1549312215-Complex_Analysis_for_Mathematics_and_Engineering_5th_edition__Mathews

11.5 • STEADY STATE TEMPERATURES 453

2. Find the temperature function T ( x, y) in the infinite strip bounded by the lines
   y = - x and y = 1-x that satisfies the following boundary values (shown in Figure
   11.22).

T(x, - x) = 25,

T(x,l-x)= 75 ,

y

Figure 11. 22

for alb:;

for all x.

3. Find the temperature function T (x, y) in the first quadrant x > 0, y > 0 that
   satisfies the following boundary values (shown in Figure 11.23).

T(x, 0) = 10,

T(x, 0) = 20,

T(O, y) = 20,

T(O, y) = 10,

y

for x > l ;

for 0 < x < l;

for 0:::; y < l;

for y < 1.

T=10 T= 10

Figure 11.23

4. Find the temperature function T (x, y) inside the unit disk lzl < 1 that satisfies
   the following boundary values (shown in Figure 11.24). Hint: Use w = i (l - z).
   l+z

T(x, y) = 20 ,

T(x, y) = 60 ,

for x + iy = z = e'^9 ,

for x + iy = z = e'^9 ,

'Ir

0 < 6 < 2;

'Ir

2 < fJ < 27r.