Homework 1
due 2/29 14:00
1. A one-dimensional heat conduction problem is simplified as follows.
dT
d 2T
 m2T  0, 0  x  L , where m is real and positive, subject to T (0)  0 ,
2
dx
dx
C.
xL
Solve the problem for the following two cases:
(a) cos(mL)  0 .
(b) cos(mL)  0 .
2. A two-dimensional rectangular plate is subjected
to prescribed temperature boundary conditions on
three sides, and a uniform heat flux is applied to
T1
W
q s
T1
the plate on the remaining side, as shown in the
figure. Derive an expression for the steady-state
temperature distribution T(x, y).
1
T1
L