1549312215-Complex_Analysis_for_Mathematics_and_Engineering_5th_edition__Mathews

456 CHAPTER 11 • APPLICATIONS OF HARMONIC FUNCTIONS

9. Find the temperature function T (x, y) in the first quadrant x > 0, y > 0 that
   satisfies the following boundary conditions (shown in Figure 11.29).

T(x, 0) = 100,

T(O, y) = -50,

8T

an = Tv (x, 0) = 0,

8T

an = T., (0, y) = 0,

ar _

an -^0

y

ar _

an -^0

Figure 11.29

for x > l ;

for y > l;

for 0 < x < l;

for 0<y<1.

10. Find the temperature function T (x, y) in the infinite strip 0 < y < 1f that satisfies
    the following boundary conditions (shown in Figure 11.30). Hint: Use w = e'.

T(x, 0) = 50 ,

T(x, 7r) = - 50 ,

8T

8n = T 11 (x, O) = 0,

8T

&n = Tv (x, 7r) = 0,

iJT -O

an -

iJT - O

an -

Figure 11.30

y

0

for x > O;

for x > O;

for x < O;

for x < 0.