Chapter 2
Heat Conduction Equation
231
For a medium in which the heat conduction equation is given by
∂
∂
∂
∂
α
∂
∂
2
2
2
2
1
T
x
T
y
T
t
+=
:
(
a
) Heat transfer is transient, (
b
) it is twodimensional, (
c
) there is no heat generation, and (
d
) the thermal
conductivity is constant.
232
For a medium in which the heat conduction equation is given by
0
1
=
+
⎟
⎠
⎞
⎜
⎝
⎛
+
⎟
⎠
⎞
⎜
⎝
⎛
g
z
T
k
z
r
T
kr
r
r
&
∂
:
(
a
) Heat transfer is steady, (
b
) it is twodimensional, (
c
) there is heat generation, and (
d
) the thermal
conductivity is variable.
233
For a medium in which the heat conduction equation is given by
t
T
T
r
r
T
r
r
r
α
∂φ
θ
1
sin
1
1
2
2
2
2
2
2
=
+
⎟
⎠
⎞
⎜
⎝
⎛
:
(
a
) Heat transfer is transient, (
b
) it is twodimensional, (
c
) there is no heat generation, and (
d
) the thermal
conductivity is constant.
Boundary and Initial Conditions; Formulation of Heat Conduction Problems
234C
The mathematical expressions of the thermal conditions at the boundaries are called the
boundary
conditions.
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 Fall '10
 Dr.DanielArenas
 Thermodynamics, Conductivity, Mass, Heat

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