Page 396 - Bird R.B. Transport phenomena

378 Chapter 12 Temperature Distributions with More Than One Independent Variable

Center of slab Surface of slab Axis of cylinder Surface of cylinder
1.0 1.0 0
— — — e D i at/R = 0.4 - — - •
2
at/b 2 = 1.0 i • i i -
0.8 0.2 0.8 0.2
~O6~ 7/ / \\
0.6 0.6 0.2 0.4
т-т 0 0.4 — — - 1 \
0.4 / 0.6 0.4 / 0.6
Г А
0.2 / / o.oyJ
0.2 / / f 0.8 0.2 / 0.8
0.1 0.04,/
— — — * o.oy
1.0 1.0
0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0
r/R
Fig. 12.1-1. Temperature profiles for unsteady-state Fig. 12.1-2. Temperature profiles for unsteady-state
heat conduction in a slab of finite thickness 2b. The heat conduction in a cylinder of radius R. The initial
initial temperature of the slab is T , and T is the tempera- temperature of the cylinder is T , and T, is the tempera-
o
}
o
ture imposed at the slab surfaces for time t > 0. ture imposed at the cylinder surface for time t > 0.
[H. S. Carslaw and J. C. Jaeger, Conduction of Heat in [H. S. Carslaw and J. C. Jaeger, Conduction of Heat in
Solids, 2nd edition, Oxford University Press (1959), Solids, 2nd edition, Oxford University Press (1959),
p. 101.] p. 200.]

Center of sphere Surface of sphere

1.0 i*—

1.0

Fig. 12.1-3. Temperature profiles for unsteady-state
heat conduction in a sphere of radius R. The initial
temperature of the sphere is T , and T is the tempera-
}
o
ture imposed at the sphere surface for time t > 0.
[H. S. Carslaw and J. C. Jaeger, Conduction of Heat in
Solids, 2nd edition, Oxford University Press (1959),
p. 234.]