
Heat Conduction Equation 179
Solution
Let’s select a coordinate system such that the left and right sides of this wall are at
coordinates x = 0 mm and x = 5 mm, respectively. Temperature of this wall at
steady-state is a function of x only; T = T(x). The differential equation governing
heat conduction inside this wall and the associated boundary conditions are
dT
dx
T
T
2
2
0
0 105
5
=
=
,
() ,
()
Boundary Conditions:
==
70.
The general solution of this equation is
The application of the boundary conditions gives
TC
T
() ,
()
0 105 105
570
2
mm °C °C
mm °C
=⇒=
=⇒770 5 105 7
11
°C mm °C °C/mm=⋅ +⇒=−CC.
Substituting for C
1
and C
2
gives the expression ...