1549312215-Complex_Analysis_for_Mathematics_and_Engineering_5th_edition__Mathews

T(x, O} = 0,

T(x, O} = O,

T(x, y) = 100,

11.5 • STEADY STATE TEMPERATURES 455

for x > l;

for x < - 1;

if z = e'^8 , 0 < 8 < 1r.

7. Find the temperature function T (x, y) in the domain 1 < r < 2, 0 < (} < ~ that
   satisfies the following boundary conditions (shown in Figure 11.27).

·9 1r

for x + i y = z = e' , 0 < 8 < 2;

·9 1r

for x + iy = z = 2e' , 0 < 8 < - ;

2

T(x, y) = 0 ,

T(x, y) = 50,

8T

on = Tv (x, 0) = 0, for^1 < x < 2;

8T

f}n = T" (0, y) = 0, for^1 < y < 2.

2i

iJT -O

iJn -

y

Figure 11.27

iJT 2

• iJ11 - o -

x

8. Find the temperature function T (x, y) in the domain 0 < r < 1, 0 < Arg z < Ct
   that satisfies the following boundary conditions (shown in Figure 11.28). Hint:
   Use w =Log z.

T (x, 0) = 100,

T (x, y) = 50 ,

8T

• = 0
  &n '

y

0 T= 100

Figure 11. 28

for 0 < x < l;

forx+iy= z = re"", O<r<l;

for x + iy = z = e^19 , 0 < (} < Ct.