1549312215-Complex_Analysis_for_Mathematics_and_Engineering_5th_edition__Mathews

11. 5 • STEADY STATE TEMPERATURES 457

11. Find the temperature function T (x, y) in the upper half-plane Im (z) > 0 that
    satisfies t he following boundary conditions (shown in Figure 11.31).

T(x, 0) = 100

T(x, 0) = -100

{}T

&n = Ty (x, 0) = 0

l:JT

(}n = T 11 (x, 0) = 0

y

for 0 < x < 1;

for - 1 < x < O;

for x > l;

forx<-1.

ar -oT=- 100 T=looar - o

an - an -

Figure 11.31

12. Find the temperature function T (x, y) in the first quadrant x > 0, y > 0 that
    satisfies the following boundary conditions (shown in Figure 11.32).

T(x, 0) = 50,

T(O, y) = - 50,

{}T

&n = Tx (0, y) = 0,

ar _

an -^0

y

0 T=SO

Figure 11. 32

13. For the temperature function

for x > O;

fory > l ;

for 0 < y < 1.

T (x, y) = 1 00--^100 Arctan 1 - x^2 -^2

2

y

11' y