1.1.1.1 Fourier’s Conduction Law
dT
T 1 − T 2
q
""
= −k
= k
(1.1)
dx
L
and
q
""
≡
"" A c
q
or q = q
A c
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Heat Conduction Equations

1.1 Introduction
1.1.1 Conduction
Conduction is caused by the temperature gradient through a solid material. For example, Figure 1.1 shows that heat is conducted from the hightemperature side to the low-temperature side through a building or a
container wall. This is a one-dimensional (1-D) steady-state heat conduction
problem if T 1 and T 2 are uniform. According to Fourier’s conduction law, the
temperature profile is linear through the plane wall.
where q "" is the heat flux (W
2
/m ), q the heat rate (W or J/s), k the thermal
conductivity of solid material (W/m K), A c the cross-sectional area for
conduction, perpendicular to heat flow (m 2 ), and L the conduction length (m).
One can predict heat rate or heat loss through the plane wall by knowing T 1 ,
T 2 , k, L, and A c . This is the simple 1-D steady-state problem. However, in reallife application, there are many two-dimensional (2-D) or three-dimensional
(3-D) steady-state heat conduction problems; there are cases where heat generation occurs in the solid material during heat conduction; and transient
heat conduction problems take place in many engineering applications. In
addition, some special applications involve heat conduction with moving
boundary. All these more complicated heat conduction problems will be
discussed in the following chapters.
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