J.V. BECK, DEPT . OF MECH G., MI CH. STATE UNIV. 1990 LIST OF NUMBERS IN CARSLAW AND JAEGE (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, -aa 4 X00T5 C&J 54 4 F(x)=0, -aa 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, 00 14 X10B0T5 C&J 62 15 F(x)=V, ab 15 X10B-T0 C&J 63 1 16 X10B5T0 C&J 63 2,3 f(t)=V0, 0ta 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(wte1), 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, 0ta 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, 0ta 34 X20B3T0 C&J 76 12 f(t)=a sqrt(kt), 0ta 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, 0L 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 0ta 99 X23B05T0 C&J 127 3,4 f2=V0, 0ta 100 X33B66T0 C&J 127 5 f1=f2=Vsin(wt+e), -L0; =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 0z>-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, 0 196 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 0a 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 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 -a0 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 X3B1C3XC3X…C3X3B0T0 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 , 0a 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