,t)=q0 sqrt(t**m), m=-1,0,1...
79 X33B00T- C&J 118 12 0<x<L h1 = h2
80 X33B00T- C&J 119 1 -L<x<L h1 = h2
81 X23B00T- C&J 119 1 0<x<L
82 X33B00T- C&J 120 8 F(x) is even function L<x<L
83 X23B00T- C&J 120 8
84 X33B00T- C&J 120 11 F(x) is odd function of x
85 X13B00T- C&J 120 11
86 X33B00T1 C&J 122 12 h1=h2, -L<x<L
87 X23B00T1 C&J 122 12
88 X33B00T(1,2) C&J 124 13 F(x)=a-bx**2
89 X23B00T2 C&J 124 13 F(x)=a-bx**2
90 X23B10T0 C&J 125 14 0<x<L
91 X13B01T0 C&J 125 15
92 X13B10T0 C&J 126 16
93 X13B01T2 C&J 126 17 F(x)=Vx/L, 0<x<L f2(t)=V
94 X33B01T0 C&J 126 19 -L<x<L, h1 = h2
95 X33B00T- C&J 126 21-24 general result, h1 not = h2
96 X33B--T0 C&J 127 1 same function at x = -L,L
97 X23B0-T0 C&J 127 1 0<x<L
98 X33B55T0 C&J 127 3,4 f1=f2=V0, 0<t<ta;f1=f2=V1,t>ta
99 X23B05T0 C&J 127 3,4 f2=V0, 0<t<ta;f2=V1, t>ta
100 X33B66T0 C&J 127 5 f1=f2=Vsin(wt+e), -L<x<L
101 X23B06T0 C&J 127 5 f2=Vsin(wt+e), 0<x<L
102 X33B232T0 C&J 127 9 f1=f2=Kt, -L<x<L
103 X23B02T0 C&J 127 9 f2=Kt, 0<x<L
104 X24B01T00 C&J 128 5
105 X24B00T01 C&J 128 6
106 X14B01T00 C&J 128 7
107 X14B00T01 C&J 128 8
108 X14B10T00 C&J 129 9
109 X24B10T00 C&J 129 10
110 X25B00T10 C&J 129 11
111 X25B0-T00 C&J 129 13
112 X62B10T00 C&J 129 14 Contact resistance between fluid
and solid
113 X11B00T0G1 C&J 130 7 -L<x<L
114 X21B00T0G1 C&J 130 7 0<x<L
115 X11B00T0G3 C&J 131 8 -L<x<L, g=at**n/2, n=-1,0,1,2,...
116 X21B00T0G3 C&J 131 8 0<x<L, g=at**n/2, n=-1,0,1,2,...
117 X11B00T0Gt- C&J 131 9 -L<x<L
118 X21B00T0Gt- C&J 131 9 0<x<L
119 X11B00T0Gx- C&J 132 10a -L<x<L
120 X21B00T0Gx- C&J 132 10a 0<x<L
121 X11B00Gx- C&J 132 10b -L<x<L Steady state
122 X21B00Gx- C&J 132 10b 0<x<L Steady state
123 X33B00T0G1 C&J 132 12 L<x<L
124 X23B00T0G1 C&J 132 12 0<x<L, h1 = h2
125 X13B00T0G1 C&J 132 13 0<x<L
126 X11B00T0Gt4 C&J 132 14 -L<x<L, g(t)=a exp(-bt)
127 X21B00T0Gt4 C&J 132 14 0<x<L, g(t)=a exp(-bt)
128 X10F0B1T0 C&J 135 7
129 X11F0B11T0 C&J 135 8 -L<x<L
130 X21F0B01T0 C&J 135 8 0<x<L
131 X10F0B1 C&J 135 1 Steady state
132 X11F0B11 C&J 139 1 Steady state
133 X12F0B10 C&J 142 6
134 X12F0B10 C&J 142 14 Steady state, fin taper linear
at a small angle A
x=0, area=D, x=L, area=D-2AL
135 R12F0B10 C&J 143 20 Circular fin
136 RF--0 C&J 143 24 Circular fin, variable thickness, z=D/r
137 R12F0B10 C&J 143 27 z=D/r*r
138 X11F0B--T- C&J 144 4
139 X21F0B0-T- C&J 144 5
140 X22F0B00T- C&J 144 6
141 X33F0B00T1 C&J 144 7 -L<x<L
142 X23F0B00T1 C&J 144 7 0<x<L
143 X33F0B00T- C&J 145 8 Eqs. (9-11) needed also
144 X11F0B55T0 C&J 146 6,7 Periodic steps in time
145 X10F0B1V1 C&J 148 4 Steady state fin
146 X11F0B11V1 C&J 148 5 Steady state fin, T(0)=V1, T(2L)=V2
147 X12F0B10V1 C&J 148 5 Steady state fin 0<x<L, V1=V2
148 X11F0B00G1 C&J 152 6 Steady state, 0<x<L
148 X12F0B00G1 C&J 152 6 Steady state, 0<x<L
148 X1F0B1G1CX1F0B1G1 C&J 157 5 Steady state composite wire
149 X1F0B1CX2F0B0 C&J 157 9 Steady state composite fin
150 X1F0B0G1CX2F0B0G1 C&J 157 11 Steady state composite fin
151 X11F0B00T0G1 C&J 159 3 Transient fin
152 X11F0B11 C&J 160 5 Steady state, -L<x<L
152 X11B00Y10B1 C&J 164 11 Steady state, 2-D
152 X11B-0Y10B0 C&J 165 18 Solution in form of integral
152 X11B-0Y00 C&J 166 19
152 X10B-Y00 C&J 166 20
152 X11B00Y11B10 C&J 167 10
152 X23B00Y12B-0 C&J 167 16
152 X23B00Y12B10 C&J 168 17
152 X33B00Y11B11 C&J 168 17
152 X23B00Y13B-0 C&J 168 19
152 X23B00Y13B10 C&J 168 20
152 X33B00Y13B10 C&J 168 20
152 X23B00Y11B-0 C&J 168 21
152 X23B00Y11B10 C&J 168 22
152 X33B00Y11B10 C&J 168 22
152 X33B00Y11B11 C&J 169 23 T(x,0)=V1, T(x,b)=V2
152 X11B00Y11B-0F0 C&J 170 10
152 X33B00Y33B00G1 C&J 171 5
152 X11B00Y11B00G1 C&J 171 6
152 X10B0Y10B0T1 C&J 171 2
152 X30B0Y30B0T1 C&J 172 4,5
152 X11B00Y10B0T1 C&J 173 8 -L<x<L
152 X33B00Y30B0T1 C&J 173 9 -L<x<L
152 X11B00Y30B0T1 C&J 173 10 -L<x<L
152 X11B00Y11B00T1 C&J 173 11
152 X33B00Y33B00T1 C&J 173 12
152 X11B11Y11B00Z11B00 C&J 177 9 Steady state
152 X11B11Y33B00Z33B00 C&J 179 23 Steady state, -b<y<b, -c<z<c
152 X11B11Y23B00Z23B00 C&J 179 23 Steady state, 0<y<b, 0<y<c
152 X13B10Y33B00Z33B00 C&J 180 27 Steady state
152 X10B1Y33B00Z33B00 C&J 180 29 Steady state -b<y<b, -c<z<c
152 X10B1Y23B00Z23B00 C&J 180 29 Steady state 0<y<b, 0<z<c
152 X11B-0Y11B00Z11B00 C&J 183 20,21 Steady state 0<x<a, 0<y<b, 0<z<c
152 X10B0Y10B0Z10B0T1 C&J 184 1
152 X30B0Y30B0Z30B0T1 C&J 184 2
152 X11B00Y11B00Z1ZB0T1 C&J 184 3,4
152 X11B00Y11B00Z11B00T1 C&J 184 5 or eq. 6 and 7
152 X33B00Y33B00Z33B00T1 C&J 184 8
152 X11B11Y11B11Z11B11T0 C&J 185 11 Same T on all surfaces
152 X11B--Y11B--Z11B-1T0 C&J 185 12 Same f(t) on all surfaces
152 X11B22Y11B22Z11B22T0 C&J 185 13 Same f(t) = at on all surfaces
152 X11B00Y11B00Z11B00T- C&J 187 5 Initial Temp = F(x,y,z)
153 R11B11 C&J 189 3 T(a)=T1 T(b)=T2 a<r<b , steady state
154 R13B11 C&J 189 5 Steady state
155 R01B0G1 C&J 191 17
156 R03B0G1 C&J 191 18
157 R0G1CR3B0 C&J 192 22,23 Insulated wire with energy generation
158 R01B0G2 C&J 192 27 Linear variation of electrical
resistance of wire with temperature
159 R21B00G2 C&J 192 28 Linear variation of electrical
resistance of wire with temperature
160 R01B0T- C&J 198 4
161 R01B0T1 C&J 199 5
162 R01B0T3 C&J 199 7 T(r,0)=V-Kr
163 R01B1T0 C&J 199 8 Eq. (10), same page is dimensionless
164 R01B-T0 C&J 201 12
165 R01B2T0 C&J 201 13 T(a,t)=kt
166 R01B6T0 C&J 201 14 T(a,t)=Vsin(wt+C)
167 R03B0T- C&J 201 3
168 R03B0T1 C&J 202 4
169 R03B1T0 C&J 202 8 Fluid at V
170 R03B2T0 C&J 202 10 Fluid at kt
171 R03B6T0 C&J 202 11 Fluid at V sin(wt+e)
172 R02B1T0 C&J 203 1
173 R02B0T- C&J 204 3
174 R01B0T0G1 C&J 204 1
175 R01B0T0Gt4 C&J 204 2 g = a exp(-bt)
176 R03B0T0G1 C&J 205 3
177 R11B00T- C&J 207 12
178 R11B00T1 C&J 207 13
179 R1B11T- C&J 207 15 T(a,t)=T1 T(B,t)=T2
180 R01B-f00Z00 C&J 209 6 T(a,t)=f(f,z) Steady state
181 R01B(z-)Z00 C&J 209 7 T(a,t)=f(z), Steady state
182 R01B5Z00 C&J 209 8 T(a,t)=1, z>0; =0, Z<0; Steady state
183 R01B5Z00V(z1) C&J 209 11 T(a,t)=1, z>; =0, z<0; Steady state, Velocity = U
184 R01B0f00T- C&J 211 1
185 R03B0f00T- C&J 211 2 T(r,f,0)=F(r,f)
186 R01B0f00Z00T- C&J 212 4 T(r,f,z,0)=F(r,f,z)
187 R01B0f11B00T- C&J 213 5 T(r,f,0)=F(r,f)
188 R01B0f11B00T1 C&J 213 6
188 R00Z(1,2)0B(1,0) C&J 215 5,9 Steady, T(r,0)=TO for 0<r<a
188 R00Z20B5 C&J 215 7 q=c for 0<r<a
188 R00Z00C5R00Z0 C&J 216 12 Heat transfer only 0<r<a
13 T=0 at z=00; T=TO at z=-00; two half spaces in contact
188 R00Z20B5 C&J 216 16 Average temperature
188 R00Z(2,1)0B C&J 217 17
188 R03B0Z11B-0 C&J 219 8,9
188 R03B0Z11B10 C&J 219 10
188 R03B0Z13B-0 C&J 219 13
188 R01B0Z11B-0 C&J 219 14
188 R01B-Z11B00 C&J 220 16
188 R01B-Z33B00 C&J 220 17
188 R02B5Z22B00 C&J 220 19 f=c, -L+b>z>-L; f=-c, L>z>L-b, f=0 otherwise
188 R11B-0Z11B00 C&J 220 20
188 R21B-0Z11B00 C&J 221 22
188 R21B50Z11B00 C&J 221 24
188 R0G1CR1B0Z11B00 C&J 221 25 Composite source wire with volumetric energy
188 R0G1CR1B0Z11B00 C&J 222 27
188 R11B00Z11B-0 C&J 222 28
188 R13B-OZ33B00 C&J 222 29
188 R01B0Z10B- C&J 222 31
188 R01B-Z10B0 C&J 222 32
188 R03B0Z10B- C&J 223 33
188 R01B-Z30B0 C&J 223 34
188 R02B0B0Z22B55 C&J 223 35 q=c, 0<r<a at z=0, q=0, a<r<b
q=c, 0<r<a tat z=L, q=0, a<r<b
188 R01B0Z11B00G1 C&J 224 38
188 R21B0-Z11B00 C&J 224 39
188 R21B00Z11B C&J 224 40
188 R01B0Z11B00G* C&J 224 41 g=a(1+bT)
188 R01B0Z11B00F1 C&J 224 41
188 R01B0Z11B00T1 C&J 225 45
188 R01B1Z11B11T0 C&J 227 6
188 R03B0Z33B00T1 C&J 227 7
188 R01B0Z33B00T1 C&J 227 8
188 R01B0Z11B00T1 C&J 227 10
188 R03B0Z10B0T1 C&J 227 11
188 R01B0Z30B0T1 C&J 227 12
188 R01B0Z11B00f00T1- C&J 229 middle of pages
190 RS13B11 C&J 231 4 Steady state
191 RS33B11 C&J 231 5 Steady state
192 RS01B0G1 C&J 232 12 Steady state
193 RS03B0G1 C&J 232 13 Steady state
194 RS10B1 C&J 232 14 Steady state
195 RS0GC3RS0 C&J 232 14B Steady state.MATL1 0<r<A, MATL2 R>
196 RS01B-T- C&J 233 3
197 RS01B1T0 C&J 233 4,5 TWO FORMS OF SOLUTION
198 RS01B2T0 C&J 235 10 T(a,t)=kt 0<r<A
199 RS01B6T0 C&J 235 12 T(a,t)=sin(wt+e) 0<r<A
200 RS01B0T2 C&J 235 13, T(r,0)=V(A-R)/A , 0<r<A
201 RS01B0T3 C&J 236 15 T(r,0)=V(A*A-R*R)/A*A 0<r<A
202 RS01B0T6 C&J 236 17 T(r,0)=(V/R)*sin(pi*R/A) 0<r<A
203 RS01B0T7 C&J 236 18 T(r,0)=Vexp(C(R-A)) 0<r<A
204 RS01B0T5 C&J 236 19, T(r,0)=<V 0<r<B, 0 B<r<A! TWO FORMS OF SOLUTION
205 RS01B0T- C&J 237 21 FOR SMALL VALUE OF kt/(A*A)
206 RS01B0T3 C&J 237 23 T(r,0)=BO+B1*R+B2*R**2+B3*R**3
207 RS03B0T- C&J 237 8
208 RS03B0T1 C&J 238 10
209 RS03B2T0 C&J 238 11 VO=kt
210 RS03B6T0 C&J 238 12 VO=Vsin(wt+e)
211 RS04B0T-0 C&J 240 2 -4*pi*A*A*K*DV/DR=M'C'DU/DT, R=A
212 RS04B0T10 C&J 240 5
213 RS02B1T0 C&J 242 1
214 RS01B0T0G1 C&J 243 6,7 EQ7 FOR SMALL VALUE OF kt/A*A
215 RS01B0T0GR2 C&J 243 8,9 G(R)=GO(A-R)/A
216 RS01B0T0GR3 C&J 243 10, G(R)=GO(A*A-R*R)/G*G TWO FORMS
OF SOLUTION
217 RS01B0TGR6 C&J 244 12 G(R)=(GO/R)sin(pi*R/A)
218 RS01B0T0GGR7 C&J 244 13 G(R)=GOexp(R-A)
219 RS01B0T0GT7 C&J 245 14, G(T)=GOexp(-A*T) TWO FORM OF SOL
220 RS01B0T0GT5 C&J 245 16 G(T)=<0 0<r<B, GOexp(-C*T) B<r<A!
221 RS01B0T0GR- C&J 245 17 G=G(R)
222 RS03B1T3 C&J 245 19
223 RS03B1T3 C&J 246 20B
224 RS11B11T- C&J 246 1
225 RS33B00T- C&J 246 2
226 RS12B01T0 C&J 247 3
227 RS10B-T- C&J 247 1
228 RS10B1T0 C&J 247 2
229 RS30B1T0 C&J 248 3
230 RS20B1T0 C&J 248 4
231 RS01B-Q00L00 C&J 250 4 T(A,Q,L,t)=F(Q,L)
232 RS00Q11B00L00T- C&J 252 12
X00Y00Z00T0Gxyzt7 C&J 256 2 Green's function
233 RS00Tr5 C&J 257 6 T(r,0) = V, 0<r<a, T(r,0) = 0 for r>a
234 RS00Tr5 C&J 257 7 Small a
235 RS00T0Grt7 C&J 257 7b Greens's function for source at r = 0
X00Y00Z00T0Gxyzt7 C&J 257 8 Anisotropic material, different conductivities in x,y and z
236 X00F0T0Gxt7 C&J 257 9 Green's function for rod losing heat to surroundings (fin)
237 X00F0Y00F0TOGxyt7 C&J 258 10 Green's function for sheet fin with source at origin
238 X00Y00T0Gxyt7 C&J 258 1 Green's function
R0000T0Grt7 C&J 258 3 Green's function
239 X00T0Gxt7 C&J 259 4 Green's function
240 R00T0Grt7 C&J 259 5 Green's function
241 RS00T0Grt7 C&J 259 6 Green's function
242 R00X00T0Grxt7 C&J 260 7 Green's function
243 R00Z00T0Gzt7 C&J 260 9 Instantaneous disk source, g(r,0,t) = g0?(t') for r ' < a
at z ' =
244 R00T C&J 260 11 T(r,0)=F(r)
245 R00Tr5 C&J 260 12 T(r,0) = V, 0<r<a; T(r,0) = 0, r > a
246 X00Y00Z00T0Gxyzt7 C&J 261 1
247 RS00T0Gr7 C&J 261 2 Point source at r = 0
248 R00T0Gt C&J 261 3 Line source with time variable strength
249 R00T0Gr7 C&J 261 5 Line source with constantiable strength
250 X10B0Y00T0Gxy7 C&J 262 7 Constant line source in semi-infinite body with isothermal surface
251 X00T0G(x7t-) C&J 262 8 Time variable plane heat source at x'
252 X00G(x7t1) C&J 263 9 Constant plane heat source at x'
253 RS00T0G(r7t-) C&J 263 10 Arbitrary time variable spherical source
254 RS00T0G(r7t1) C&J 263 11 Constant spherical source
255 RS00T0G(r7t6) C&J 263 12 Periodic point heat source at r' = 0
256 R00T0G(r7t6) C&J 263 13 Periodic line heat source at r' = 0
257 X00Z20Bx5T0 C&J 264 1 T(x,0,t) given for q = constant over x<0
258 X00Z20Bx5T0 C&J 264 3 T(x,0,t) given for q = constant over -a<x<a
259 R00Z20Br5T0 C&J 264 4 T(0,z,t) given for q = constant over 0<r<a
X00Y00Z20B(xy5) C&J 265 6,7 Maximum and average heated surface temperatures, rectangular heat source
R00Z00T0Grz5t1 C&J 266 1 T(0,0,t) for constantant energy generation over 0 < r < a, -b < z < b
R00Z00T0Grz5t1 C&J 266 1 T(0,0,t) for constant energy generation over 0 < r < a, -b < z < b
260 X00Y00Z00T0Ux1G(xyz7t1) C&J 267 1 Moving point heat source (or moving medium about a fixed point heat source at origin)
X00Y00Z00Ux1Gxyz7 C&J 267 1 Steady solution for moving point heat source (or moving medium about a fixed point heat source)
261 X00Z00Ux1Gxy7 C&J 267 3 Steady solution for moving line heat source (or moving medium about a fixed point heat source)
262 X00Y00Z22B00UX1GPX0 C&J 268 7
263 X00Y00Z22B00VX1GPX0Y3Z0T1 C&J 268 8 Heat emitted during time period (0,t), THEN t∞.
Approach OO for s.s. at y-axis
264 X00Y00Z00VX1GPX7Y3Z0T1 C&J 269 10 For s.s along strip, -B<x<B, -OO<Y<OO, Z=0
265 X1GPX7T7Z0T1 C&J 270 13 Heat emitted along rectalinear source,
-B<x<B -L<Y<L T approach OO for s.s.
266 X00Y00Z00T0GDX7Y7T0 C&J 271 4 Instantaneous line doublet
267 X00Y00Z00T0GDX7T0 C&J 271 5 Instantaneous plane doublet
268 X00Y00Z00GDX7T0 C&J 271 6 Continuous plane doublet
269 X10B0T- C&J 274 1 Source at the plane X'
270 X11B00T- C&J 274 2 Alternating source-sinks, sink at
-X'+2NA, sourse at X'+2NA
271 X11B-0T0GDX6T- C&J 276 6 Doublet at 2NA N=0, 1,2,G*P(T)=2K*
272 X20B0T- C&J 276 7 Source at X=X', sink at X=-X'
273 X21B00T- C&J 276 8 Alt source at +/-4NA+/-X', sink at +/-(4N+2)A+/-X
274 X10B1T0 C&J 305 5
275 X10B3T0 C&J 305 6 T(0,t)=V0 t^(n/2); n = any positive integer
276 X10B-T0 C&J 305 7
277 X30B1T0 C&J 306 top
278 X40B0T(10) C&J 306 11
279 X40B1T(00) C&J 306 12
280 X60B0T(10) C&J 307 18
281 X30B0T0Gt3 C&J 308 23 g(t)=k0 t^(n/2), n = -1, 0, and any positive integer
282 X10B0T0Gx5 C&J 308 28
283 X21B01T0 C&J 309 3 Best for small dimensionless times
284 X11B01T0 C&J 310 6 Best for small dimensionless times
285 X22B01T0 C&J 310 8 Best for small dimensionless times
286 X23B00T1 C&J 311 11 Best for small dimensionless times
287 X11B00T0Gt3 C&J 311 12 g(t)=k0 t^(n/2), n = -1, 0, and any positive integer
288 X21B01T0 C&J 313 6
289 X21B0-T0 C&J 313 7
290 X11B01T0 C&J 313 10
291 X11B00T0Gt4 C&J 315 20 g(t) = a exp(-ct)
292 X23B00T1 C&J 316 24
293 X62B00T(10) C&J 317 29,30 Well-stirred fluid with convective condition between fluid and solid
294 X10B6T0 C&J 319 8 T(0,t) = Vsin(ωt+e)
295 X1B1CX0T00 C&J 321 16,17
296 X1B0G1CX0T00 C&J 323 24,26
297 X1B1CX1B0T00 C&J 324 30, EQ 30 -L<x<0, EQ 31 0<x<A
298 R01B1T0 C&J 328 7
299 R01B2T0 C&J 328 8
300 R02B1T0 C&J 329 11
301 R03B1T0 C&J 329 15
302 R05B0T(10) C&J 330 20
303 R01B0T1G1 C&J 330 24
304 R01B1T0 C&J 331 3 For small values of time, κt/a2<0. 02, r/a not small
305 R02B1T0 C&J 331 5 For small values of time, κt/a2<0. 02, r/a not small
306 R03B1T0 C&J 331 6 For small values of time, κt/a2<0. 02, r/a not small
307 R33B11T0 C&J 333 10
308 R21B10T0 C&J 334 12
309 R10B1T0 C&J 335 6
310 R10B1T0 C&J 336 7 For small values of time, κt/a2<0.02, r/a not large
311 R30B0T1 C&J 337 15
312 R20B1T0 C&J 338 17
313 R20B1T0 C&J 339 18 For small values of time, κt/a2<0.02, r/a not large
315 R10B6T0 C&J 339 20
316 R10B0Z10B0T1 C&J 339 21 Product solution
317 R20B1T0 C&J 341 11 For large values of time, κt/a2
318 R40B0T(10) C&J 342 3
R40B0T-10 C&J 342 5 Solution for 0<r<a, which is independent of r
319 R40B1T(00) C&J 342 7 Interior cylinder has constant energy generation
R50B0T(10) C&J 344 9,11 Temperature at r=0
R50B1T(00) C&J 344 13,14 Temperature at r=0
R50B1T(00) C&J 345 16,17 Temperature at r=0, small times
R50B1T(00) C&J 345 16,17 Temperature at r=0, large times
320 R0CR0T(10) C&J 346 7,8
321 R0G1CR0T00 C&J 347 13,14
322 RS01B0T1 C&J 348 6
323 RS00T0Gr5 C&J 349 13,14
324 RS50B1T00 C&J 349 18
325 RS50B1T00 C&J 350 19 Solution for small times, 0<r<a
326 RS50B1T00 C&J 350 20 Solution for large times, 0<r<a
327 R50B0T(10) C&J 350 21 Temperature at 0<r<a
328 R50B0T(10) C&J 350 22 Temperature at 0<r<a, small time solution
329 R50B0T(10) C&J 350 23 Temperature at 0<r<a, large time solution
330 R41B0T(11) C&J 350 24
331 R41B1T(00) C&J 350 27
332 R0CR1B0T11 C&J 352 39,40 Additional terms in eqs. 43,44 may be needed
X10B0T0Gxt7 C&J 357 1 Green's function
333 X10B-T0Gx- C&J 357 2 Green's function solution for arbitrary conditions
X00T0Gxt7 C&J 358 3 Green's function
334 X30B0T0Gxt7 C&J 358 6 Green's function
335 X30B-T- C&J 359 7 Green's function solution for arbitrary conditions
336 X11B00T0Gxt7 C&J 360 2 Green's function
337 X33B00T0Gxt7 C&J 360 4 Green's function
338 X22B00T0Gxt7 C&J 361 7 Green's function
339 X10B0Y10B0T0Gxt7 C&J 361 2 Green's function
340 X11B00Y11B00T0Gxt7 C&J 361 3 Green's function
341 X22B00Y22B00T0Gxt7 C&J 362 4 Green's function
342 X11B00Y11B00Z11B00T- C&J 362 2 Green's function solution for arbitrary initial T
343 X11B-0Y11B00Z11B00T0 C&J 362 3 Green's function solution for arbitrary T at x=0
344 X11B00Y11B00Z11B00T0G- C&J 363 4 Green's function solution for arbitrary source
345 X11B00Y11B00Z11B00T0G1 C&J 363 5 Green's function solution for constant source
346 X0CX0T0Gxt7 C&J 364 8,9 Green's function for composite
347 X0C3X0T0Gxt7 C&J 364 11,12 Green's function, imperfect contact
348 X1B0CX1B0T00Gxt7 C&J 365 13,14 Green's function finite composite plate
349 X1B0CX0T00Gxt7 C&J 365 16 Green's function for composite
350 RS00T0Grt7 C&J 366 1 Green's function sphere
RS01B0T0Grt7 C&J 366 7,9 Green's function, two forms of solution
351 RS03B0T0Grt7 C&J 367 10 Green's function
352 RS33B00T0Grt7 C&J 367 13 Green's function
353 RS30B0T0Grt7 C&J 368 16 Green's function
R00ToGrt7 C&J 368 1 Green's function
354 R01B0T0Grt7 C&J 369 5 Green's function
355 R03B0T0Grt7 C&J 369 7 Green's function
356 R05B0T(00)Grt7 C&J 370 9 Green's function
357 R33B00T0Grt7 C&J 370 11 Green's function
358 R30B0T0Grt7 C&J 370 12 Green's function
359 X10B0Y00Z00T0Gxyxt7 C&J 370 1 Green's function
X10Byzt-Y00Z00Txyz- C&J 371 3 Green's function solution, arbitrary conditions
X30B0Y00Z00T0Gxyzt7 C&J 371 4 Green's function
X00Y00Z00T0Gxyzt7 C&J 371 1 Green's function
360 X00Y00Z11B00T0Gxyzt7 C&J 373 12,15 Two forms of Green's function
361 X00Y00Z33B00T0Gxyzt7 C&J 373 17 Green's function
362 X00Y00Z22B00T0Gxyzt7 C&J 374 18,19 Two forms of Green's function
363 R00X40B0T00Grxt7 C&J 375 7 Green's function with type 4 boundary cond. Eq. 2
364 X00Y00Z0CZ0T0Gt7 C&J 376 5,6 Green's function source at (0,0,z') for z=0
365 R01B0f00Z00T0Grfzt7 C&J 377 6 Green's function with source at (r',f',0)
366 R03B0f00Z00T0Grfzt7 C&J 378 7 Green's function with source at (r',f',0)
367 R10B0f00Z00T0Grfzt7 C&J 378 8 Green's function
368 R30B0f00Z00T0Grfzt7 C&J 378 3 Green's function
369 R00f11B00T0Grft7 C&J 379 7 Green's function
370 R00f22B00T0Grft7 C&J 379 8 Green's function
R00f11B00T0Grft7 C&J 380 9 Green's function,wedge of angle 2?
371 R01B0f00Z11B00T0Grfzt7 C&J 380 2 Green's function
R11B00f00Z11B00T0Gr C&J 380 3 Green's function
372 RS01B0f00T0Grft7 C&J 382 8 Green's function for a point source at sphere origin
373 RS03B0f00Grft7 C&J 382 11 Green's function for a point source at sphere origin
374 RS10B0f00Grft7 C&J 382 13 Green's function for a point source at (r',0,0)
375 RS30B0f00T0Grft7 C&J 382 14 Green's function for a point source at (r',0,0)
376 RS00f01B0T0Grft7 C&J 384 7 Green's function for a point source at origin of cone
377 RS00f00q01B0T0Grfqt7 C&J 385 11 Green's function for a point source in spheres (r,q,f) coordinates
378 R02B0f00T0Grft7 C&J 386 11,12 Continuous source through (f',0)
379 X10B2T2G1V1 C&J 388 7 F(x)=To +Ax, T(0,t)=T1 +bt
380 X30B0T1V1 C&J 389 10
381 X10B6V1 C&J 389 14 Steady periodic, constant velocity
382 X11B01F0T0V1 C&J 391 3
X11B05T0 C&J 400 6
X11B0-T0 C&J 401 10,12 Steady periodic square wave
X20B-T0 C&J 402 14,15 Steady periodic square wave
RS00G-T0 C&J 402 17 Steady periodic point source
R00G-T0 C&J 402 20 Steady periodic line source
383 X21B00T0G- C&J 404 6 g(T)=K(A+BT) for t>0
384 X23B00T0G- C&J 405 10 g(T)=K(A+BT), t>0
385 R01B0T0G- C&J 405 13 g(T)=K(A+BT), t>0
386 X21B00G- C&J 406 19 g(T)=B exp(T), steady state
X10B1T0 C&J 413 12 Space variable conductivity, k = k0xn
X3B1C3XC3XC3X3B0T0 C&J 416 9 Chain of n laminated slabs
388 X11B10Y11B00Z11B00T0 C&J 417 6
X11Bt60Y11B00Z11B00T0 C&J 417 8,9
X11B11Y33B00Z00B00T0 C&J 418 11,12 Transient part. For S.S. part, C&J 6.2 (23)
389 R03B0X11B10T0 C&J 418 13
390 R03B0X13B10T0 C&J 418 14
391 R03B0X10B1T0 C&J 419 17
392 R01B1X10B0T0 C&J 419 19
393 R00f11B10T0 C&J 420 23
394 R00f11B11T0 C&J 420 24 T(r,0,t) = 1, T(r,?0,t) = 1
395 RS00f01B1T0 C&J 420 25
R00X11B00f00 C&J 423 5,6 Green's function, steady state
R01B0X00f00 C&J 423 7 Green's function, steady state
R01B0X11B00f00 C&J 423 8,9 Green's function, steady state
398 X0CX0Y11B05 C&J 428 22,23
401 R00Z20B5 C&J 462 8 -kdT(r,0)/dz =q0 , 0<r<a, dT(r,0)/dz =0, r>a
402 X11B11T0 C&J 463 T(0,t) = T(L,t) = 1
403 X11B00Y11B-0 C&J 464
404 R00f11B11T0 C&J 465 10 T(r,0,t) = T(r,f0,t) = 1